Solving Word Problems by Adding and Subtracting Fractions and Mixed Numbers
Learn how to solve fraction word problems with examples and interactive exercises.
Example 1: Rachel rode her bike for one-fifth of a mile on Monday and two-fifths of a mile on Tuesday. How many miles did she ride altogether?
Analysis: To solve this problem, we will add two fractions with like denominators.
Solution:
Answer: Rachel rode her bike for three-fifths of a mile altogether.
Analysis: To solve this problem, we will subtract two fractions with unlike denominators.
Answer: Stefanie swam one-third of a lap farther in the morning.
Analysis: To solve this problem, we will add three fractions with unlike denominators. Note that the first is an improper fraction.
Answer: It took Nick three and one-fourth hours to complete his homework altogether.
Analysis: To solve this problem, we will add two mixed numbers, with the fractional parts having like denominators.
Answer: Diego and his friends ate six pizzas in all.
Analysis: To solve this problem, we will subtract two mixed numbers, with the fractional parts having like denominators.
Answer: The Cocozzelli family took one-half more days to drive home.
Analysis: To solve this problem, we will add two mixed numbers, with the fractional parts having unlike denominators.
Answer: The warehouse has 21 and one-half meters of tape in all.
Analysis: To solve this problem, we will subtract two mixed numbers, with the fractional parts having unlike denominators.
Answer: The electrician needs to cut 13 sixteenths cm of wire.
Analysis: To solve this problem, we will subtract a mixed number from a whole number.
Answer: The carpenter needs to cut four and seven-twelfths feet of wood.
Summary: In this lesson we learned how to solve word problems involving addition and subtraction of fractions and mixed numbers. We used the following skills to solve these problems:
Add fractions with like denominators.
Subtract fractions with like denominators.
Find the LCD.
Add fractions with unlike denominators.
Subtract fractions with unlike denominators.
Add mixed numbers with like denominators.
Subtract mixed numbers with like denominators.
Add mixed numbers with unlike denominators.
Subtract mixed numbers with unlike denominators.
Directions: Subtract the mixed numbers in each exercise below. Be sure to simplify your result, if necessary. Click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.
Note: To write the fraction three-fourths, enter 3/4 into the form. To write the mixed number four and two-thirds, enter 4, a space, and then 2/3 into the form.
RESULTS BOX:
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Fraction word prob.
Fraction word problems
Here you will learn about fraction word problems, including solving math word problems within a real-world context involving adding fractions, subtracting fractions, multiplying fractions, and dividing fractions.
Students will first learn about fraction word problems as part of number and operations—fractions in 4 th grade.
What are fraction word problems?
Fraction word problems are math word problems involving fractions that require students to use problem-solving skills within the context of a real-world situation.
To solve a fraction word problem, you must understand the context of the word problem, what the unknown information is, and what operation is needed to solve it. Fraction word problems may require addition, subtraction, multiplication, or division of fractions.
After determining what operation is needed to solve the problem, you can apply the rules of adding, subtracting, multiplying, or dividing fractions to find the solution.
For example,
Natalie is baking 2 different batches of cookies. One batch needs \cfrac{3}{4} cup of sugar and the other batch needs \cfrac{2}{4} cup of sugar. How much sugar is needed to bake both batches of cookies?
You can follow these steps to solve the problem:
Step-by-step guide: Adding and subtracting fractions
Step-by-step guide: Adding fractions
Step-by-step guide: Subtracting fractions
Step-by-step guide: Multiplying and dividing fractions
Step-by-step guide: Multiplying fractions
Step-by-step guide: Dividing fractions
Common Core State Standards
How does this relate to 4 th grade math to 6 th grade math?
Grade 4: Number and Operations—Fractions (4.NF.B.3d) Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
Grade 4: Number and Operations—Fractions (4.NF.B.4c) Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat \cfrac{3}{8} of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
Grade 5: Number and Operations—Fractions (5.NF.A.2) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result \cfrac{2}{5}+\cfrac{1}{2}=\cfrac{3}{7} by observing that \cfrac{3}{7}<\cfrac{1}{2} .
Grade 5: Number and Operations—Fractions (5.NF.B.6) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
Grade 5: Number and Operations—Fractions (5.NF.B.7c) Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share \cfrac{1}{2} \: lb of chocolate equally? How many \cfrac{1}{3} cup servings are in 2 cups of raisins?
Grade 6: The Number System (6.NS.A.1) Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for \cfrac{2}{3} \div \cfrac{4}{5} and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that \cfrac{2}{3} \div \cfrac{4}{5}=\cfrac{8}{9} because \cfrac{3}{4} of \cfrac{8}{9} is \cfrac{2}{3}. (In general, \cfrac{a}{b} \div \cfrac{c}{d}=\cfrac{a d}{b c} \, ) How much chocolate will each person get if 3 people share \cfrac{1}{2} \: lb of chocolate equally? How many \cfrac{3}{4} cup servings are in \cfrac{2}{3} of a cup of yogurt? How wide is a rectangular strip of land with length \cfrac{3}{4} \: m and area \cfrac{1}{2} \: m^2?
[FREE] Fraction Operations Worksheet (Grade 4 to 6)
Use this quiz to check your grade 4 to 6 students’ understanding of fraction operations. 10+ questions with answers covering a range of 4th to 6th grade fraction operations topics to identify areas of strength and support!
How to solve fraction word problems
In order to solve fraction word problems:
Determine what operation is needed to solve.
Write an equation.
Solve the equation.
State your answer in a sentence.
Fraction word problem examples
Example 1: adding fractions (like denominators).
Julia ate \cfrac{3}{8} of a pizza and her brother ate \cfrac{2}{8} of the same pizza. How much of the pizza did they eat altogether?
The problem states how much pizza Julia ate and how much her brother ate. You need to find how much pizza Julia and her brother ate altogether , which means you need to add.
2 Write an equation.
3 Solve the equation.
To add fractions with like denominators, add the numerators and keep the denominators the same.
4 State your answer in a sentence.
The last step is to go back to the word problem and write a sentence to clearly say what the solution represents in the context of the problem.
Julia and her brother ate \cfrac{5}{8} of the pizza altogether.
Example 2: adding fractions (unlike denominators)
Tim ran \cfrac{5}{6} of a mile in the morning and \cfrac{1}{3} of a mile in the afternoon. How far did Tim run in total?
The problem states how far Tim ran in the morning and how far he ran in the afternoon. You need to find how far Tim ran in total , which means you need to add.
To add fractions with unlike denominators, first find a common denominator and then change the fractions accordingly before adding.
\cfrac{5}{6}+\cfrac{1}{3}= \, ?
The least common multiple of 6 and 3 is 6, so 6 can be the common denominator.
That means \cfrac{1}{3} will need to be changed so that its denominator is 6. To do this, multiply the numerator and the denominator by 2.
\cfrac{1 \times 2}{3 \times 2}=\cfrac{2}{6}
Now you can add the fractions and simplify the answer.
Example 3: subtracting fractions (like denominators)
Pia walked \cfrac{4}{7} of a mile to the park and \cfrac{3}{7} of a mile back home. How much farther did she walk to the park than back home?
The problem states how far Pia walked to the park and how far she walked home. Since you need to find the difference ( how much farther ) between the two distances, you need to subtract.
To subtract fractions with like denominators, subtract the numerators and keep the denominators the same.
\cfrac{4}{7}-\cfrac{3}{7}=\cfrac{1}{7}
Pia walked \cfrac{1}{7} of a mile farther to the park than back home.
Example 4: subtracting fractions (unlike denominators)
Henry bought \cfrac{7}{8} pound of beef from the grocery store. He used \cfrac{1}{3} of a pound of beef to make a hamburger. How much of the beef does he have left?
The problem states how much beef Henry started with and how much he used. Since you need to find how much he has left , you need to subtract.
To subtract fractions with unlike denominators, first find a common denominator and then change the fractions accordingly before subtracting.
\cfrac{7}{8}-\cfrac{1}{3}= \, ?
The least common multiple of 8 and 3 is 24, so 24 can be the common denominator.
That means both fractions will need to be changed so that their denominator is 24.
To do this, multiply the numerator and the denominator of each fraction by the same number so that it results in a denominator of 24. This will give you an equivalent fraction for each fraction in the problem.
Andre has \cfrac{3}{4} of a candy bar left. He gives \cfrac{1}{2} of the remaining bit of the candy bar to his sister. What fraction of the whole candy bar does Andre have left now?
It could be challenging to determine the operation needed for this problem; many students may automatically assume it is subtraction since you need to find how much of the candy bar is left.
However, since you know Andre started with a fraction of the candy bar and you need to find a fraction OF a fraction, you need to multiply.
The difference here is that Andre did NOT give his sister \cfrac{1}{2} of the candy bar, but he gave her \cfrac{1}{2} of \cfrac{3}{4} of a candy bar.
To solve the word problem, you can ask, “What is \cfrac{1}{2} of \cfrac{3}{4}? ” and set up the equation accordingly. Think of the multiplication sign as meaning “of.”
\cfrac{1}{2} \times \cfrac{3}{4}= \, ?
To multiply fractions, multiply the numerators and multiply the denominators.
\cfrac{1}{2} \times \cfrac{3}{4}=\cfrac{3}{8}
Andre gave \cfrac{1}{2} of \cfrac{3}{4} of a candy bar to his sister, which means he has \cfrac{1}{2} of \cfrac{3}{4} left. Therefore, Andre has \cfrac{3}{8} of the whole candy bar left.
Example 6: dividing fractions
Nia has \cfrac{7}{8} cup of trail mix. How many \cfrac{1}{4} cup servings can she make?
The problem states the total amount of trail mix Nia has and asks how many servings can be made from it.
To solve, you need to divide the total amount of trail mix (which is \cfrac{7}{8} cup) by the amount in each serving ( \cfrac{1}{4} cup) to find out how many servings she can make.
To divide fractions, multiply the dividend by the reciprocal of the divisor.
You can simplify \cfrac{28}{8} to \cfrac{7}{2} and then 3 \cfrac{1}{2}.
Nia can make 3 \cfrac{1}{2} cup servings.
Teaching tips for fraction word problems
Encourage students to look for key words to help determine the operation needed to solve the problem. For example, subtracting fractions word problems might ask students to find “how much is left” or “how much more” one fraction is than another.
Provide students with an answer key to word problem worksheets to allow them to obtain immediate feedback on their solutions. Encourage students to attempt the problems independently first, then check their answers against the key to identify any mistakes and learn from them. This helps reinforce problem-solving skills and confidence.
Be sure to incorporate real-world situations into your math lessons. Doing so allows students to better understand the relevance of fractions in everyday life.
As students progress and build a strong foundational understanding of one-step fraction word problems, provide them with multi-step word problems that involve more than one operation to solve.
Take note that students will not divide a fraction by a fraction as shown above until 6 th grade (middle school), but they will divide a unit fraction by a whole number and a whole number by a fraction in 5 th grade (elementary school), where the same mathematical rules apply to solving.
There are many alternatives you can use in place of printable math worksheets to make practicing fraction word problems more engaging. Some examples are online math games and digital workbooks.
Easy mistakes to make
Misinterpreting the problem Misreading or misunderstanding the word problem can lead to solving for the wrong quantity or using the wrong operation.
Not finding common denominators When adding or subtracting fractions with unlike denominators, students may forget to find a common denominator, leading to an incorrect answer.
Forgetting to simplify Unless a problem specifically says not to simplify, fractional answers should always be written in simplest form.
Related fractions operations lessons
Fractions operations
Multiplicative inverse
Reciprocal math
Fractions as divisions
Practice fraction word problem questions
1. Malia spent \cfrac{5}{6} of an hour studying for a math test. Then she spent \cfrac{1}{3} of an hour reading. How much longer did she spend studying for her math test than reading?
Malia spent \cfrac{1}{2} of an hour longer studying for her math test than reading.
Malia spent \cfrac{5}{18} of an hour longer studying for her math test than reading.
Malia spent \cfrac{1}{2} of an hour longer reading than studying for her math test.
Malia spent 1 \cfrac{1}{6} of an hour longer studying for her math test than reading.
To find the difference between the amount of time Malia spent studying for her math test than reading, you need to subtract. Since the fractions have unlike denominators, you need to find a common denominator first.
You can use 6 as the common denominator, so \cfrac{1}{3} becomes \cfrac{3}{6}. Then you can subtract.
\cfrac{3}{6} can then be simplified to \cfrac{1}{2}.
Finally, you need to choose the answer that correctly answers the question within the context of the situation. Therefore, the correct answer is “Malia spent \cfrac{1}{2} of an hour longer studying for her math test than reading.”
2. A square garden is \cfrac{3}{4} of a meter wide and \cfrac{8}{9} of a meter long. What is its area?
The area of the garden is 1\cfrac{23}{36} square meters.
The area of the garden is \cfrac{27}{32} square meters.
The area of the garden is \cfrac{2}{3} square meters.
The perimeter of the garden is \cfrac{2}{3} meters.
To find the area of a square, you multiply the length and width. So to solve, you multiply the fractional lengths by mulitplying the numerators and multiplying the denominators.
\cfrac{24}{36} can be simplified to \cfrac{2}{3}.
Therefore, the correct answer is “The area of the garden is \cfrac{2}{3} square meters.”
3. Zoe ate \cfrac{3}{8} of a small cake. Liam ate \cfrac{1}{8} of the same cake. How much more of the cake did Zoe eat than Liam?
Zoe ate \cfrac{3}{64} more of the cake than Liam.
Zoe ate \cfrac{1}{4} more of the cake than Liam.
Zoe ate \cfrac{1}{8} more of the cake than Liam.
Liam ate \cfrac{1}{4} more of the cake than Zoe.
To find how much more cake Zoe ate than Liam, you subtract. Since the fractions have the same denominator, you subtract the numerators and keep the denominator the same.
\cfrac{2}{8} can be simplified to \cfrac{1}{4}.
Therefore, the correct answer is “Zoe ate \cfrac{1}{4} more of the cake than Liam.”
4. Lila poured \cfrac{11}{12} cup of pineapple and \cfrac{2}{3} cup of mango juice in a bottle. How many cups of juice did she pour into the bottle altogether?
Lila poured 1 \cfrac{7}{12} cups of juice in the bottle altogether.
Lila poured \cfrac{1}{4} cups of juice in the bottle altogether.
Lila poured \cfrac{11}{18} cups of juice in the bottle altogether.
Lila poured 1 \cfrac{3}{8} cups of juice in the bottle altogether.
To find the total amount of juice that Lila poured into the bottle, you need to add. Since the fractions have unlike denominators, you need to find a common denominator first.
You can use 12 as the common denominator, so \cfrac{2}{3} becomes \cfrac{8}{12}. Then you can add.
\cfrac{19}{12} can be simplified to 1 \cfrac{7}{12}.
Therefore, the correct answer is “Lila poured 1 \cfrac{7}{12} cups of juice in the bottle altogether.”
5. Killian used \cfrac{9}{10} of a gallon of paint to paint his living room and \cfrac{7}{10} of a gallon to paint his bedroom. How much paint did Killian use in all?
Killian used \cfrac{2}{10} gallons of paint in all.
Killian used \cfrac{1}{5} gallons of paint in all.
Killian used \cfrac{63}{100} gallons of paint in all.
Killian used 1 \cfrac{3}{5} gallons of paint in all.
To find the total amount of paint Killian used, you add the amount he used for the living room and the amount he used for the kitchen. Since the fractions have the same denominator, you add the numerators and keep the denominators the same.
\cfrac{16}{10} can be simplified to 1 \cfrac{6}{10} and then further simplified to 1 \cfrac{3}{5}.
Therefore, the correct answer is “Killian used 1 \cfrac{3}{5} gallons of paint in all.”
6. Evan pours \cfrac{4}{5} of a liter of orange juice evenly among some cups.
He put \cfrac{1}{10} of a liter into each cup. How many cups did Evan fill?
Evan filled \cfrac{2}{25} cups.
Evan filled 8 cups.
Evan filled \cfrac{9}{10} cups.
Evan filled 7 cups.
To find the number of cups Evan filled, you need to divide the total amount of orange juice by the amount being poured into each cup. To divide fractions, you mulitply the first fraction (the dividend) by the reciprocal of the second fraction (the divisor).
\cfrac{40}{5} can be simplifed to 8.
Therefore, the correct answer is “Evan filled 8 cups.”
Fraction word problems FAQs
Fraction word problems are math word problems involving fractions that require students to use problem-solving skills within the context of a real-world situation. Fraction word problems may involve addition, subtraction, multiplication, or division of fractions.
To solve fraction word problems, first you need to determine the operation. Then you can write an equation and solve the equation based on the arithmetic rules for that operation.
Fraction word problems and decimal word problems are similar because they both involve solving math problems within real-world contexts. Both types of problems require understanding the problem, determining the operation needed to solve it (addition, subtraction, multiplication, division), and solving it based on the arithmetic rules for that operation.
The next lessons are
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Fractions questions and problems with solutions.
Questions and problems with solutions on fractions are presented. Detailed solutions to the examples are also included. In order to master the concepts and skills of fractions, you need a thorough understanding (NOT memorizing) of the rules and properties and lot of practice and patience. I hope the examples, questions, problems in the links below will help you.
Fractions and Mixed Numbers , define fractions and mixed numbers, and introduce important vocabulary.
Evaluate Fractions of Quantities .
Fractions Rules including questions with Solutions
Properties of Fractions
Complex Fractions with Variables
Equivalent Fractions examples and questions with solutions.
Reduce Fractions examples and questions with solutions.
Reduce Fractions Calculator
Simplify Fractions , examples and questions including solutions.
Factor Fractions , examples with questions including solutions.
Adding Fractions. Add fractions with same denominator or different denominator. Several examples with detailed solutions and exercises.
Multiply Fractions. Multiply a fraction by another fraction or a number by a fraction. Examples with solutions and exercises.
Divide Fractions. Divide a fraction by a fraction, a fraction by a number of a number by a fraction. Several examples with solutions and exercises with answers.
Fractions Per Grade
Fractions and Mixed Numbers , questions and problems with solutions for grade 7
Fractions and Mixed Numbers , questions and problems with solutions for grade 6
Fractions , questions for grade 5 and their solutions
Fractions , questions for grade 4 their answers.
Fractions Calculators
Fractions Calculator including reducing, adding and multiplying fractions.
This worksheet generator produces a variety of worksheets for the four basic operations (addition, subtraction, multiplication, and division) with fractions and mixed numbers, including with negative fractions. You can make the worksheets in both html and PDF formats. You can choose like or unlike fractions, make missing number problems, restrict the problems to use proper fractions or to not to simplify the answers. Further, you can control the values of numerator, denominator, and the whole-number part to make the fractions or mixed numbers as easy or difficult as you like.
Each worksheet is randomly generated and thus unique. The and is placed on the second page of the file.
You can generate the worksheets — both are easy to print. To get the PDF worksheet, simply push the button titled " " or " ". To get the worksheet in html format, push the button " " or " ". This has the advantage that you can save the worksheet directly from your browser (choose File → Save) and then in Word or other word processing program.
Sometimes the generated worksheet is not exactly what you want. Just try again! To get a different worksheet using the same options:
Tip: chose value 1 to be a fraction and value 2 to be a mixed number, and then tick the box of "Value 1 - Value 2 random switching" to make problems where either the first or the second number is a mixed number. Just experiment with the options to customize the worksheets as you like!
(2 fractions, easy, for 4th grade) (3 fractions, for 4th grade) (for 4th grade) (for 5th grade) (for 6th grade) (for 5th grade) (mixed problems, for 5th grade) (answers are whole numbers, for 5th grade) (mixed problems, for 6th grade) (incl. negative fractions, for 7th-8th grade) (incl. negative fractions, for 7th-8th grade) (negative fractions, for 7th-8th grade)
Drag unit fraction pieces (1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/9, 1,10, 1/12, 1,16, and 1/20) onto a square that represents one whole. You can see that, for example, 6 pieces of 1/6 fit into one whole, or that 3 pieces of 1/9 are equal to 1/3, and many other similar relationships.
Use the generator below to make customized worksheets for fraction operations.
Min:
Max:
List:
Numerator
Denominator
Whole number
Min:
Max:
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Numerator
Denominator
Whole number
Key to Fractions Workbooks
These workbooks by Key Curriculum Press feature a number of exercises to help your child learn about fractions. Book 1 teaches fraction concepts, Book 2 teaches multiplying and dividing, Book 3 teaches adding and subtracting, and Book 4 teaches mixed numbers. Each book has a practice test at the end.
Fractions Worksheets
Welcome to the fractions worksheets page at Math-Drills.com where the cup is half full! This is one of our more popular pages most likely because learning fractions is incredibly important in a person's life and it is a math topic that many approach with trepidation due to its bad rap over the years. Fractions really aren't that difficult to master especially with the support of our wide selection of worksheets.
This page includes Fractions worksheets for understanding fractions including modeling, comparing, ordering, simplifying and converting fractions and operations with fractions. We start you off with the obvious: modeling fractions. It is a great idea if students can actually understand what a fraction is, so please do spend some time with the modeling aspect. Relating modeling to real life helps a great deal too as it is much easier to relate to half a cookie than to half a square. Ask most students what you get if you add half a cookie and another half a cookie, and they'll probably let you know that it makes one delicious snack.
The other fractions worksheets on this page are devoted to helping students understand the concept of fractions. From comparing and ordering to simplifying and converting... by the time students master the material on this page, operations of fractions will be a walk in the park.
Most Popular Fractions Worksheets this Week
Fraction Circles
Fraction circle manipulatives are mainly used for comparing fractions, but they can be used for a variety of other purposes such as representing and identifying fractions, adding and subtracting fractions, and as probability spinners. There are a variety of options depending on your purpose. Fraction circles come in small and large versions, labeled and unlabeled versions and in three different color schemes: black and white, color, and light gray. The color scheme matches the fraction strips and use colors that are meant to show good contrast among themselves. Do note that there is a significant prevalence of color-blindness in the population, so don't rely on all students being able to differentiate the colors.
Suggested activity for comparing fractions: Photocopy the black and white version onto an overhead projection slide and another copy onto a piece of paper. Alternatively, you can use two pieces of paper and hold them up to the light for this activity. Use a pencil to represent the first fraction on the paper copy. Use a non-permanent overhead pen to represent the second fraction. Lay the slide over the paper and compare the two circles. You should easily be able to tell which is greater or lesser or if the two fractions are equal. Re-use both sheets by erasing the pencil and washing off the marker.
Adding fractions with fraction circles will involve two copies on paper. Cut out the fraction circles and segments of one copy and leave the other copy intact. To add 1/3 + 1/2, for example, place a 1/3 segment and a 1/2 segment into a circle and hold it over various fractions on the intact copy to see what 1/2 + 1/3 is equivalent to. 5/6 or 10/12 should work.
Small Fraction Circles Small Fraction Circles in Black and White with Labels Small Fraction Circles in Color with Labels Small Fraction Circles in Light Gray with Labels Small Fraction Circles in Black and White Unlabeled Small Fraction Circles in Color Unlabeled Small Fraction Circles in Light Gray Unlabeled
Large Fraction Circles Large Fraction Circles in Black and White with Labels Large Fraction Circles in Color with Labels Large Fraction Circles in Light Gray with Labels Large Fraction Circles in Black and White Unlabeled Large Fraction Circles in Color Unlabeled Large Fraction Circles in Light Gray Unlabeled
Fraction Strips
Fractions strips are often used for comparing fractions. Students are able to see quite easily the relationships and equivalence between fractions with different denominators. It can be quite useful for students to have two copies: one copy cut into strips and the other copy kept intact. They can then use the cut-out strips on the intact page to individually compare fractions. For example, they can use the halves strip to see what other fractions are equivalent to one-half. This can also be accomplished with a straight edge such as a ruler without cutting out any strips. Pairs or groups of strips can also be compared side-by-side if they are cut out. Addition and subtraction (etc.) are also possibilities; for example, adding a one-quarter and one-third can be accomplished by shifting the thirds strip so that it starts at the end of one-quarter then finding a strip that matches the end of the one-third mark (7/12 should do it).
Teachers might consider copying the fraction strips onto overhead projection acetates for whole class or group activities. Acetate versions are also useful as a hands-on manipulative for students in conjunction with an uncut page.
The "Smart" Fraction Strips include strips in a more useful order, eliminate the 7ths and 11ths strips as they don't have any equivalents and include 15ths and 16ths. The colors are consistent with the classic versions, so the two sets can be combined.
Classic Fraction Strips with Labels Classic Fraction Strips in Black and White With Labels Classic Fraction Strips in Color With Labels Classic Fraction Strips in Gray With Labels
Unlabeled Classic Fraction Strips Classic Fraction Strips in Black and White Unlabeled Classic Fraction Strips in Color Unlabeled Classic Fraction Strips in Gray Unlabeled
Smart Fraction Strips with Labels Smart Fraction Strips in Black and White With Labels Smart Fraction Strips in Color With Labels Smart Fraction Strips in Gray With Labels
Modeling fractions
Fractions can represent parts of a group or parts of a whole. In these worksheets, fractions are modeled as parts of a group. Besides using the worksheets in this section, you can also try some more interesting ways of modeling fractions. Healthy snacks can make great models for fractions. Can you cut a cucumber into thirds? A tomato into quarters? Can you make two-thirds of the grapes red and one-third green?
Modeling Fractions with Groups of Shapes Coloring Groups of Shapes to Represent Fractions Identifying Fractions from Colored Groups of Shapes (Only Simplified Fractions up to Eighths) Identifying Fractions from Colored Groups of Shapes (Halves Only) Identifying Fractions from Colored Groups of Shapes (Halves and Thirds) Identifying Fractions from Colored Groups of Shapes (Halves, Thirds and Fourths) Identifying Fractions from Colored Groups of Shapes (Up to Fifths) Identifying Fractions from Colored Groups of Shapes (Up to Sixths) Identifying Fractions from Colored Groups of Shapes (Up to Eighths) Identifying Fractions from Colored Groups of Shapes (OLD Version; Print Too Light)
Modeling Fractions with Circles Modeling Halves, Thirds and Fourths Coloring Halves, Thirds and Fourths Modeling Halves, Thirds, Fourths, and Fifths Coloring Halves, Thirds, Fourths, and Fifths Modeling Halves to Sixths Coloring Halves to Sixths Modeling Halves to Eighths Coloring Halves to Eighths Modeling Halves to Twelfths Coloring Halves to Twelfths
Ratio and Proportion Worksheets
The equivalent fractions models worksheets include only the "baking fractions" in the A versions. To see more difficult and varied fractions, please choose the B to J versions after loading the A version. More picture ratios can be found on holiday and seasonal pages. Try searching for picture ratios to find more.
Picture Ratios Autumn Trees Part-to-Part Picture Ratios ( Grouped ) Autumn Trees Part-to-Part and Part-to-Whole Picture Ratios ( Grouped )
Equivalent Fractions Equivalent Fractions With Blanks ( Multiply Right ) ✎ Equivalent Fractions With Blanks ( Divide Left ) ✎ Equivalent Fractions With Blanks ( Multiply Right or Divide Left ) ✎ Equivalent Fractions With Blanks ( Divide Right ) ✎ Equivalent Fractions With Blanks ( Multiply Left ) ✎ Equivalent Fractions With Blanks ( Multiply Left or Divide Right ) ✎ Equivalent Fractions With Blanks ( Multiply or Divide Right ) ✎ Equivalent Fractions With Blanks ( Multiply or Divide Left ) ✎ Equivalent Fractions With Blanks ( Multiply or Divide in Either Direction ) ✎ Are These Fractions Equivalent? (Multiplier 2 to 5) Are These Fractions Equivalent? (Multiplier 5 to 15) Equivalent Fractions Models Equivalent Fractions Models with the Simplified Fraction First Equivalent Fractions Models with the Simplified Fraction Second
Equivalent Ratios Equivalent Ratios with Blanks Only on Right Equivalent Ratios with Blanks Anywhere Equivalent Ratios with x 's
Comparing and Ordering Fractions
Comparing fractions involves deciding which of two fractions is greater in value or if the two fractions are equal in value. There are generally four methods that can be used for comparing fractions. First is to use common denominators . If both fractions have the same denominator, comparing the fractions simply involves comparing the numerators. Equivalent fractions can be used to convert one or both fractions, so they have common denominators. A second method is to convert both fractions to a decimal and compare the decimal numbers. Visualization is the third method. Using something like fraction strips , two fractions can be compared with a visual tool. The fourth method is to use a cross-multiplication strategy where the numerator of the first fraction is multiplied by the denominator of the second fraction; then the numerator of the second fraction is multiplied by the denominator of the first fraction. The resulting products can be compared to decide which fraction is greater (or if they are equal).
Comparing Proper Fractions Comparing Proper Fractions to Sixths ✎ Comparing Proper Fractions to Ninths (No Sevenths) ✎ Comparing Proper Fractions to Ninths ✎ Comparing Proper Fractions to Twelfths (No Sevenths; No Elevenths) ✎ Comparing Proper Fractions to Twelfths ✎
The worksheets in this section also include improper fractions. This might make the task of comparing even easier for some questions that involve both a proper and an improper fraction. If students recognize one fraction is greater than one and the other fraction is less than one, the greater fraction will be obvious.
Comparing Proper and Improper Fractions Comparing Proper and Improper Fractions to Sixths ✎ Comparing Proper and Improper Fractions to Ninths (No Sevenths) ✎ Comparing Proper and Improper Fractions to Ninths ✎ Comparing Proper and Improper Fractions to Twelfths (No Sevenths; No Elevenths) ✎ Comparing Proper and Improper Fractions to Twelfths ✎ Comparing Improper Fractions to Sixths ✎ Comparing Improper Fractions to Ninths (No Sevenths) ✎ Comparing Improper Fractions to Ninths ✎ Comparing Improper Fractions to Twelfths (No Sevenths; No Elevenths) ✎ Comparing Improper Fractions to Twelfths ✎
This section additionally includes mixed fractions. When comparing mixed and improper fractions, it is useful to convert one of the fractions to the other's form either in writing or mentally. Converting to a mixed fraction is probably the better route since the first step is to compare the whole number portions, and if one is greater than the other, the proper fraction portion can be ignored. If the whole number portions are equal, the proper fractions must be compared to see which number is greater.
Comparing Proper, Improper and Mixed Fractions Comparing Proper, Improper and Mixed Fractions to Sixths ✎ Comparing Proper, Improper and Mixed Fractions to Ninths (No Sevenths) ✎ Comparing Proper, Improper and Mixed Fractions to Ninths ✎ Comparing Proper, Improper and Mixed Fractions to Twelfths (No Sevenths; No Elevenths) ✎ Comparing Proper, Improper and Mixed Fractions to Twelfths ✎
Comparing Improper and Mixed Fractions Comparing Improper and Mixed Fractions to Sixths ✎ Comparing Improper and Mixed Fractions to Ninths (No Sevenths) ✎ Comparing Improper and Mixed Fractions to Ninths ✎ Comparing Improper and Mixed Fractions to Twelfths (No Sevenths; No Elevenths) ✎ Comparing Improper and Mixed Fractions to Twelfths ✎
Comparing Mixed Fractions Comparing Mixed Fractions to Sixths ✎ Comparing Mixed Fractions to Ninths (No Sevenths) ✎ Comparing Mixed Fractions to Ninths ✎ Comparing Mixed Fractions to Twelfths (No Sevenths; No Elevenths) ✎ Comparing Mixed Fractions to Twelfths ✎
Many of the same strategies that work for comparing fractions also work for ordering fractions. Using manipulatives such as fraction strips, using number lines, or finding decimal equivalents will all have your student(s) putting fractions in the correct order in no time. We've probably said this before, but make sure that you emphasize that when comparing or ordering fractions, students understand that the whole needs to be the same. Comparing half the population of Canada with a third of the population of the United States won't cut it. Try using some visuals to reinforce this important concept. Even though we've included number lines below, feel free to use your own strategies.
Ordering Fractions with Easy Denominators on a Number Line Ordering Fractions with Easy Denominators to 10 on a Number Line Ordering Fractions with Easy Denominators to 24 on a Number Line Ordering Fractions with Easy Denominators to 60 on a Number Line Ordering Fractions with Easy Denominators to 100 on a Number Line
Ordering Fractions with Easy Denominators on a Number Line (Including Negative Fractions) Ordering Fractions with Easy Denominators to 10 + Negatives on a Number Line Ordering Fractions with Easy Denominators to 24 + Negatives on a Number Line Ordering Fractions with Easy Denominators to 60 + Negatives on a Number Line Ordering Fractions with Easy Denominators to 100 + Negatives on a Number Line
Ordering Fractions with All Denominators on a Number Line Ordering Fractions with All Denominators to 10 on a Number Line Ordering Fractions with All Denominators to 24 on a Number Line Ordering Fractions with All Denominators to 60 on a Number Line Ordering Fractions with All Denominators to 100 on a Number Line
Ordering Fractions with All Denominators on a Number Line (Including Negative Fractions) Ordering Fractions with All Denominators to 10 + Negatives on a Number Line Ordering Fractions with All Denominators to 24 + Negatives on a Number Line Ordering Fractions with All Denominators to 60 + Negatives on a Number Line Ordering Fractions with All Denominators to 100 + Negatives on a Number Line
The ordering fractions worksheets in this section do not include a number line, to allow for students to use various sorting strategies.
Ordering Positive Fractions Ordering Positive Fractions with Like Denominators Ordering Positive Fractions with Like Numerators Ordering Positive Fractions with Like Numerators or Denominators Ordering Positive Fractions with Proper Fractions Only Ordering Positive Fractions with Improper Fractions Ordering Positive Fractions with Mixed Fractions Ordering Positive Fractions with Improper and Mixed Fractions
Ordering Positive and Negative Fractions Ordering Positive and Negative Fractions with Like Denominators Ordering Positive and Negative Fractions with Like Numerators Ordering Positive and Negative Fractions with Like Numerators or Denominators Ordering Positive and Negative Fractions with Proper Fractions Only Ordering Positive and Negative Fractions with Improper Fractions Ordering Positive and Negative Fractions with Mixed Fractions Ordering Positive and Negative Fractions with Improper and Mixed Fractions
Simplifying & Converting Fractions Worksheets
Rounding fractions helps students to understand fractions a little better and can be applied to estimating answers to fractions questions. For example, if one had to estimate 1 4/7 × 6, they could probably say the answer was about 9 since 1 4/7 is about 1 1/2 and 1 1/2 × 6 is 9.
Rounding Fractions with Helper Lines Rounding Fractions to the Nearest Whole with Helper Lines Rounding Mixed Numbers to the Nearest Whole with Helper Lines Rounding Fractions to the Nearest Half with Helper Lines Rounding Mixed Numbers to the Nearest Half with Helper Lines
Rounding Fractions Rounding Fractions to the Nearest Whole Rounding Mixed Numbers to the Nearest Whole Rounding Fractions to the Nearest Half Rounding Mixed Numbers to the Nearest Half
Learning how to simplify fractions makes a student's life much easier later on when learning operations with fractions. It also helps them to learn that different-looking fractions can be equivalent. One way of demonstrating this is to divide out two equivalent fractions. For example 3/2 and 6/4 both result in a quotient of 1.5 when divided. By practicing simplifying fractions, students will hopefully recognize unsimplified fractions when they start adding, subtracting, multiplying and dividing with fractions.
Converting Between Improper and Mixed Fractions Converting Mixed Fractions to Improper Fractions Converting Improper Fractions to Mixed Fractions Converting Between (both ways) Mixed and Improper Fractions
Converting Between Fractions and Decimals Converting Fractions to Terminating Decimals Converting Fractions to Terminating and Repeating Decimals Converting Terminating Decimals to Fractions Converting Terminating and Repeating Decimals to Fractions Converting Fractions to Hundredths
Converting Between Fractions, Decimals, Percents and Ratios with Terminating Decimals Only Converting Fractions to Decimals, Percents and Part-to- Part Ratios ( Terminating Decimals Only) Converting Fractions to Decimals, Percents and Part-to- Whole Ratios ( Terminating Decimals Only) Converting Decimals to Fractions, Percents and Part-to- Part Ratios ( Terminating Decimals Only) Converting Decimals to Fractions, Percents and Part-to- Whole Ratios ( Terminating Decimals Only) Converting Percents to Fractions, Decimals and Part-to- Part Ratios ( Terminating Decimals Only) Converting Percents to Fractions, Decimals and Part-to- Whole Ratios ( Terminating Decimals Only) Converting Part-to-Part Ratios to Fractions, Decimals and Percents ( Terminating Decimals Only) Converting Part-to-Whole Ratios to Fractions, Decimals and Percents ( Terminating Decimals Only) Converting Various Fractions, Decimals, Percents and Part-to- Part Ratios ( Terminating Decimals Only) Converting Various Fractions, Decimals, Percents and Part-to- Whole Ratios ( Terminating Decimals Only)
Converting Between Fractions, Decimals, Percents and Ratios with Terminating and Repeating Decimals Converting Fractions to Decimals, Percents and Part-to- Part Ratios Converting Fractions to Decimals, Percents and Part-to- Whole Ratios Converting Decimals to Fractions, Percents and Part-to- Part Ratios Converting Decimals to Fractions, Percents and Part-to- Whole Ratios Converting Percents to Fractions, Decimals and Part-to- Part Ratios Converting Percents to Fractions, Decimals and Part-to- Whole Ratios Converting Part-to-Part Ratios to Fractions, Decimals and Percents Converting Part-to-Whole Ratios to Fractions, Decimals and Percents Converting Various Fractions, Decimals, Percents and Part-to- Part Ratios Converting Various Fractions, Decimals, Percents and Part-to- Whole Ratios Converting Various Fractions, Decimals, Percents and Part-to- Part Ratios with 7ths and 11ths Converting Various Fractions, Decimals, Percents and Part-to- Whole Ratios with 7ths and 11ths
Multiplying Fractions
Multiplying fractions is usually less confusing operationally than any other operation and can be less confusing conceptually if approached in the right way. The algorithm for multiplying is simply multiply the numerators then multiply the denominators. The magic word in understanding the multiplication of fractions is, "of." For example what is two-thirds OF six? What is a third OF a half? When you use the word, "of," it gets much easier to visualize fractions multiplication. Example: cut a loaf of bread in half, then cut the half into thirds. One third OF a half loaf of bread is the same as 1/3 x 1/2 and tastes delicious with butter.
Multiplying Two Proper Fraction Multiplying Two Proper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Proper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ ✎ Multiplying Two Proper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Proper Fractions with No Simplifying (Printable Only) Multiplying Two Proper Fractions with All Simplifying (Printable Only) Multiplying Two Proper Fractions with Some Simplifying (Printable Only)
Multiplying Proper and Improper Fractions Multiplying Proper and Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper and Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper and Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper and Improper Fractions with No Simplifying (Printable Only) Multiplying Proper and Improper Fractions with All Simplifying (Printable Only) Multiplying Proper and Improper Fractions with Some Simplifying (Printable Only)
Multiplying Two Improper Fractions Multiplying Two Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Improper Fractions with No Simplifying (Printable Only) Multiplying Two Improper Fractions with All Simplifying (Printable Only) Multiplying Two Improper Fractions with Some Simplifying (Printable Only)
Multiplying Proper and Mixed Fractions Multiplying Proper and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper and Mixed Fractions with No Simplifying (Printable Only) Multiplying Proper and Mixed Fractions with All Simplifying (Printable Only) Multiplying Proper and Mixed Fractions with Some Simplifying (Printable Only)
Multiplying Two Mixed Fractions Multiplying Two Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Mixed Fractions with No Simplifying (Printable Only) Multiplying Two Mixed Fractions with All Simplifying (Printable Only) Multiplying Two Mixed Fractions with Some Simplifying (Printable Only)
Multiplying Whole Numbers and Proper Fractions Multiplying Whole Numbers and Proper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Proper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Proper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Proper Fractions with No Simplifying (Printable Only) Multiplying Whole Numbers and Proper Fractions with All Simplifying (Printable Only) Multiplying Whole Numbers and Proper Fractions with Some Simplifying (Printable Only)
Multiplying Whole Numbers and Improper Fractions Multiplying Whole Numbers and Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Improper Fractions with No Simplifying (Printable Only) Multiplying Whole Numbers and Improper Fractions with All Simplifying (Printable Only) Multiplying Whole Numbers and Improper Fractions with Some Simplifying (Printable Only)
Multiplying Whole Numbers and Mixed Fractions Multiplying Whole Numbers and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Mixed Fractions with No Simplifying (Printable Only) Multiplying Whole Numbers and Mixed Fractions with All Simplifying (Printable Only) Multiplying Whole Numbers and Mixed Fractions with Some Simplifying (Printable Only)
Multiplying Proper, Improper and Mixed Fractions Multiplying Proper, Improper and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper, Improper and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper, Improper and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper, Improper and Mixed Fractions with No Simplifying (Printable Only) Multiplying Proper, Improper and Mixed Fractions with All Simplifying (Printable Only) Multiplying Proper, Improper and Mixed Fractions with Some Simplifying (Printable Only)
Conceptually, dividing fractions is probably the most difficult of all the operations, but we're going to help you out. The algorithm for dividing fractions is just like multiplying fractions, but you find the inverse of the second fraction or you cross-multiply. This gets you the right answer which is extremely important especially if you're building a bridge. We told you how to conceptualize fraction multiplication, but how does it work with division? Easy! You just need to learn the magic phrase: "How many ____'s are there in ______? For example, in the question 6 ÷ 1/2, you would ask, "How many halves are there in 6?" It becomes a little more difficult when both numbers are fractions, but it isn't a giant leap to figure it out. 1/2 ÷ 1/4 is a fairly easy example, especially if you think in terms of U.S. or Canadian coins. How many quarters are there in a half dollar?
Dividing Two Proper Fractions Dividing Two Proper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Proper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Proper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Proper Fractions with No Simplifying (Printable Only) Dividing Two Proper Fractions with All Simplifying (Printable Only) Dividing Two Proper Fractions with Some Simplifying (Printable Only)
Dividing Proper and Improper Fractions Dividing Proper and Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper and Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper and Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper and Improper Fractions with No Simplifying (Printable Only) Dividing Proper and Improper Fractions with All Simplifying (Printable Only) Dividing Proper and Improper Fractions with Some Simplifying (Printable Only)
Dividing Two Improper Fractions Dividing Two Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Improper Fractions with No Simplifying (Printable Only) Dividing Two Improper Fractions with All Simplifying (Printable Only) Dividing Two Improper Fractions with Some Simplifying (Printable Only)
Dividing Proper and Mixed Fractions Dividing Proper and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper and Mixed Fractions with No Simplifying (Printable Only) Dividing Proper and Mixed Fractions with All Simplifying (Printable Only) Dividing Proper and Mixed Fractions with Some Simplifying (Printable Only)
Dividing Two Mixed Fractions Dividing Two Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Mixed Fractions with No Simplifying (Printable Only) Dividing Two Mixed Fractions with All Simplifying (Printable Only) Dividing Two Mixed Fractions with Some Simplifying (Printable Only)
Dividing Whole Numbers and Proper Fractions Dividing Whole Numbers and Proper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Proper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Proper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Proper Fractions with No Simplifying (Printable Only) Dividing Whole Numbers and Proper Fractions with All Simplifying (Printable Only) Dividing Whole Numbers and Proper Fractions with Some Simplifying (Printable Only)
Dividing Whole Numbers and Improper Fractions Dividing Whole Numbers and Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Improper Fractions with No Simplifying (Printable Only) Dividing Whole Numbers and Improper Fractions with All Simplifying (Printable Only) Dividing Whole Numbers and Improper Fractions with Some Simplifying (Printable Only)
Dividing Whole Numbers and Mixed Fractions Dividing Whole Numbers and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Mixed Fractions with No Simplifying (Printable Only) Dividing Whole Numbers and Mixed Fractions with All Simplifying (Printable Only) Dividing Whole Numbers and Mixed Fractions with Some Simplifying (Printable Only)
Dividing Proper, Improper and Mixed Fractions Dividing Proper, Improper and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper, Improper and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper, Improper and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper, Improper and Mixed Fractions with No Simplifying (Printable Only) Dividing Proper, Improper and Mixed Fractions with All Simplifying (Printable Only) Dividing Proper, Improper and Mixed Fractions with Some Simplifying (Printable Only)
This section includes worksheets with both multiplication and division mixed on each worksheet. Students will have to pay attention to the signs.
Multiplying and Dividing Two Proper Fractions Multiplying and Dividing Two Proper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Proper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Proper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Proper Fractions with No Simplifying (Printable Only) Multiplying and Dividing Two Proper Fractions with All Simplifying (Printable Only) Multiplying and Dividing Two Proper Fractions with Some Simplifying (Printable Only)
Multiplying and Dividing Proper and Improper Fractions Multiplying and Dividing Proper and Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper and Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper and Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper and Improper Fractions with No Simplifying (Printable Only) Multiplying and Dividing Proper and Improper Fractions with All Simplifying (Printable Only) Multiplying and Dividing Proper and Improper Fractions with Some Simplifying (Printable Only)
Multiplying and Dividing Two Improper Fractions Multiplying and Dividing Two Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Improper Fractions (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Improper Fractions with No Simplifying (Printable Only) Multiplying and Dividing Two Improper Fractions with All Simplifying (Printable Only) Multiplying and Dividing Two Improper Fractions (Printable Only)
Multiplying and Dividing Proper and Mixed Fractions Multiplying and Dividing Proper and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper and Mixed Fractions with No Simplifying (Printable Only) Multiplying and Dividing Proper and Mixed Fractions with All Simplifying (Printable Only) Multiplying and Dividing Proper and Mixed Fractions with Some Simplifying (Printable Only)
Multiplying and Dividing Two Mixed Fractions Multiplying and Dividing Two Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Mixed Fractions with No Simplifying (Printable Only) Multiplying and Dividing Two Mixed Fractions with All Simplifying (Printable Only) Multiplying and Dividing Two Mixed Fractions with Some Simplifying (Printable Only)
Multiplying and Dividing Whole Numbers and Proper Fractions Fractions Multiplying and Dividing Whole Numbers and Proper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Proper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Proper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Proper Fractions with No Simplifying (Printable Only) Multiplying and Dividing Whole Numbers and Proper Fractions with All Simplifying (Printable Only) Multiplying and Dividing Whole Numbers and Proper Fractions with Some Simplifying (Printable Only)
Multiplying and Dividing Whole Numbers and Improper Fractions Multiplying and Dividing Whole Numbers and Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Improper Fractions with No Simplifying (Printable Only) Multiplying and Dividing Whole Numbers and Improper Fractions with All Simplifying (Printable Only) Multiplying and Dividing Whole Numbers and Improper Fractions with Some Simplifying (Printable Only)
Multiplying and Dividing Whole Numbers and Mixed Fractions Multiplying and Dividing Whole Numbers and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Mixed Fractions with No Simplifying (Printable Only) Multiplying and Dividing Whole Numbers and Mixed Fractions with All Simplifying (Printable Only) Multiplying and Dividing Whole Numbers and Mixed Fractions with Some Simplifying (Printable Only)
Multiplying and Dividing Proper, Improper and Mixed Fractions Multiplying and Dividing Proper, Improper and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper, Improper and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper, Improper and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper, Improper and Mixed Fractions with No Simplifying (Printable Only) Multiplying and Dividing Proper, Improper and Mixed Fractions with All Simplifying (Printable Only) Multiplying and Dividing Proper, Improper and Mixed Fractions with Some Simplifying (Printable Only)
Adding fractions requires the annoying common denominator. Make it easy on your students by first teaching the concepts of equivalent fractions and least common multiples. Once students are familiar with those two concepts, the idea of finding fractions with common denominators for adding becomes that much easier. Spending time on modeling fractions will also help students to understand fractions addition. Relating fractions to familiar examples will certainly help. For example, if you add a 1/2 banana and a 1/2 banana, you get a whole banana. What happens if you add a 1/2 banana and 3/4 of another banana?
Adding Two Proper Fractions with Equal Denominators and Proper Fraction Results Adding Two Proper Fractions with Equal Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Equal Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Equal Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Equal Denominators, Proper Fractions Result, and No Simplifying (Printable Only) Adding Two Proper Fractions with Equal Denominators, Proper Fractions Result, and All Simplifying (Printable Only) Adding Two Proper Fractions with Equal Denominators, Proper Fractions Result, and Some Simplifying (Printable Only)
Adding Two Proper Fractions with Equal Denominators and Mixed Fraction Results Adding Two Proper Fractions with Equal Denominators, Mixed Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Equal Denominators, Mixed Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Equal Denominators, Mixed Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Equal Denominators, Mixed Fractions Result, and No Simplifying (Printable Only) Adding Two Proper Fractions with Equal Denominators, Mixed Fractions Result, and All Simplifying (Printable Only) Adding Two Proper Fractions with Equal Denominators, Mixed Fractions Result, and Some Simplifying (Printable Only)
Adding Two Proper Fractions with Similar Denominators and Proper Fraction Results Adding Two Proper Fractions with Similar Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Similar Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Similar Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Similar Denominators, Proper Fractions Result, and No Simplifying (Printable Only) Adding Two Proper Fractions with Similar Denominators, Proper Fractions Result, and All Simplifying (Printable Only) Adding Two Proper Fractions with Similar Denominators, Proper Fractions Result, and Some Simplifying (Printable Only)
Adding Two Proper Fractions with Similar Denominators and Mixed Fraction Results Adding Two Proper Fractions with Similar Denominators, Mixed Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Similar Denominators, Mixed Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Similar Denominators, Mixed Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Similar Denominators, Mixed Fractions Result, and No Simplifying (Printable Only) Adding Two Proper Fractions with Similar Denominators, Mixed Fractions Result, and All Simplifying (Printable Only) Adding Two Proper Fractions with Similar Denominators, Mixed Fractions Result, and Some Simplifying (Printable Only)
Adding Two Proper Fractions with Unlike Denominators and Proper Fraction Results Adding Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Unlike Denominators, Proper Fractions Result, and No Simplifying (Printable Only) Adding Two Proper Fractions with Unlike Denominators, Proper Fractions Result, and All Simplifying (Printable Only) Adding Two Proper Fractions with Unlike Denominators, Proper Fractions Result, and Some Simplifying (Printable Only)
Adding Two Proper Fractions with Unlike Denominators and Mixed Fraction Results Adding Two Proper Fractions with Unlike Denominators, Mixed Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Unlike Denominators, Mixed Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Unlike Denominators, Mixed Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Unlike Denominators, Mixed Fractions Result, and No Simplifying (Printable Only) Adding Two Proper Fractions with Unlike Denominators, Mixed Fractions Result, and All Simplifying (Printable Only) Adding Two Proper Fractions with Unlike Denominators, Mixed Fractions Result, and Some Simplifying (Printable Only)
Adding Proper and Improper Fractions with Equal Denominators Adding Proper and Improper Fractions with Equal Denominators and No Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Equal Denominators and All Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Equal Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Equal Denominators and No Simplifying (Printable Only) Adding Proper and Improper Fractions with Equal Denominators and All Simplifying (Printable Only) Adding Proper and Improper Fractions with Equal Denominators and Some Simplifying (Printable Only)
Adding Proper and Improper Fractions with Similar Denominators Adding Proper and Improper Fractions with Similar Denominators and No Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Similar Denominators and All Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Similar Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Similar Denominators and No Simplifying (Printable Only) Adding Proper and Improper Fractions with Similar Denominators and All Simplifying (Printable Only) Adding Proper and Improper Fractions with Similar Denominators and Some Simplifying (Printable Only)
Adding Proper and Improper Fractions with Unlike Denominators Adding Proper and Improper Fractions with Unlike Denominators and No Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Unlike Denominators and All Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Unlike Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Unlike Denominators and No Simplifying (Printable Only) Adding Proper and Improper Fractions with Unlike Denominators and All Simplifying (Printable Only) Adding Proper and Improper Fractions with Unlike Denominators and Some Simplifying (Printable Only)
A common strategy to use when adding mixed fractions is to convert the mixed fractions to improper fractions, complete the addition, then switch back. Another strategy which requires a little less brainpower is to look at the whole numbers and fractions separately. Add the whole numbers first. Add the fractions second. If the resulting fraction is improper, then it needs to be converted to a mixed number. The whole number portion can be added to the original whole number portion.
Adding Two Mixed Fractions with Equal Denominators Adding Two Mixed Fractions with Equal Denominators and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Equal Denominators and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Equal Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Equal Denominators and No Simplifying (Printable Only) Adding Two Mixed Fractions with Equal Denominators and All Simplifying (Printable Only) Adding Two Mixed Fractions with Equal Denominators and Some Simplifying (Printable Only)
Adding Two Mixed Fractions with Similar Denominators Adding Two Mixed Fractions with Similar Denominators and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Similar Denominators and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Similar Denominators and Some Simplifying Adding Two Mixed Fractions with Similar Denominators and No Simplifying (Printable Only) Adding Two Mixed Fractions with Similar Denominators and All Simplifying (Printable Only) Adding Two Mixed Fractions with Similar Denominators and Some Simplifying (Printable Only)
Adding Two Mixed Fractions with Unlike Denominators Adding Two Mixed Fractions with Unlike Denominators and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Unlike Denominators and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Unlike Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Unlike Denominators and No Simplifying (Printable Only) Adding Two Mixed Fractions with Unlike Denominators and All Simplifying (Printable Only) Adding Two Mixed Fractions with Unlike Denominators and Some Simplifying (Printable Only)
Subtracting Fractions
There isn't a lot of difference between adding and subtracting fractions. Both require a common denominator which requires some prerequisite knowledge. The only difference is the second and subsequent numerators are subtracted from the first one. There is a danger that you might end up with a negative number when subtracting fractions, so students might need to learn what it means in that case. When it comes to any concept in fractions, it is always a good idea to relate it to a familiar or easy-to-understand situation. For example, 7/8 - 3/4 = 1/8 could be given meaning in the context of a race. The first runner was 7/8 around the track when the second runner was 3/4 around the track. How far ahead was the first runner? (1/8 of the track).
Subtracting Two Proper Fractions with Equal Denominators and Proper Fraction Results Subtracting Two Proper Fractions with Equal Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Equal Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Equal Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Equal Denominators, Proper Fractions Results, and No Simplifying (Printable Only) Subtracting Two Proper Fractions with Equal Denominators, Proper Fractions Results, and All Simplifying (Printable Only) Subtracting Two Proper Fractions with Equal Denominators, Proper Fractions Results, and Some Simplifying (Printable Only)
Subtracting Two Proper Fractions with Similar Denominators and Proper Fraction Results Subtracting Two Proper Fractions with Similar Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Similar Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Similar Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Similar Denominators, Proper Fractions Results, and No Simplifying (Printable Only) Subtracting Two Proper Fractions with Similar Denominators, Proper Fractions Results, and All Simplifying (Printable Only) Subtracting Two Proper Fractions with Similar Denominators, Proper Fractions Results, and Some Simplifying (Printable Only)
Subtracting Two Proper Fractions with Unlike Denominators and Proper Fraction Results Subtracting Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and No Simplifying (Printable Only) Subtracting Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and All Simplifying (Printable Only) Subtracting Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and Some Simplifying (Printable Only)
Subtracting Proper and Improper Fractions with Equal Denominators and Proper Fraction Results Subtracting Proper and Improper Fractions with Equal Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Equal Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Equal Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Equal Denominators, Proper Fractions Results, and No Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Equal Denominators, Proper Fractions Results, and All Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Equal Denominators, Proper Fractions Results, and Some Simplifying (Printable Only)
Subtracting Proper and Improper Fractions with Similar Denominators and Proper Fraction Results Subtracting Proper and Improper Fractions with Similar Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Similar Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Similar Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Similar Denominators, Proper Fractions Results, and No Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Similar Denominators, Proper Fractions Results, and All Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Similar Denominators, Proper Fractions Results, and Some Simplifying (Printable Only)
Subtracting Proper and Improper Fractions with Unlike Denominators and Proper Fraction Results Subtracting Proper and Improper Fractions with Unlike Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Unlike Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Unlike Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Unlike Denominators, Proper Fractions Results, and No Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Unlike Denominators, Proper Fractions Results, and All Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Unlike Denominators, Proper Fractions Results, and Some Simplifying (Printable Only)
Subtracting Proper and Improper Fractions with Equal Denominators and Mixed Fraction Results Subtracting Proper and Improper Fractions with Equal Denominators, Mixed Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Equal Denominators, Mixed Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Equal Denominators, Mixed Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Equal Denominators, Mixed Fractions Results, and No Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Equal Denominators, Mixed Fractions Results, and All Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Equal Denominators, Mixed Fractions Results, and Some Simplifying (Printable Only)
Subtracting Proper and Improper Fractions with Similar Denominators and Mixed Fraction Results Subtracting Proper and Improper Fractions with Similar Denominators, Mixed Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Similar Denominators, Mixed Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Similar Denominators, Mixed Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Similar Denominators, Mixed Fractions Results, and No Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Similar Denominators, Mixed Fractions Results, and All Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Similar Denominators, Mixed Fractions Results, and Some Simplifying (Printable Only)
Subtracting Proper and Improper Fractions with Unlike Denominators and Mixed Fraction Results Subtracting Proper and Improper Fractions with Unlike Denominators, Mixed Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Unlike Denominators, Mixed Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Unlike Denominators, Mixed Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Unlike Denominators, Mixed Fractions Results, and No Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Unlike Denominators, Mixed Fractions Results, and All Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Unlike Denominators, Mixed Fractions Results, and Some Simplifying (Printable Only)
Subtracting Mixed Fractions with Equal Denominators Subtracting Mixed Fractions with Equal Denominators, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Equal Denominators, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Equal Denominators, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Equal Denominators, and No Simplifying (Printable Only) Subtracting Mixed Fractions with Equal Denominators, and All Simplifying (Printable Only) Subtracting Mixed Fractions with Equal Denominators, and Some Simplifying (Printable Only)
Subtracting Mixed Fractions with Similar Denominators Subtracting Mixed Fractions with Similar Denominators, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Similar Denominators, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Similar Denominators, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Similar Denominators, and No Simplifying (Printable Only) Subtracting Mixed Fractions with Similar Denominators, and All Simplifying (Printable Only) Subtracting Mixed Fractions with Similar Denominators, and Some Simplifying (Printable Only)
Subtracting Mixed Fractions with Unlike Denominators Subtracting Mixed Fractions with Unlike Denominators, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Unlike Denominators, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Unlike Denominators, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Unlike Denominators, and No Simplifying (Printable Only) Subtracting Mixed Fractions with Unlike Denominators, and All Simplifying (Printable Only) Subtracting Mixed Fractions with Unlike Denominators, and Some Simplifying (Printable Only)
Adding and Subtracting Fractions
Mixing up the signs on operations with fractions worksheets makes students pay more attention to what they are doing and allows for a good test of their skills in more than one operation.
Adding and Subtracting Proper and Improper Fractions Adding and Subtracting Proper and Improper Fractions with Equal Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding and Subtracting Proper and Improper Fractions with Similar Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding and Subtracting Proper and Improper Fractions with Unlike Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding and Subtracting Proper and Improper Fractions with Equal Denominators and Some Simplifying (Printable Only) Adding and Subtracting Proper and Improper Fractions with Similar Denominators and Some Simplifying (Printable Only) Adding and Subtracting Proper and Improper Fractions with Unlike Denominators and Some Simplifying (Printable Only)
Adding and Subtracting Mixed Fractions Adding and Subtracting Mixed Fractions with Equal Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding and Subtracting Mixed Fractions with Similar Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding and Subtracting Mixed Fractions with Unlike Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding and Subtracting Mixed Fractions with Equal Denominators and Some Simplifying (Printable Only) Adding and Subtracting Mixed Fractions with Similar Denominators and Some Simplifying (Printable Only) Adding and Subtracting Mixed Fractions with Unlike Denominators and Some Simplifying (Printable Only) Adding/Subtracting Three Fractions/Mixed Fractions
All Operations Fractions Worksheets
All Operations with Two Proper Fractions with Equal Denominators and Proper Fraction Results All Operations with Two Proper Fractions with Equal Denominators, Proper Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Equal Denominators, Proper Fractions Results and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Equal Denominators, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Equal Denominators, Proper Fractions Results and No Simplifying (Printable Only) All Operations with Two Proper Fractions with Equal Denominators, Proper Fractions Results and All Simplifying (Printable Only) All Operations with Two Proper Fractions with Equal Denominators, Proper Fractions Results and Some Simplifying (Printable Only)
All Operations with Two Proper Fractions with Similar Denominators and Proper Fraction Results All Operations with Two Proper Fractions with Similar Denominators, Proper Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Similar Denominators, Proper Fractions Results and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Similar Denominators, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Similar Denominators, Proper Fractions Results and No Simplifying (Printable Only) All Operations with Two Proper Fractions with Similar Denominators, Proper Fractions Results and All Simplifying (Printable Only) All Operations with Two Proper Fractions with Similar Denominators, Proper Fractions Results and Some Simplifying (Printable Only)
All Operations with Two Proper Fractions with Unlike Denominators and Proper Fraction Results All Operations with Two Proper Fractions with Unlike Denominators, Proper Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Unlike Denominators, Proper Fractions Results and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Unlike Denominators, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Unlike Denominators, Proper Fractions Results and No Simplifying (Printable Only) All Operations with Two Proper Fractions with Unlike Denominators, Proper Fractions Results and All Simplifying (Printable Only) All Operations with Two Proper Fractions with Unlike Denominators, Mixed Fractions Results and Some Simplifying (Printable Only)
All Operations with Proper and Improper Fractions with Equal Denominators All Operations with Proper and Improper Fractions with Equal Denominators and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Equal Denominators and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Equal Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Equal Denominators and No Simplifying (Printable Only) All Operations with Proper and Improper Fractions with Equal Denominators and All Simplifying (Printable Only) All Operations with Proper and Improper Fractions with Equal Denominators and Some Simplifying (Printable Only)
All Operations with Proper and Improper Fractions with Similar Denominators All Operations with Proper and Improper Fractions with Similar Denominators and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Similar Denominators and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Similar Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Similar Denominators and No Simplifying (Printable Only) All Operations with Proper and Improper Fractions with Similar Denominators and All Simplifying (Printable Only) All Operations with Proper and Improper Fractions with Similar Denominators and Some Simplifying (Printable Only)
All Operations with Proper and Improper Fractions with Unlike Denominators All Operations with Proper and Improper Fractions with Unlike Denominators and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Unlike Denominators and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Unlike Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Unlike Denominators and No Simplifying (Printable Only) All Operations with Proper and Improper Fractions with Unlike Denominators and All Simplifying (Printable Only) All Operations with Proper and Improper Fractions with Unlike Denominators and Some Simplifying (Printable Only)
All Operations with Two Mixed Fractions with Equal Denominators All Operations with Two Mixed Fractions with Equal Denominators and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Equal Denominators and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Equal Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Equal Denominators and No Simplifying (Printable Only) All Operations with Two Mixed Fractions with Equal Denominators and All Simplifying (Printable Only) All Operations with Two Mixed Fractions with Equal Denominators and Some Simplifying (Printable Only)
All Operations with Two Mixed Fractions with Similar Denominators All Operations with Two Mixed Fractions with Similar Denominators and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Similar Denominators and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Similar Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Similar Denominators and No Simplifying (Printable Only) All Operations with Two Mixed Fractions with Similar Denominators and All Simplifying (Printable Only) All Operations with Two Mixed Fractions with Similar Denominators and Some Simplifying (Printable Only)
All Operations with Two Mixed Fractions with Unlike Denominators All Operations with Two Mixed Fractions with Unlike Denominators and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Unlike Denominators and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Unlike Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Unlike Denominators and No Simplifying (Printable Only) All Operations with Two Mixed Fractions with Unlike Denominators and All Simplifying (Printable Only) All Operations with Two Mixed Fractions with Unlike Denominators and Some Simplifying (Printable Only)
All Operations with 3 Fractions All Operations with Three Fractions Including Some Improper Fractions All Operations with Three Fractions Including Some Negative and Some Improper Fractions
Operations with Negative Fractions Worksheets
Although some of these worksheets are single operations, it should be helpful to have all of these in the same location. There are some special considerations when completing operations with negative fractions. It is usually very helpful to change any mixed numbers to an improper fraction before proceeding. It is important to pay attention to the signs and know the rules for multiplying positives and negatives (++ = +, +- = -, -+ = - and -- = +).
Adding with Negative Fractions Adding Negative Proper Fractions with Unlike Denominators Up to Sixths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Negative Proper Fractions with Unlike Denominators Up to Twelfths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Negative Mixed Fractions with Unlike Denominators Up to Sixths, Proper Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ Adding Negative Mixed Fractions with Unlike Denominators Up to Twelfths, Proper Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ Adding Negative Proper Fractions with Denominators Up to Sixths, Proper Fraction Results and Some Simplifying (Printable Only) Adding Negative Proper Fractions with Denominators Up to Twelfths, Proper Fraction Results and Some Simplifying (Printable Only) Adding Negative Mixed Fractions with Denominators Up to Sixths and Some Simplifying (Printable Only) Adding Negative Mixed Fractions with Denominators Up to Twelfths and Some Simplifying (Printable Only)
Subtracting with Negative Fractions Subtracting Negative Proper Fractions with Unlike Denominators Up to Sixths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Negative Proper Fractions with Unlike Denominators Up to Twelfths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Negative Mixed Fractions with Unlike Denominators Up to Sixths, Mixed Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Negative Mixed Fractions with Unlike Denominators Up to Twelfths, Mixed Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Negative Proper Fractions with Denominators Up to Sixths, Proper Fraction Results and Some Simplifying (Printable Only) Subtracting Negative Proper Fractions with Denominators Up to Twelfths, Proper Fraction Results and Some Simplifying (Printable Only) Subtracting Negative Mixed Fractions with Denominators Up to Sixths and Some Simplifying (Printable Only) Subtracting Negative Mixed Fractions with Denominators Up to Twelfths and Some Simplifying (Printable Only)
Multiplying with Negative Fractions Multiplying Negative Proper Fractions with Denominators Up to Sixths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Negative Proper Fractions with Denominators Up to Twelfths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Negative Mixed Fractions with Denominators Up to Sixths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Negative Mixed Fractions with Denominators Up to Twelfths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Negative Proper Fractions with Denominators Up to Sixths, Proper Fraction Results and Some Simplifying (Printable Only) Multiplying Negative Proper Fractions with Denominators Up to Twelfths, Proper Fraction Results and Some Simplifying (Printable Only) Multiplying Negative Mixed Fractions with Denominators Up to Sixths and Some Simplifying (Printable Only) Multiplying Negative Mixed Fractions with Denominators Up to Twelfths and Some Simplifying (Printable Only)
Dividing with Negative Fractions Dividing Negative Proper Fractions with Denominators Up to Sixths, Mixed Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Negative Proper Fractions with Denominators Up to Twelfths, Mixed Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Negative Mixed Fractions with Denominators Up to Twelfths, Mixed Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ Dividing Negative Mixed Fractions with Denominators Up to Twelfths, Mixed Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ Dividing Negative Proper Fractions with Denominators Up to Sixths, Proper Fraction Results and Some Simplifying (Printable Only) Dividing Negative Proper Fractions with Denominators Up to Twelfths, Proper Fraction Results and Some Simplifying (Printable Only) Dividing Negative Mixed Fractions with Denominators Up to Sixths and Some Simplifying (Printable Only) Dividing Negative Mixed Fractions with Denominators Up to Twelfths and Some Simplifying (Printable Only)
Order of Operations with Fractions Worksheets
The order of operations worksheets in this section actually reside on the Order of Operations page, but they are included here for your convenience.
Order of Operations with Fractions 2-Step Order of Operations with Fractions 3-Step Order of Operations with Fractions 4-Step Order of Operations with Fractions 5-Step Order of Operations with Fractions 6-Step Order of Operations with Fractions
Order of Operations with Fractions (No Exponents) 2-Step Order of Operations with Fractions (No Exponents) 3-Step Order of Operations with Fractions (No Exponents) 4-Step Order of Operations with Fractions (No Exponents) 5-Step Order of Operations with Fractions (No Exponents) 6-Step Order of Operations with Fractions (No Exponents)
Order of Operations with Positive and Negative Fractions 2-Step Order of Operations with Positive & Negative Fractions 3-Step Order of Operations with Positive & Negative Fractions 4-Step Order of Operations with Positive & Negative Fractions 5-Step Order of Operations with Positive & Negative Fractions 6-Step Order of Operations with Positive & Negative Fractions
Featured here is a vast collection of fraction word problems, which require learners to simplify fractions, add like and unlike fractions; subtract like and unlike fractions; multiply and divide fractions. The fraction word problems include proper fraction, improper fraction, and mixed numbers. Solve each word problem and scroll down each printable worksheet to verify your solutions using the answer key provided. Thumb through some of these word problem worksheets for free!
Represent and Simplify the Fractions: Type 1
Presented here are the fraction pdf worksheets based on real-life scenarios. Read the basic fraction word problems, write the correct fraction and reduce your answer to the simplest form.
Download the set
Represent and Simplify the Fractions: Type 2
Before representing in fraction, children should perform addition or subtraction to solve these fraction word problems. Write your answer in the simplest form.
Adding Fractions Word Problems Worksheets
Conjure up a picture of how adding fractions plays a significant role in our day-to-day lives with the help of the real-life scenarios and circumstances presented as word problems here.
(15 Worksheets)
Subtracting Fractions Word Problems Worksheets
Crank up your skills with this set of printable worksheets on subtracting fractions word problems presenting real-world situations that involve fraction subtraction!
Multiplying Fractions Word Problems Worksheets
This set of printables is for the ardently active children! Explore the application of fraction multiplication and mixed-number multiplication in the real world with this exhilarating practice set.
Fraction Division Word Problems Worksheets
Gift children a broad view of the real-life application of dividing fractions! Let them divide fractions by whole numbers, divide 2 fractions, divide mixed numbers, and solve the word problems here.
Today we are going to look at some examples of word problems with fractions.
Although they may seem more difficult, in reality, word problems involving fractions are just as easy as those involving whole numbers. The only thing we have to do is:
Read the problem carefully.
Think about what it is asking us to do.
Think about the information we need.
Simplify, if necessary.
Think about whether our solution makes sense (in order to check it).
As you can see, the only difference in fraction word problems is step 5 (simplify) .
There are some word problems which, depending on the information provided, we should express as a fraction. For example:
In my fruit basket, there are 13 pieces of fruit, 5 of which are apples.
How can we express the number of apples as a fraction?
5 – The number of apples (5) corresponds to the numerator (the number which expresses the number of parts that we wish to represent).
13 – The total number of fruits (13) corresponds to the denominator (the number which expresses the number of total possible parts).
The solution to this problem is an irreducible fraction (a fraction which cannot be simplified). Therefore, there is nothing left to do.
Word problems with fractions: involving two fractions
In these problems, we should remember how to carry out operations with fractions.
Carefully read the following problem and the steps we have taken to solve it:
What fraction of the payment has Maria spent?
We find the common denominator:
We calculate:
Word problems with fractions: involving a fraction and a whole number
Finally, we are going to look at an example of a word problem with a fraction and a whole number. Now we will have to convert all the information into a fraction with the same denominator (as we did in the example above) in order to calculate
We convert 1 into a fraction with the same denominator:
What do you think of this post? Do you see how easy it is to solve word problems with fractions?
To keep learning, try Smartick’s free trial.
Learn More:
Understand What a Fraction Is and When It Is Used
Fraction Word Problems: Addition, Subtraction, and Mixed Numbers
Learn and Practice How to Subtract or Add Fractions
Learn How to Subtract Fractions
Review and Practice the Two Methods of Dividing Fractions
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38 Comments
Thanks for your help
it simplifies the teaching and learning process
Thanks for the explanation… really grateful 🙏
Thank you for such good explanations, it helped me a lot
It is really good it helped me improve my math a lot.
same it helps me in my math too
Wow, it really helps a lot
Good exercises
Interesting
wow it worked
Hi can you not show the answer till the bottom of the page or your giving away the answer so if you solved number one problem the number one aware to the question will be there at the bottom of the page because it is way to easy if it is right there
I like that you are doing for as Thank you
I really want to be part of this
wow, this help me a lot
A big help for my kids lesson
Thank for helping me
Thank you for all the homework you have given us. God bless you
Thank you for this problems that involved fractions
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Please help me with my math homework
Hi Letlhogonolo,
Thank you very much for your comment. If you want to learn more content like this and practice elementary school math, just sign up at Smartick . You have a free trial period with no strings attached. If you have any additional questions or doubts you can write to my colleagues of the pedagogical team at [email protected] .
Best regards!
I like it… but you can level up please 🙄
Roll two dices, the first dice is the numerator, the second is the denominator, this is the first fraction. Roll both dices again and repeat the process to generate the second fraction. Write a division story problem that incorporates these two fractions.
Seems easy of the examples but when I have fraction word promblems in front of me then its still hard for me to figure it out.The examples on this site still is helpful.I will use the site that you give on here to get further practice.Thank you for the examples on here
Interesting and very helpful. I’m going to continue using this site and tell others about it too.
I really like it
Hey I am in grade five and it is super helpful for my exams thanks and maybe if you could make more it would be appriciated thx 🙂
Good efforts
i kinda like it pls write some more problems
I think it was really good how you are helping fellow students! But I think you can improve if there were more problems for solving! Thanks
Cool, it helps a lot.
it is helpfull
Fractions Questions
Fractions questions are given here will help the students to understand how to perform arithmetic operations on fractions. We know that fractions is one of the most important concepts of Class 7 Maths. In this article, you will get the questions on fractions, along with their solutions, based on the latest NCERT curriculum.
What are Fractions?
In maths, a fraction is defined as a part of the whole thing, and it can be written in the form a/b, where a and b are whole numbers, also, b ≠ 0. Based on the numerical values of numerator and denominator, we can define different types of fractions .
Proper fraction: A proper fraction is a number representing a part of a whole. This whole may be a single object or a group of objects.
Improper fraction: An improper fraction is a number in which the numerator is greater than the denominator.
Mixed fraction: A mixed fraction is a combination of a whole number and a proper fraction.
Learn more about fractions here.
Fractions Questions and Answers
1. How many 2/3 kg pieces can be cut from a cake of weight 4 kg?
Let p be the number 2/3 kg pieces that are cut from a 4 kg cake.
So, p × (2/3) = 4
p = 4 × (3/2)
Therefore, six 2/3 kg pieces can be cut from a cake of weight 4 kg.
2. What is the product of 5/129 and its reciprocal?
Given fraction: 5/129
Here, numerator = 5
Denominator = 129
Reciprocal of 5/129 = 129/5
The product of 5/129 and its reciprocal = (5/129) × (129/5) = 1.
3. Sunita and Rehana want to make dresses for their dolls. Sunita has 3/4 m of cloth, and she gave 1/3 of it to Rehana. How much did Rehana have?
Length of cloth Sunita has = 3/4 m
According to the given,
Sunita has 3/4 m of cloth, and she gave 1/3 of it to Rehana.
Therefore, the length of cloth Rehana has
= 1/3 of 3/4 m
= (1/3) x (3/4) m
4. Anuradha can do a piece of work in 6 hours. What part of the work can she do in 1 hour, in 5 hours, in 6 hours?
Let m be the whole work to be done.
The part of work done by Anuradha in 6 hours = m
Thus, the part of work done by her in 1 hour = m/6
The part of work done by her in 5 hours = (m/6) x 5 = 5m/6
The part of work done by her in 6 hours = (m/6) x 6 = m
Therefore, Anuradha can do 1/6 part of work in 1 hour, 5/6 part of work in 5 hours and the complete work in 6 hours.
5. Multiply the following fractions.
(i) (⅖) × 5 ¼
(ii) 2 ⅗ × 3
Here, 5 ¼ is a mixed fraction.
Let us convert this mixed fraction into an improper fraction.
5 ¼ = [(5 × 4) + 1]/4 = 21/4
Thus, (⅖) × 5 ¼ = (⅖) × (21/4) = 21/10
Here, 2 ⅗ is a mixed fraction.
2 ⅗ = [(2 × 5) + 3]/5 = 13/5
Therefore, 2 ⅗ × 3 = (13/5) × 3 = 39/5
6. Divide 3/10 by (1/4 of 3/5).
1/4 od 3/5 = (1/4) × (3/5) = 3/(4 × 5) = 3/20
3/10 ÷ (1/4 of 3/5)
= 3/10 ÷ 3/20
= (3/10) × (20/3)
\(\begin{array}{l}\text{7. Find the value of }\frac{1}{4\frac{2}{7}}+\frac{1}{3\frac{11}{13}}\frac{1}{\frac{5}{9}}.\end{array} \)
First, simplify the denominators.
= (7/30) + (13/50) + (9/5)
= (35 + 39 + 270)/150 {since the LCM of 30, 50 and 5 is 150}
8. Evaluate the following:
(i) 3 ½ ÷ 4
(ii) 4 ⅓ ÷ 3
Here, 3 ½ is a mixed fraction.
3 ½ = (3 × 2 + 1)/2 = 7/2
3 ½ ÷ 4 = 7/2 ÷ 4 = (7/2) × (¼) = 7/8
Here, 4 ⅓ is a mixed fraction.
4 ⅓ = (4 × 3 + 1)/3 = 13/3
4 ⅓ ÷ 3 = 13/3 ÷ 3 = (13/3) × (⅓) = 13/9
9. 1/8 of a number equals 2/5 ÷ 1/20. What is the number?
Let p be the number.
(1/8) × p = 2/5 ÷ 1/20
p/8 = (2/5) × (20/1)
p/8 = 2 × 4
Hence, 64 is the required number.
10. Raj travels 360 km on three-fifths of his petrol tank. How far would he travel at the same rate with a full tank of petrol?
Distance travelled by Raj with three-fifths (i.e. ⅗) of petrol tank = 360 km
Distance travelled by him with a full petrol tank = (360 ÷ 3/5) km
= (360 x 5)/3 km
= 120 x 5 km
Video Lesson on Fractions
Practice Questions on Fractions
1. The weight of an object on the moon is 1/6 its weight on the Earth. If an object weighs 5 3/5 kg on the Earth, how much would it weigh on the moon?
2. Lipika reads a book for 1 ¾ hour every day. She reads the entire book in 6 days. How many hours in all were required by her to read the book?
3. Multiply and reduce to the lowest form (if possible).
11/2 × 3/10
4. Arrange the following in descending order:
2/9, 2/3, 8/21
1/5, 3/7, 7/10
5. Write five equivalent fractions of 8/11.
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Fractions Worksheets
Fraction worksheets for grades 1 through 6.
Our fraction worksheets start with the introduction of the concepts of " equal parts ", "parts of a whole" and "fractions of a group or set"; and proceed to operations on fractions and mixed numbers.
Converting improper fractions to / from mixed numbers
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Convert decimals to fractions (tenths, hundredths), no simplification
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Convert mixed numbers to decimals (denominators of 10, 100 or 1000)
Convert fractions to decimals (common denominators of 2, 4, 5, ...)
Convert mixed numbers to decimals (common denominators of 2, 4, 5, ...)
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Grade 6 addition and subtraction of fractions worksheets
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What can QuickMath do?
QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students.
The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction.
The equations section lets you solve an equation or system of equations. You can usually find the exact answer or, if necessary, a numerical answer to almost any accuracy you require.
The inequalities section lets you solve an inequality or a system of inequalities for a single variable. You can also plot inequalities in two variables.
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The numbers section has a percentages command for explaining the most common types of percentage problems and a section for dealing with scientific notation.
A mixed number is a combination of a whole number and a fraction.
How can I compare two fractions?
To compare two fractions, first find a common denominator, then compare the numerators.Alternatively, compare the fractions by converting them to decimals.
How do you add or subtract fractions with different denominators?
To add or subtract fractions with different denominators, convert the fractions to have a common denominator. Then you can add or subtract the numerators of the fractions, leaving the denominator unchanged.
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We can still add the same amount to both sides of an equation without changing the solution.
Solve for x : \(x - \frac{5}{6} = \frac{1}{3}\).
To “undo” subtracting 5/6, add 5/6 to both sides of the equation and simplify.
\[ \begin{aligned} x - \frac{5}{6} = \frac{1}{3} ~ & \textcolor{red}{ \text{ Original equation.}} \\ x - \frac{5}{6} + \frac{5}{6} = \frac{1}{3} + \frac{5}{6} ~ & \textcolor{red}{ \text{ Add } \frac{5}{6} \text{ to both sides.}} \\ x = \frac{1 \cdot 2}{3 \cdot 2} + \frac{5}{6} ~ & \textcolor{red}{ \text{ Equivalent fractions, LCD = 6.}} \\ x = \frac{2}{6} + \frac{5}{6} ~ & \textcolor{red}{ \text{ Simplify.}} \\ x = \frac{7}{6} ~ & \textcolor{red}{ \text{ Add.}} \end{aligned}\nonumber \]
It is perfectly acceptable to leave your answer as an improper fraction. If you desire, or if you are instructed to do so, you can change your answer to a mixed fraction (7 divided by 6 is 1 with a remainder of 1). That is \(x = 1 \frac{1}{6}\).
Checking the Solution
Substitute 7/6 for x in the original equation and simplify.
Readers are encouraged to check this solution in the original equation.
Solve for x : \(x + \frac{3}{4} = - \frac{1}{2}\)
Undoing Multiplication
We “undo” multiplication by dividing. For example, to solve the equation 2 x = 6, we would divide both sides of the equation by 2. In similar fashion, we could divide both sides of the equation
\[ \frac{3}{5} x = \frac{4}{10}\nonumber \]
by 3/5. However, it is more efficient to take advantage of reciprocals. For convenience, we remind readers of the Multiplicative Inverse Property .
Multiplicative Inverse Property
Let a / b be any fraction. The number b / a is called the multiplicative inverse or reciprocal of a / b . The product of reciprocals is 1.
\[ \frac{a}{b} \cdot \frac{b}{a} = 1.\nonumber \]
Let’s put our knowledge of reciprocals to work.
Solve for x : \(\frac{3}{5}x = \frac{4}{10}\).
To “undo” multiplying by 3/5, multiply both sides by the reciprocal 5/3 and simplify.
\[ \begin{aligned} \frac{3}{5} x = \frac{4}{10} ~ & \textcolor{red}{ \text{ Original equation.}} \\ \frac{5}{3} \left( \frac{3}{5} x \right) = \frac{5}{3} \left( \frac{4}{10} \right) & ~ \textcolor{red}{ \text{ Multiply both sides by 5/3.}} \\ \left( \frac{5}{3} \cdot \frac{3}{5} \right) x = \frac{20}{30} ~ & \textcolor{red}{ \begin{array}{l} \text{ On the left, use the associative property to regroup.} \\ \text{ On the right, multiply.} \end{array}} \\ 1x = \frac{2}{3} ~ & \textcolor{red}{ \begin{array}{l} \text{ On the left, } \frac{5}{3} \cdot \frac{3}{5} = 1. \\ \text{ On the right, reduce: } \frac{20}{30} = \frac{2}{3}. \end{array}} \\ x = \frac{2}{3} ~ & \textcolor{red}{ \text{ On the left, } 1x = x.} \end{aligned}\nonumber \]
Substitute 2/3 for x in the original equation and simplify.
Because this last statement is true, we conclude that 2/3 is a solution of the equation (3/5) x = 4/10.
Solve for y : \( \frac{2}{3} y = \frac{4}{5}\)
Solve for x : \(- \frac{8}{9} x = \frac{5}{18}\).
To “undo” multiplying by −8/9, multiply both sides by the reciprocal −9/8 and simplify.
\[ \begin{aligned} - \frac{8}{9} x = \frac{5}{18} ~ & \textcolor{red}{ \text{ Original equation.}} \\ - \frac{9}{8} \left( - \frac{8}{9} x \right) = - \frac{9}{8} \left( \frac{5}{18} \right) ~ & \textcolor{red}{ \text{ Multiply both sides by } -9/8.} \\ \left[ - \frac{9}{8} \cdot \left( - \frac{8}{9} \right) \right] x = - \frac{3 \cdot 3}{2 \cdot 2 \cdot 2} \cdot \frac{5}{2 \cdot 3 \cdot 3} ~ & \textcolor{red}{ \begin{array}{l} \text{ On the left, use the associative property to regroup.} \\ \text{ On the right, prime factor.} \end{array}} 1x = \frac{ \cancel{3} \cdot \cancel{3}}{2 \cdot 2 \cdot 2} \cdot \frac{5}{2 \cdot \cancel{3} \cdot \cancel{3}} ~ & \textcolor{red}{ \begin{array}{l} \text{ On the left, } - \frac{9}{8} \cdot \left( - \frac{8}{9} \right) = 1. \\ \text{ On the right, cancel common factors.} \end{array}} \\ x = - \frac{5}{16} ~ & \textcolor{red}{ \text{ On the left, } 1x = x. \text{ Multiply on the right.}} \end{aligned}\nonumber \]
Solve for z: \(− \frac{2}{7} z = \frac{4}{21}\)
Clearing Fractions from the Equation
Although the technique demonstrated in the previous examples is a solid mathematical technique, working with fractions in an equation is not always the most efficient use of your time.
To clear all fractions from an equation, multiply both sides of the equation by the least common denominator of the fractions that appear in the equation.
Let’s put this idea to work.
In Example 1, we were asked to solve the following equation for x :
\[x - \frac{5}{6} = \frac{1}{3}.\nonumber \]
Take a moment to review the solution technique in Example 1. We will now solve this equation by first clearing all fractions from the equation.
Multiply both sides of the equation by the least common denominator for the fractions appearing in the equation.
\[ \begin{aligned} x - \frac{5}{6}= \frac{1}{3} ~ & \textcolor{red}{ \text{ Original equation.}} \\ 6 \left( x - \frac{5}{6} \right) = 6 \left( \frac{1}{3} \right) ~ & \textcolor{red}{ \text{ Multiply both sides by 6.}} \\ 6x - 6 \left( \frac{5}{6} \right) = 6 \left( \frac{1}{3} \right) ~ & \textcolor{red}{ \text{ Distribute the 6.}} \\ 6x-5 = 2 ~ & \textcolor{red}{ \text{ On each side, multiply first.}} \\ ~ & \textcolor{red}{6 \left( \frac{5}{6} \right) = 5 \text{ and } 6 \left( \frac{1}{3} \right) = 2.} \end{aligned}\nonumber \]
Note that the equation is now entirely clear of fractions, making it a much simpler equation to solve.
\[ \begin{aligned} 6x - 5 + 5 = 2 + 5 ~ & \textcolor{red}{ \text{ Add 5 to both sides.}} \\ 6x = 7 ~ & \textcolor{red}{ \text{ Simplify both sides.}} \\ \frac{6x}{6} = \frac{7}{6} ~ & \textcolor{red}{ \text{ Divide both sides by 6.}} \\ x = \frac{7}{6} ~ & \textcolor{red}{ \text{ Simplify.}} \end{aligned}\nonumber \]
Note that this is the same solution found in Example 1.
Solve for t : \(t - \frac{2}{7} = - \frac{1}{4}\)
In Example 4, we were asked to solve the following equation for x .
\[- \frac{8}{9}x = \frac{5}{18}\nonumber \]
Take a moment to review the solution in Example 4. We will now solve this equation by first clearing all fractions from the equation.
Multiply both sides of the equation by the least common denominator for the fractions that appear in the equation.
\[ \begin{aligned} - \frac{8}{9} x = \frac{5}{18} ~ & \textcolor{red}{ \text{ Original equation.}} \\ 18 \left( - \frac{8}{9} x \right) = 18 \left( \frac{5}{18} \right) ~ & \textcolor{red}{ \text{ Multiply both sides by 18.}} \\ -16x=5 ~ & \textcolor{red}{ \text{ On each side, cancel and multiply.}} \\ ~ & \textcolor{red}{ 18 \left( - \frac{8}{9} \right) = -16 \text{ and } 18 \left( \frac{5}{18} \right) = 5.} \end{aligned}\nonumber \]
Note that the equation is now entirely free of fractions. Continuing,
\[ \begin{aligned} \frac{-16x}{-16} = \frac{5}{-16} ~ & \textcolor{red}{ \text{ Divide both sides by } -16.} \\ x = - \frac{5}{16} ~ & \textcolor{red}{ \text{ Simplify.}} \end{aligned}\nonumber \]
Note that this is the same as the solution found in Example 4.
Solve for u :
\[ - \frac{7}{9} u = \frac{14}{27}\nonumber \]
Solve for x : \(\frac{2}{3}x + \frac{3}{4} = \frac{1}{2}\).
Solve for s : \( \frac{3}{2} - \frac{2s}{5} = \frac{s}{3} - \frac{1}{5}\).
Add texts here. Do not delete this text first.
Applications
Let’s look at some applications that involve equations containing fractions. For convenience, we repeat the Requirements for Word Problem Solutions .
Requirements for Word Problem Solutions
Statements such as “Let P represent the perimeter of the rectangle.”
Labeling unknown values with variables in a table.
Labeling unknown quantities in a sketch or diagram.
Set up an Equation . Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
Solve the Equation . You must always solve the equation set up in the previous step.
Answer the Question . This step is easily overlooked. For example, the problem might ask for Jane’s age, but your equation’s solution gives the age of Jane’s sister Liz. Make sure you answer the original question asked in the problem. Your solution should be written in a sentence with appropriate units. 5. Look Back. It is important to note that this step does not imply that you should simply check your solution in your equation. After all, it’s possible that your equation incorrectly models the problem’s situation, so you could have a valid solution to an incorrect equation. The important question is: “Does your answer make sense based on the words in the original problem statement.”
In the third quarter of a basketball game, announcers informed the crowd that attendance for the game was 12,250. If this is two-thirds of the capacity, find the full seating capacity for the basketball arena.
We follow the Requirements for Word Problem Solutions .
1. Set up a Variable Dictionary . Let F represent the full seating capacity. Note: It is much better to use a variable that “sounds like” the quantity that it represents. In this case, letting F represent the full seating capacity is much more descriptive than using x to represent the full seating capacity.
2. Set up an Equation . Two-thirds of the full seating capacity is 12,250.
\[ \begin{aligned} \colorbox{cyan}{Two-thirds} & \text{ of } & \colorbox{cyan}{Full Seating Capacity} & \text{ is } & 12,250 \\ \frac{2}{3} & \cdot & F & = & 12,250 \end{aligned}\nonumber \]
Hence, the equation is
\[ \frac{2}{3} F = 12250.\nonumber \]
3. Solve the Equation . Multiply both sides by 3 to clear fractions, then solve.
\[ \begin{aligned} \frac{2}{3} F = 12250 ~ & \textcolor{red}{ \text{ Original equation.}} \\ 3 \left( \frac{2}{3} F \right) = 3(12250) ~ & \textcolor{red}{ \text{ Multiply both sides by 3.}} \\ 2F = 36750 ~ & \textcolor{red}{ \text{ Simplify both sides.}} \\ \frac{2F}{2} = \frac{36750}{2} ~ & \textcolor{red}{ \text{ Divide both sides by 2.}} \\ F = 18375 ~ & \textcolor{red}{ \text{ Simplify both sides.}} \end{aligned}\nonumber \]
4. Answer the Question . The full seating capacity is 18,375.
5. Look Back . The words of the problem state that 2/3 of the seating capacity is 12,250. Let’s take two-thirds of our answer and see what we get.
This is the correct area (20 square inches), so our solution is correct.
The area of a triangle is 161 square feet. If the base of the triangle measures \(40 \frac{1}{4}\) feet, find the height of the triangle.
1. Is 1/4 a solution of the equation \(x + \frac{5}{8} = \frac{5}{8}\)?
2. Is 1/4 a solution of the equation \(x + \frac{1}{3} = \frac{5}{12}\)?
3. Is −8/15 a solution of the equation \(\frac{1}{4} x = − \frac{1}{15}\)?
4. Is −18/7 a solution of the equation \(− \frac{3}{8} x = \frac{25}{28}\)?
5. Is 1/2 a solution of the equation \(x + \frac{4}{9} = \frac{17}{18}\)?
6. Is 1/3 a solution of the equation \(x + \frac{3}{4} = \frac{13}{12}\)?
7. Is 3/8 a solution of the equation \(x − \frac{5}{9} = − \frac{13}{72}\)?
8. Is 1/2 a solution of the equation \(x − \frac{3}{5} = − \frac{1}{10}\)?
9. Is 2/7 a solution of the equation \(x − \frac{4}{9} = − \frac{8}{63}\)?
10. Is 1/9 a solution of the equation \(x − \frac{4}{7} = − \frac{31}{63}\)?
11. Is 8/5 a solution of the equation \( \frac{11}{14}x = \frac{44}{35}\)?
12. Is 16/9 a solution of the equation \(\frac{13}{18} x = \frac{104}{81}\)?
In Exercises 13-24, solve the equation and simplify your answer.
13. \(2x − 3=6x + 7\)
14. \(9x − 8 = −9x − 3\)
15. \(−7x +4=3x\)
16. \(6x +9= −6x\)
17. \(−2x = 9x − 4\)
18. \(−6x = −9x + 8\)
19. \(−8x = 7x − 7\)
20. \(−6x = 5x + 4\)
21. \(−7x +8=2x\)
22. \(−x − 7=3x\)
23. \(−9x +4=4x − 6\)
24. \(−2x +4= x − 7\)
In Exercises 25-48, solve the equation and simplify your answer.
25. \(x + \frac{3}{2 = \frac{1}{2}\)
26. \(x − \frac{3}{4} = \frac{1}{4}\)
27. \(− \frac{9}{5} x = \frac{1}{2}\)
28. \(\frac{7}{3} x = − \frac{7}{2}\)
29. \(\frac{3}{8} x = \frac{8}{7}\)
30. \(− \frac{1}{9} x = − \frac{3}{5}\)
31. \(\frac{2}{5} x = − \frac{1}{6}\)
32. \(\frac{1}{6} x = \frac{2}{9}\)
33. \(− \frac{3}{2} x = \frac{8}{7}\)
34. \(− \frac{3}{2} x = − \frac{7}{5}\)
35. \(x + \frac{3}{4} = \frac{5}{9}\)
36. \(x − \frac{1}{9} = − \frac{3}{2}\)
37. \(x − \frac{4}{7} = \frac{7}{8}\)
38. \(x + \frac{4}{9} = − \frac{3}{4}\)
39. \(x + \frac{8}{9} = \frac{2}{3}\)
40. \(x − \frac{5}{6} = \frac{1}{4}\)
41. \(x + \frac{5}{2} = − \frac{9}{8}\)
42. \(x + \frac{1}{2} = \frac{5}{3}\)
43. \(− \frac{8}{5} x = \frac{7}{9}\)
44. \(− \frac{3}{2} x = − \frac{5}{9}\)
45. \(x − \frac{1}{4} = − \frac{1}{8}\)
46. \(x − \frac{9}{2} = − \frac{7}{2}\)
47. \(− \frac{1}{4} x = \frac{1}{2}\)
48. \(− \frac{8}{9} x = − \frac{8}{3}\)
In Exercises 49-72, solve the equation and simplify your answer.
49. \(− \frac{7}{3} x − \frac{2}{3} = \frac{3}{4} x + \frac{2}{3}\)
50. \(\frac{1}{2} x − \frac{1}{2} = \frac{3}{2} x + \frac{3}{4}\)
51. \(− \frac{7}{2} x − \frac{5}{4} = \frac{4}{5}\)
52. \(− \frac{7}{6} x + \frac{5}{6} = − \frac{8}{9}\)
53. \(− \frac{9}{7} x + \frac{9}{2} = − \frac{5}{2}\)
54. \(\frac{5}{9} x − \frac{7}{2} = \frac{1}{4}\)
55. \(\frac{1}{4} x − \frac{4}{3} = − \frac{2}{3}\)
56. \(\frac{8}{7} x + \frac{3}{7} = \frac{5}{3}\)
57. \(\frac{5}{3} x + \frac{3}{2} = − \frac{1}{4}\)
58. \(\frac{1}{2} x − \frac{8}{3} = − \frac{2}{5}\)
59. \(− \frac{1}{3} x + \frac{4}{5} = − \frac{9}{5} x − \frac{5}{6}\)
60. \(− \frac{2}{9} x − \frac{3}{5} = \frac{4}{5} x − \frac{3}{2}\)
61. \(− \frac{4}{9} x − \frac{8}{9} = \frac{1}{2} x − \frac{1}{2}\)
62. \(− \frac{5}{4} x − \frac{5}{3} = \frac{8}{7} x + \frac{7}{3}\)
63. \(\frac{1}{2} x − \frac{1}{8} = − \frac{1}{8} x + \frac{5}{7}\)
64. \(− \frac{3}{2} x + \frac{8}{3} = \frac{7}{9} x − \frac{1}{2}\)
65. \(− \frac{3}{7} x − \frac{1}{3} = − \frac{1}{9}\)
66. \(\frac{2}{3} x + \frac{2}{9} = − \frac{9}{5}\)
67. \(− \frac{3}{4} x + \frac{2}{7} = \frac{8}{7} x − \frac{1}{3}\)
68. \(\frac{1}{2} x + \frac{1}{3} = − \frac{5}{2} x − \frac{1}{4}\)
69. \(− \frac{3}{4} x − \frac{2}{3} = − \frac{2}{3} x − \frac{1}{2}\)
70. \(\frac{1}{3} x − \frac{5}{7} = \frac{3}{2} x + \frac{4}{3}\)
71. \(− \frac{5}{2} x + \frac{9}{5} = \frac{5}{8}\)
72. \(\frac{9}{4} x + \frac{4}{3} = − \frac{1}{6}\)
73. At a local soccer game, announcers informed the crowd that attendance for the game was 4,302. If this is 2/9 of the capacity, find the full seating capacity for the soccer stadium.
74. At a local basketball game, announcers informed the crowd that attendance for the game was 5,394. If this is 2/7 of the capacity, find the full seating capacity for the basketball stadium.
75. The area of a triangle is 51 square inches. If the length of the base is \(8 \frac{1}{2}\) inches, find the height (altitude) of the triangle.
76. The area of a triangle is 20 square inches. If the length of the base is \(2 \frac{1}{2}\) inches, find the height (altitude) of the triangle.
77. The area of a triangle is 18 square inches. If the length of the base is \(4 \frac{1}{2}\) inches, find the height (altitude) of the triangle.
78. The area of a triangle is 44 square inches. If the length of the base is \(5 \frac{1}{2}\) inches, find the height (altitude) of the triangle.
79. At a local hockey game, announcers informed the crowd that attendance for the game was 4,536. If this is 2/11 of the capacity, find the full seating capacity for the hockey stadium.
80. At a local soccer game, announcers informed the crowd that attendance for the game was 6,970. If this is 2/7 of the capacity, find the full seating capacity for the soccer stadium.
81. Pirates . About one-third of the world’s pirate attacks in 2008 occurred off the Somali coast. If there were 111 pirate attacks off the Somali coast, estimate the number of pirate attacks worldwide in 2008.
82. Nuclear arsenal . The U.S. and Russia agreed to cut nuclear arsenals of long-range nuclear weapons by about a third, down to 1, 550. How many long-range nuclear weapons are there now? Associated Press-Times-Standard 04/04/10 Nuclear heartland anxious about missile cuts.
83. Seed vault . The Svalbard Global Seed Vault has amassed half a million seed samples, and now houses at least one-third of the world’s crop seeds. Estimate the total number of world’s crop seeds. Associated Press-Times-Standard 03/15/10 Norway doomsday seed vault hits half-million mark.
84. Freight train . The three and one-half mile long Union Pacific train is about 2 1 2 times the length of a typical freight train. How long is a typical freight train? Associated Press-Times-Standard 01/13/10 Unusally long train raises safety concerns.
13. \(− \frac{5}{2}\)
15. \(\frac{2}{5}\)
17. \(\frac{4}{11}\)
19. \(\frac{7}{15}\)
21. \(\frac{8}{9}\)
23. \(\frac{10}{13}\)
25. \(−1\)
27. \(− \frac{5}{18}\)
29. \(\frac{64}{21}\)
31. \(− \frac{5}{12}\)
33. \(− \frac{16}{21}\)
35. \(− \frac{7}{36}\)
37. \(\frac{81}{56}\)
39. \(− \frac{2}{9}\)
41. \(− \frac{29}{8}\)
43. \(− \frac{35}{72}\)
45. \(\frac{1}{8}\)
47. \(−2\)
49. \(− \frac{16}{37}\)
51. \(− \frac{41}{70}\)
53. \(\frac{49}{9}\)
55. \(\frac{8}{3}\)
57. \(− \frac{21}{20}\)
59. \(− \frac{49}{44}\)
61. \(− \frac{7}{17}\)
63. \(\frac{47}{35}\)
65. \(− \frac{14}{27}\)
67. \(\frac{52}{159}\)
69. \(− 2\)
71. \(\frac{47}{100}\)
81. There were about 333 pirate attacks worldwide.
83. 1,500,000
To get additional practice, check out the sample problems in each of the topic above. We provide full solutions with steps for all practice problems. There's no better way to find math help online than with Cymath, so also make sure you download our mobile app for and today! Learn more than what the answer is - with the math helper app, you'll learn the steps behind it too.
Even simple math problems become easier to solve when broken down into steps. From basic additions to calculus, the process of problem solving usually takes a lot of practice before answers could come easily. As problems become more complex, it becomes even more important to understand the step-by-step process by which we solve them. At Cymath, our goal is to take your understanding of math to a new level.
If you find Cymath useful, try today! It offers an ad-free experience and more detailed explanations. In short, goes into more depth than the standard version, giving students more resources to learn the step-by-step process of solving math problems.
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Fraction Word Problems (Difficult)
Here are some examples of more difficult fraction word problems. We will illustrate how block models (tape diagrams) can be used to help you to visualize the fraction word problems in terms of the information given and the data that needs to be found.
Related Pages Fraction Word Problems Singapore Math Lessons Fraction Problems Using Algebra Algebra Word Problems
Block modeling (also known as tape diagrams or bar models) are widely used in Singapore Math and the Common Core to help students visualize and understand math word problems.
Example: 2/9 of the people on a restaurant are adults. If there are 95 more children than adults, how many children are there in the restaurant?
Solution: Draw a diagram with 9 equal parts: 2 parts to represent the adults and 7 parts to represent the children.
5 units = 95 1 unit = 95 ÷ 5 = 19 7 units = 7 × 19 = 133
Answer: There are 133 children in the restaurant.
Example: Gary and Henry brought an equal amount of money for shopping. Gary spent $95 and Henry spent $350. After that Henry had 4/7 of what Gary had left. How much money did Gary have left after shopping?
350 – 95 = 255 3 units = 255 1 unit = 255 ÷ 3 = 85 7 units = 85 × 7 = 595
Answer: Gary has $595 after shopping.
Example: 1/9 of the shirts sold at Peter’s shop are striped. 5/8 of the remainder are printed. The rest of the shirts are plain colored shirts. If Peter’s shop has 81 plain colored shirts, how many more printed shirts than plain colored shirts does the shop have?
Solution: Draw a diagram with 9 parts. One part represents striped shirts. Out of the remaining 8 parts: 5 parts represent the printed shirts and 3 parts represent plain colored shirts.
3 units = 81 1 unit = 81 ÷ 3 = 27 Printed shirts have 2 parts more than plain shirts. 2 units = 27 × 2 = 54
Answer: Peter’s shop has 54 more printed colored shirts than plain shirts.
Solve a problem involving fractions of fractions and fractions of remaining parts
Example: 1/4 of my trail mix recipe is raisins and the rest is nuts. 3/5 of the nuts are peanuts and the rest are almonds. What fraction of my trail mix is almonds?
How to solve fraction word problem that involves addition, subtraction and multiplication using a tape diagram or block model
Example: Jenny’s mom says she has an hour before it’s bedtime. Jenny spends 3/5 of the hour texting a friend and 3/8 of the remaining time brushing her teeth and putting on her pajamas. She spends the rest of the time reading her book. How long did Jenny read?
How to solve a four step fraction word problem using tape diagrams?
Example: In an auditorium, 1/6 of the students are fifth graders, 1/3 are fourth graders, and 1/4 of the remaining students are second graders. If there are 96 students in the auditorium, how many second graders are there?
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Unit 1: Algebra foundations
Unit 2: solving equations & inequalities, unit 3: working with units, unit 4: linear equations & graphs, unit 5: forms of linear equations, unit 6: systems of equations, unit 7: inequalities (systems & graphs), unit 8: functions, unit 9: sequences, unit 10: absolute value & piecewise functions, unit 11: exponents & radicals, unit 12: exponential growth & decay, unit 13: quadratics: multiplying & factoring, unit 14: quadratic functions & equations, unit 15: irrational numbers, unit 16: creativity in algebra.
The 7 Best AI Tools to Help Solve Math Problems
How do you make seven even? Use these tools to solve the big math problems in life.
Quick Links
The test questions, wolframalpha, microsoft mathsolver.
While OpenAI's ChatGPT is one of the most widely known AI tools, there are numerous other platforms that students can use to improve their math skills.
I tested seven AI tools on two common math problems so you know what to expect from each platform and how to use each of them.
I used two math problems to test each tool and standardize the inputs.
Solve for b: (2 / (b - 3)) - (6 / (2b + 1)) = 4
Simplify the expression: (4 / 12) + (9 / 8) x (15 / 3) - (26 / 10)
These two problems give each AI tool a chance to show reasoning, problem-solving, accuracy, and how it can guide a learner through the process.
Thetawise provides more than simple answers; you can also opt to have the AI model tutor you by sharing a detailed step-by-step breakdown of the solution. Using the platform is fairly straightforward, given that all you need to do is navigate to the platform and key in the math problem at hand. Alternatively, you can even upload a photo of the math problem onto the platform, and the AI will analyze the image and provide you with an answer.
The AI platform gave us a step-by-step breakdown of the problem:
It resulted in the answer:
While the answer is correct, the tool also provides further options for students to generate a more detailed breakdown of the steps or ask more specific questions.
WolframAlpha is an AI tool capable of solving advanced arithmetic, calculus, and algebra equations. While WolframAlpha's free version provides you with a direct answer, the paid version of the tool generates step-by-step solutions. If you want to make the best use of WolframAlpha's capabilities, you can sign up for the Pro version, which costs $5 per month for the annual plan if you're a student.
As expected, Wolfram Alpha solved both problems, showcasing its ability to handle different problems and provide precise answers quickly.
Julius works pretty similarly to the other AI tools on this list. That said, the highlight of this platform is that it has a built-in community forum, which users can use to discuss their prompts, results, or even issues they might be facing with the platform. Its active user base helps you quickly exchange ideas and receive feedback or advice. The platform's default version uses a combination of GPT-4 and Calude-3, based on whichever model best suits the prompt you input.
We tested the platform's accuracy by submitting the same problems that we did with the other AI tools. When submitting your prompt, you have the option of typing your question or uploading an image or a Google Sheet.
Julius provided correct solutions and offered options to help users verify the solution.
One of the oldest AI platforms, Microsoft's MathSolver is a great option if you want a tool capable of providing free step-by-step solutions to calculus, algebra, and other math problems. Here's how it fared when we submitted our math problems.
Microsoft's MathSolver provided the correct answers, and you can view the steps to the solution, take a quiz, solve similar problems, and more. This can be a great way to practice and perfect your understanding of different concepts.
Symbolab allows you to practice your math skills via quizzes, track your progress, and provide solutions to mathematical problems of different types, including calculus, fractions, trigonometry, and more. You can also use the Digital Notebook feature to keep track of any math problems you solve and share them with your friends. Another highlight of this platform is that educators can use the tool to create a virtual classroom, generate assessments, and share feedback, among other things.
The platform not only displays the answer but also lets you view a breakdown of the steps involved in solving the problem. You can also share the answers and steps via email or social media or print them for reference.
Anthropic launched its Claude 3 AI models in March 2024. Anthropic stated that Claude Opus, the most advanced Claude 3 model, outperforms comparable AI tools on most benchmarks for AI systems, including basic mathematics, undergraduate-level expert knowledge, and graduate-level expert reasoning. To test the platform's accuracy and ease of use, we submitted our two math problems. Here's how the platform performed:
While Claude initially got the answer wrong, probing it and requesting further clarification led to a correct solution.
Remember that we used the free version of Claude to solve this problem; subscribing to Opus (its more advanced model) is recommended if you want to take advantage of Claude's more advanced problem-solving capabilities.
Given that Claude got the previous problem wrong, our second, more basic fraction-based problem will indicate if the AI's performance was an anomaly or part of a consistent pattern.
As you can see, Claude correctly solved this problem and provided a detailed step-by-step breakdown of how it arrived at the answer.
GPT-4 can solve problems with far greater accuracy than its predecessor, GPT-3.5. If you're using the free version of ChatGPT, you'll likely only have access to GPT 3.5 and GPT-4o . However, for $20 per month, you can subscribe to the Plus model, which gives you access to GPT-4 and allows you to input five times the number of messages per day compared to the free version. That said, let's check how it performs with math problems.
In both cases, GPT-4o provided the correct answer with a detailed breakdown of the steps. While the platform is free, unlike other models, it does not have a quiz feature or a community forum.
These AI tools offer unique features and capabilities that make them a good option for math problems. Ultimately, the best way to pick a tool is by testing different models to determine which platform best fits your preferences and learning needs.
Game Central
Inequalities, absolute value and rounding, related concepts.
DESCRIPTIVE FRACTION PROBLEM SOLVING / MATH TUTORIAL TAGALOG
COMMENTS
Learn How to Solve Fraction Word Problems with Examples and Interactive
Analysis: To solve this problem, we will add two mixed numbers, with the fractional parts having unlike denominators. Solution: Answer: The warehouse has 21 and one-half meters of tape in all. Example 8: An electrician has three and seven-sixteenths cm of wire. He needs only two and five-eighths cm of wire for a job.
Fraction Word Problems
To solve a fraction word problem, you must understand the context of the word problem, what the unknown information is, and what operation is needed to solve it. Fraction word problems may require addition, subtraction, multiplication, or division of fractions. ... Finally, you need to choose the answer that correctly answers the question ...
Fractions Questions and Problems with Solutions
Factor Fractions, examples with questions including solutions. Adding Fractions. Add fractions with same denominator or different denominator. Several examples with detailed solutions and exercises. Multiply Fractions. Multiply a fraction by another fraction or a number by a fraction. Examples with solutions and exercises.
Fraction Worksheets
Math explained in easy language, plus puzzles, games, quizzes, videos and worksheets. For K-12 kids, teachers and parents. Fraction Worksheets ... Fractions - Subtraction. Worksheet. Example. Fractions (Same Denominator) 15 − 25. Unit Fractions. 13 − 19. Easy Proper Fractions. 38 − 27. Harder Proper Fractions. 712 − 1525.
Fraction worksheets 1
You can choose like or unlike fractions, make missing number problems, restrict the problems to use proper fractions or to not to simplify the answers. Further, you can control the values of numerator, denominator, and the whole-number part to make the fractions or mixed numbers as easy or difficult as you like.
Fractions Worksheets
Cut out the fraction circles and segments of one copy and leave the other copy intact. To add 1/3 + 1/2, for example, place a 1/3 segment and a 1/2 segment into a circle and hold it over various fractions on the intact copy to see what 1/2 + 1/3 is equivalent to. 5/6 or 10/12 should work. Small Fraction Circles.
Solution: Step 1: Assign variables : Let x = number. Step 2: Solve the equation. Isolate variable x. Answer: The number is 21. Example: The numerator of a fraction is 3 less than the denominator. When both the numerator and denominator are increased by 4, the fraction is increased by fraction.
Fraction Word Problems Worksheets
Presented here are the fraction pdf worksheets based on real-life scenarios. Read the basic fraction word problems, write the correct fraction and reduce your answer to the simplest form. Download the set. Represent and Simplify the Fractions: Type 2. Before representing in fraction, children should perform addition or subtraction to solve ...
Word Problems with Fractions
The solution to this problem is an irreducible fraction (a fraction which cannot be simplified). Therefore, there is nothing left to do. Word problems with fractions: involving two fractions. In these problems, we should remember how to carry out operations with fractions. Carefully read the following problem and the steps we have taken to ...
Fractions
Identify your areas for growth in these lessons: Dividing fractions by fractions. Dividing fractions word problems. Start quiz. Unit test. Test your understanding of Fractions with these NaN questions. Start test. In this topic, we will explore fractions conceptually and add, subtract, multiply, and divide fractions.
Fraction Word Problems: Examples
Fraction Word Problems, The first example is a one-step word problem, The second example shows how blocks can be used to help illustrate the problem, The third example is a two-step word problem, bar modeling method in Singapore Math, Word Problem on Subtracting Fractions From Whole Numbers, with video lessons, examples and step-by-step solutions.
Fraction Word Problems (video lessons, examples and solutions)
Fraction Word Problems - Examples and Worked Solutions of Word Problems, to solve a word problem that involves adding fractions with unlike denominators, Solve a problem involving fractions of fractions and fractions of remaining parts, using bar models or tape diagrams, with video lessons, examples and step-by-step solutions.
Fractions Questions
While dividing one fraction by another fraction, we multiply the first fraction by the reciprocal of the other. 5. Multiply the following fractions. (i) (⅖) × 5 ¼. (ii) 2 ⅗ × 3. Solution: (i) (⅖) × 5 ¼. Here, 5 ¼ is a mixed fraction. Let us convert this mixed fraction into an improper fraction.
Fractions worksheets for grades 1-6
Grade 4: Fraction worksheets. Fractions to decimals. Grade 5: Fraction addition and subtraction. Fraction multiplication and division. Converting fractions, equivalent fractions, simplifying fractions. Fraction to / from decimals. Grade 6:
Fractions
Quiz. 124 − 79. 124 ÷ 89. 124 + 89 × 315 − 1026. Learn about fractions using our free math solver with step-by-step solutions.
Step-by-Step Math Problem Solver
QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students. The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and ...
It is perfectly acceptable to leave your answer as an improper fraction. If you desire, or if you are instructed to do so, you can change your answer to a mixed fraction (7 divided by 6 is 1 with a remainder of 1). That is \(x = 1 \frac{1}{6}\). Checking the Solution . Substitute 7/6 for x in the original equation and simplify.
Practice Math Problems with Answers
About Our Practice Problems. To get additional practice, check out the sample problems in each of the topic above. We provide full solutions with steps for all practice problems. There's no better way to find math help online than with Cymath, so also make sure you download our mobile app for iOS and Android today!
Mathway
Free math problem solver answers your algebra homework questions with step-by-step explanations.
Fraction Word Problems
How to solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, by using visual fraction models or equations to represent the problem. Examples and step by step solutions. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers, Common Core Grade 5, 5.nf.2
Microsoft Math Solver
Get math help in your language. Works in Spanish, Hindi, German, and more. Online math solver with free step by step solutions to algebra, calculus, and other math problems. Get help on the web or with our math app.
Math
Learn third grade math—fractions, area, arithmetic, and so much more. This course is aligned with Common Core standards. ... fractions; patterns and problem solving; area and perimeter; telling time; and data. Get ready for addition and subtraction: Get ready for 3rd grade. Get ready for multiplication and division: Get ready for 3rd grade.
Solving equations & inequalities
Unit test. Level up on all the skills in this unit and collect up to 1,100 Mastery points! Start Unit test. There are lots of strategies we can use to solve equations. Let's explore some different ways to solve equations and inequalities. We'll also see what it takes for an equation to have no solution, or infinite solutions.
33 Math Puzzles (with Answers) to Test Your Smarts
Answer: 54. The percentages consist of all numbers from 0 to 9, with the larger number first. The percentages consist of all numbers from 0 to 9, with the larger number first. Wind chill
Fraction Word Problems (Difficult)
Solution: Draw a diagram with 9 equal parts: 2 parts to represent the adults and 7 parts to represent the children. 5 units = 95. 1 unit = 95 ÷ 5 = 19. 7 units = 7 × 19 = 133. Answer: There are 133 children in the restaurant. Example: Gary and Henry brought an equal amount of money for shopping.
Algebra 1
The Algebra 1 course, often taught in the 9th grade, covers Linear equations, inequalities, functions, and graphs; Systems of equations and inequalities; Extension of the concept of a function; Exponential models; and Quadratic equations, functions, and graphs. Khan Academy's Algebra 1 course is built to deliver a comprehensive, illuminating, engaging, and Common Core aligned experience!
The 7 Best AI Tools to Help Solve Math Problems
Julius. Microsoft MathSolver. Symbolab. Claude. ChatGPT-4o. While OpenAI's ChatGPT is one of the most widely known AI tools, there are numerous other platforms that students can use to improve their math skills. I tested seven AI tools on two common math problems so you know what to expect from each platform and how to use each of them.
Solve
Integration. ∫ 01 xe−x2dx. Limits. x→−3lim x2 + 2x − 3x2 − 9. Online math solver with free step by step solutions to algebra, calculus, and other math problems. Get help on the web or with our math app.
Algebra Calculator
Polynomial. In mathematics, a polynomial is a mathematical expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An example of a polynomial of a single indeterminate x is x² − 4x + 7. An example with three indeterminates ...
![[FREE] Fraction Operations Worksheet (Grade 4 to 6)](https://thirdspacelearning.com/wp-content/uploads/2023/07/Fraction-operations-check-for-understandin-quiz-listing-image-.png "problem solving in fraction with solution and answer")
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Analysis: To solve this problem, we will add two mixed numbers, with the fractional parts having unlike denominators. Solution: Answer: The warehouse has 21 and one-half meters of tape in all. Example 8: An electrician has three and seven-sixteenths cm of wire. He needs only two and five-eighths cm of wire for a job.
To solve a fraction word problem, you must understand the context of the word problem, what the unknown information is, and what operation is needed to solve it. Fraction word problems may require addition, subtraction, multiplication, or division of fractions. ... Finally, you need to choose the answer that correctly answers the question ...
Factor Fractions, examples with questions including solutions. Adding Fractions. Add fractions with same denominator or different denominator. Several examples with detailed solutions and exercises. Multiply Fractions. Multiply a fraction by another fraction or a number by a fraction. Examples with solutions and exercises.
Math explained in easy language, plus puzzles, games, quizzes, videos and worksheets. For K-12 kids, teachers and parents. Fraction Worksheets ... Fractions - Subtraction. Worksheet. Example. Fractions (Same Denominator) 15 − 25. Unit Fractions. 13 − 19. Easy Proper Fractions. 38 − 27. Harder Proper Fractions. 712 − 1525.
You can choose like or unlike fractions, make missing number problems, restrict the problems to use proper fractions or to not to simplify the answers. Further, you can control the values of numerator, denominator, and the whole-number part to make the fractions or mixed numbers as easy or difficult as you like.
Cut out the fraction circles and segments of one copy and leave the other copy intact. To add 1/3 + 1/2, for example, place a 1/3 segment and a 1/2 segment into a circle and hold it over various fractions on the intact copy to see what 1/2 + 1/3 is equivalent to. 5/6 or 10/12 should work. Small Fraction Circles.
Solution: Step 1: Assign variables : Let x = number. Step 2: Solve the equation. Isolate variable x. Answer: The number is 21. Example: The numerator of a fraction is 3 less than the denominator. When both the numerator and denominator are increased by 4, the fraction is increased by fraction.
Presented here are the fraction pdf worksheets based on real-life scenarios. Read the basic fraction word problems, write the correct fraction and reduce your answer to the simplest form. Download the set. Represent and Simplify the Fractions: Type 2. Before representing in fraction, children should perform addition or subtraction to solve ...
The solution to this problem is an irreducible fraction (a fraction which cannot be simplified). Therefore, there is nothing left to do. Word problems with fractions: involving two fractions. In these problems, we should remember how to carry out operations with fractions. Carefully read the following problem and the steps we have taken to ...
Identify your areas for growth in these lessons: Dividing fractions by fractions. Dividing fractions word problems. Start quiz. Unit test. Test your understanding of Fractions with these NaN questions. Start test. In this topic, we will explore fractions conceptually and add, subtract, multiply, and divide fractions.
Fraction Word Problems, The first example is a one-step word problem, The second example shows how blocks can be used to help illustrate the problem, The third example is a two-step word problem, bar modeling method in Singapore Math, Word Problem on Subtracting Fractions From Whole Numbers, with video lessons, examples and step-by-step solutions.
Fraction Word Problems - Examples and Worked Solutions of Word Problems, to solve a word problem that involves adding fractions with unlike denominators, Solve a problem involving fractions of fractions and fractions of remaining parts, using bar models or tape diagrams, with video lessons, examples and step-by-step solutions.
While dividing one fraction by another fraction, we multiply the first fraction by the reciprocal of the other. 5. Multiply the following fractions. (i) (⅖) × 5 ¼. (ii) 2 ⅗ × 3. Solution: (i) (⅖) × 5 ¼. Here, 5 ¼ is a mixed fraction. Let us convert this mixed fraction into an improper fraction.
Grade 4: Fraction worksheets. Fractions to decimals. Grade 5: Fraction addition and subtraction. Fraction multiplication and division. Converting fractions, equivalent fractions, simplifying fractions. Fraction to / from decimals. Grade 6:
Quiz. 124 − 79. 124 ÷ 89. 124 + 89 × 315 − 1026. Learn about fractions using our free math solver with step-by-step solutions.
QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students. The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and ...
Free Fractions calculator - Add, Subtract, Reduce, Divide and Multiply fractions step-by-step
It is perfectly acceptable to leave your answer as an improper fraction. If you desire, or if you are instructed to do so, you can change your answer to a mixed fraction (7 divided by 6 is 1 with a remainder of 1). That is \(x = 1 \frac{1}{6}\). Checking the Solution . Substitute 7/6 for x in the original equation and simplify.
About Our Practice Problems. To get additional practice, check out the sample problems in each of the topic above. We provide full solutions with steps for all practice problems. There's no better way to find math help online than with Cymath, so also make sure you download our mobile app for iOS and Android today!
Free math problem solver answers your algebra homework questions with step-by-step explanations.
How to solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, by using visual fraction models or equations to represent the problem. Examples and step by step solutions. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers, Common Core Grade 5, 5.nf.2
Get math help in your language. Works in Spanish, Hindi, German, and more. Online math solver with free step by step solutions to algebra, calculus, and other math problems. Get help on the web or with our math app.
Learn third grade math—fractions, area, arithmetic, and so much more. This course is aligned with Common Core standards. ... fractions; patterns and problem solving; area and perimeter; telling time; and data. Get ready for addition and subtraction: Get ready for 3rd grade. Get ready for multiplication and division: Get ready for 3rd grade.
Unit test. Level up on all the skills in this unit and collect up to 1,100 Mastery points! Start Unit test. There are lots of strategies we can use to solve equations. Let's explore some different ways to solve equations and inequalities. We'll also see what it takes for an equation to have no solution, or infinite solutions.
Answer: 54. The percentages consist of all numbers from 0 to 9, with the larger number first. The percentages consist of all numbers from 0 to 9, with the larger number first. Wind chill
Solution: Draw a diagram with 9 equal parts: 2 parts to represent the adults and 7 parts to represent the children. 5 units = 95. 1 unit = 95 ÷ 5 = 19. 7 units = 7 × 19 = 133. Answer: There are 133 children in the restaurant. Example: Gary and Henry brought an equal amount of money for shopping.
The Algebra 1 course, often taught in the 9th grade, covers Linear equations, inequalities, functions, and graphs; Systems of equations and inequalities; Extension of the concept of a function; Exponential models; and Quadratic equations, functions, and graphs. Khan Academy's Algebra 1 course is built to deliver a comprehensive, illuminating, engaging, and Common Core aligned experience!
Julius. Microsoft MathSolver. Symbolab. Claude. ChatGPT-4o. While OpenAI's ChatGPT is one of the most widely known AI tools, there are numerous other platforms that students can use to improve their math skills. I tested seven AI tools on two common math problems so you know what to expect from each platform and how to use each of them.
Integration. ∫ 01 xe−x2dx. Limits. x→−3lim x2 + 2x − 3x2 − 9. Online math solver with free step by step solutions to algebra, calculus, and other math problems. Get help on the web or with our math app.
Polynomial. In mathematics, a polynomial is a mathematical expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An example of a polynomial of a single indeterminate x is x² − 4x + 7. An example with three indeterminates ...