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Use this series of fractions to find the value of x.
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A group of monkeys eat various fractions of a harvest of peanuts. What fraction is left behind?
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2011 Digits
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Multiply a sequence of n terms together. Can you work out when this product is equal to an integer?
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Yesterday, at Ulaanbaatar market, a white elephant cost the same amount as 99 wild geese. How many wild geese cost the same amount as a white elephant today?
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A property developer sells two houses, and makes a 20% loss on one and a 20% profit on the other. Overall, did he make a profit or a loss?
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How to Solve Percent Problems? (+FREE Worksheet!)
Learn how to calculate and solve percent problems using the percent formula.
Related Topics
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Step by step guide to solve percent problems
- In each percent problem, we are looking for the base, or part or the percent.
- Use the following equations to find each missing section. Base \(= \color{black}{Part} \ ÷ \ \color{blue}{Percent}\) \(\color{ black }{Part} = \color{blue}{Percent} \ ×\) Base \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base
Percent Problems – Example 1:
\(2.5\) is what percent of \(20\)?
In this problem, we are looking for the percent. Use the following equation: \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base \(→\) Percent \(=2.5 \ ÷ \ 20=0.125=12.5\%\)
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Percent problems – example 2:.
\(40\) is \(10\%\) of what number?
Use the following formula: Base \(= \color{ black }{Part} \ ÷ \ \color{blue}{Percent}\) \(→\) Base \(=40 \ ÷ \ 0.10=400\) \(40\) is \(10\%\) of \(400\).
Percent Problems – Example 3:
\(1.2\) is what percent of \(24\)?
In this problem, we are looking for the percent. Use the following equation: \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base \(→\) Percent \(=1.2÷24=0.05=5\%\)
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Percent problems – example 4:.
\(20\) is \(5\%\) of what number?
Use the following formula: Base \(= \color{black}{Part} \ ÷ \ \color{blue}{Percent}\) \(→\) Base \(=20÷0.05=400\) \( 20\) is \(5\%\) of \(400\).
Exercises for Calculating Percent Problems
Solve each problem..
- \(51\) is \(340\%\) of what?
- \(93\%\) of what number is \(97\)?
- \(27\%\) of \(142\) is what number?
- What percent of \(125\) is \(29.3\)?
- \(60\) is what percent of \(126\)?
- \(67\) is \(67\%\) of what?
Download Percent Problems Worksheet
- \(\color{blue}{15}\)
- \(\color{blue}{104.3}\)
- \(\color{blue}{38.34}\)
- \(\color{blue}{23.44\%}\)
- \(\color{blue}{47.6\%}\)
- \(\color{blue}{100}\)
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by: Effortless Math Team about 4 years ago (category: Articles , Free Math Worksheets )
Effortless Math Team
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7.3: Solving Basic Percent Problems
- Last updated
- Save as PDF
- Page ID 22503
- David Arnold
- College of the Redwoods
There are three basic types of percent problems:
- Find a given percent of a given number. For example, find 25% of 640.
- Find a percent given two numbers. For example, 15 is what percent of 50?
- Find a number that is a given percent of another number. For example, 10% of what number is 12?
Let’s begin with the first of these types.
Find a Given Percent of a Given Number
Let’s begin with our first example.
What number is 25% of 640?
Let x represent the unknown number. Translate the words into an equation.
\[ \begin{array}{c c c c c} \colorbox{cyan}{What number} & \text{ is } & \colorbox{cyan}{25%} & \text{ of } & \colorbox{cyan}{640} \\ x & = & 25 \% & \cdot & 640 \end{array}\nonumber \]
Now, solve the equation for x.
\[ \begin{aligned} x = 25 \% \cdot 640 ~ & \textcolor{red}{ \text{ Original equation.}} \\ x = 0.25 \cdot 640 ~ & \textcolor{red}{ \text{ Change 25% to a decimal: 25% = 0.25.}} \\ x = 160 ~ & \textcolor{red}{ \text{ Multiply: 0.25 \cdot 640 = 160.}} \end{aligned}\nonumber \]
Thus, 25% of 640 is 160.
Alternate Solution
We could also change 25% to a fraction.
\[ \begin{aligned} x = 25 \% \cdot 640 ~ & \textcolor{red}{ \text{ Original equation.}} \\ x = \frac{1}{4} \cdot 640 ~ & \textcolor{red}{ \text{ Change 25% to a fraction: 25% = 25/100 = 1/4.}} \\ x = \frac{640}{4} ~ & \textcolor{red}{ \text{ Multiply numerators and denominators.}} \\ x = 160 ~ & \textcolor{red}{ \text{ Divide: 640/4 = 160.}} \end{aligned}\nonumber \]
Same answer.
What number is 36% of 120?
What is number \(8 \frac{1}{3} \%\) of 120?
\[ \begin{array}{c c c c c} \colorbox{cyan}{What number} & \text{ is } & \colorbox{cyan}{8 (1/3)%} & \text{ of } & \colorbox{cyan}{120} \\ x & = & 8 \frac{1}{3} \% & \cdot & 120 \end{array}\nonumber \]
Now, solve the equation for x . Because
\[8 \frac{1}{3} \%= 8.3 \% = 0.08 \overline{3},\nonumber \]
working with decimals requires that we work with a repeating decimal. To do so, we would have to truncate the decimal representation of the percent at some place and satisfy ourselves with an approximate answer. Instead, let’s change the percent to a fraction and seek an exact answer.
\[ \begin{aligned} 8 \frac{1}{3} \% = \frac{8 \frac{1}{3}}{100} ~ & \textcolor{red}{ \text{ Percent: Parts per hundred.}} \\ = \frac{ \frac{25}{3}}{100} ~ & \textcolor{red}{ \text{ Mixed to improper fraction.}} \\ = \frac{25}{3} \cdot \frac{1}{100} ~& \textcolor{red}{ \text{ Invert and multiply.}} \\ = \frac{25}{300} ~ & \textcolor{red}{ \text{ Multiply numerators and denominators.}} \\ = \frac{1}{12} ~ & \textcolor{red}{ \text{ Reduce: Divide numerator and denominator by 25.}} \end{aligned}\nonumber \]
Now we can solve our equation for x .
\[ \begin{aligned} = 8 \frac{1}{3} \% \cdot 120 ~ & \textcolor{red}{ \text{ Original equation.}} \\ x = \frac{1}{12} \cdot 120 ~ & \textcolor{red}{8 \frac{1}{3} \% = 1/12.} \\ x = \frac{120}{12} ~ & \textcolor{red}{ \text{ Multiply numerators and denominators.}} \\ x = 10 ~ & \textcolor{red}{ \text{ Divide: 120/12 = 10.}} \end{aligned}\nonumber \]
Thus, \(8 \frac{1}{3} \%\) of 120 is 10.
What number is \(4 \frac{1}{6} \%\) of 1,200?
What number is \(105 \frac{1}{4} \%\) of 18.2?
\[ \begin{array}{c c c c c} \colorbox{cyan}{What number} & \text{ is } & \colorbox{cyan}{105 (1/4) %} & \text{ of } & 18.2 \\ x & = & 105 \frac{1}{4} \% & \cdot & 18.2 \end{array}\nonumber \]
In this case, the fraction terminates as 1/4=0.25, so
\[105 \frac{1}{4} \% = 105.25% = 1.0525.\nonumber \]
\[ \begin{aligned} x = 105 \frac{1}{4} \% \cdot 18.2 ~ & \textcolor{red}{ \text{ Original equation.}} \\ x = 1.0525 \cdot 18.2 ~ & \textcolor{red}{5 \frac{1}{4} \% = 1.0525.} \\ x = 19.1555 ~ & \textcolor{red}{ \text{ Multiply.}} \end{aligned}\nonumber \]
Thus, \(105 \frac{1}{4} \%\) of 18.2 is 19.1555.
What number is \(105 \frac{3}{4} \%\) of 222?
Find a Percent Given Two Numbers
Now we’ll address our second item on the list at the beginning of the section.
15 is what percent of 50?
Let x represent the unknown percent. Translate the words into an equation.
\[ \begin{array}{c c c c} \colorbox{cyan}{15} & \text{ is } & \colorbox{cyan}{what percent} & \text{ of } & \colorbox{cyan}{50} \\ 15 & = & x & \cdot & 50 \end{array}\nonumber \]
The commutative property of multiplication allows us to change the order of multiplication on the right-hand side of this equation.
\[15 = 50x.\nonumber \]
\[ \begin{aligned} 15 = 50x ~ & \textcolor{red}{ \text{ Original equation.}} \\ \frac{15}{50} = \frac{50x}{50} ~ & \textcolor{red}{ \text{ Divide both sides by 50.}} \\ \frac{15}{50} = x ~ & \textcolor{red}{ \text{ Simplify right-hand side.}} \\ x = 0.30 ~ & \textcolor{red}{ \text{ Divide: 15/50 = 0.30.}} \end{aligned}\nonumber \]
But we must express our answer as a percent. To do this, move the decimal two places to the right and append a percent symbol.
Thus, 15 is 30% of 50.
Alternative Conversion
At the third step of the equation solution, we had
\[x = \frac{15}{50}.\nonumber \]
We can convert this to an equivalent fraction with a denominator of 100.
\[x = \frac{15 \cdot 2}{50 \cdot 2} = \frac{30}{100}\nonumber \]
Thus, 15/50 = 30/100 = 30%.
14 is what percent of 25?
10 is what percent of 80?
\[ \begin{array}{c c c c c} \colorbox{cyan}{10} & \text{ is } & \colorbox{cyan}{what percent} & \text{ of } & \colorbox{cyan}{80} \\ 10 & = & x & \cdot & 80 \end{array}\nonumber \]
The commutative property of multiplication allows us to write the right-hand side as
\[10 = 80x.\nonumber \]
\[ \begin{aligned} 10 = 80x ~ & \textcolor{red}{ \text{ Original equation.}} \\ \frac{10}{80} = \frac{80x}{80} ~ & \textcolor{red}{ \text{ Divide both sides by 80.}} \\ \frac{1}{8} = x ~ & \textcolor{red}{ \text{ Reduce: } 10/80 = 1/8.} \\ 0.125 = x ~ & \textcolor{red}{ \text{ Divide: } 1/8 = 0.125.} \end{aligned}\nonumber \]
Thus, 10 is 12.5% of 80.
\[x = \frac{1}{8} .\nonumber \]
We can convert this to an equivalent fraction with a denominator of 100 by setting up the proportion
\[\frac{1}{8} = \frac{n}{100}\nonumber \]
Cross multiply and solve for n .
\[ \begin{aligned} 8n = 100 ~ & \textcolor{red}{ \text{ Cross multiply.}} \\ \frac{8n}{8} = \frac{100}{8} ~ & \textcolor{red}{ \text{ Divide both sides by 8.}} \\ n = \frac{25}{8} ~ & \textcolor{red}{ \text{ Reduce: Divide numerator and denominator by 4.}} \\ n = 12 \frac{1}{2} ~ & \textcolor{red}{ \text{ Change 25/2 to mixed fraction.}} \end{aligned}\nonumber \]
\[ \frac{1}{8} = \frac{12 \frac{1}{2}}{100} = 12 \frac{1}{2} \%.\nonumber \]
10 is what percent of 200?
Find a Number that is a Given Percent of Another Number
Let’s address the third item on the list at the beginning of the section.
10% of what number is 12?
\[ \begin{array}{c c c c c} \colorbox{cyan}{10%} & \text{ of } & \colorbox{cyan}{what number} & \text{ is } & \colorbox{cyan}{12} \\ 10 \% & \cdot & x & = & 12 \end{array}\nonumber \]
Change 10% to a fraction: 10% = 10/100 = 1/10.
\[ \frac{1}{10} x = 12\nonumber \]
\[ \begin{aligned} 10 \left( \frac{1}{10} x \right) = 10(12) ~ & \textcolor{red}{ \text{ Multiply both sides by 10.}} \\ x = 120 ~ & \textcolor{red}{ \text{ Simplify.}} \end{aligned}\nonumber \]
Thus, 10% of 120 is 12.
Alternative Solution
We can also change 10% to a decimal: 10% = 0.10. Then our equation becomes
\[0.10x = 12\nonumber \]
Now we can divide both sides of the equation by 0.10.
\[ \begin{aligned} \frac{0.10x}{0.10} = \frac{12}{0.10} ~ & \textcolor{red}{ \text{ Divide both sides by 0.10.}} \\ x = 120 ~ & \textcolor{red}{ \text{ Divide: 12/0.10 = 120.}} \end{aligned}\nonumber \]
20% of what number is 45?
\(11 \frac{1}{9} \%\) of what number is 20?
\[ \begin{array}{c c c c c} \colorbox{cyan}{11 (1/9) %} & \text{ of } & \colorbox{cyan}{what number} & \text{ is } \colorbox{cyan}{20} \\ 11 \frac{1}{9} \% & \cdot & x & = & 20 \end{array}\nonumber \]
Change \(11 \frac{1}{9} \%\) to a fraction.
\[ \begin{aligned} 11 \frac{1}{9} \% ~ & \textcolor{red}{ \text{ Percent: Parts per hundred.}} \\ = \frac{ \frac{100}{9}}{100} ~ & \textcolor{red}{ \text{ Mixed to improper: } 11 \frac{1}{9} = 100/9.} \\ = \frac{100}{9} \cdot \frac{1}{100} ~ & \textcolor{red}{ \text{ Invert and multiply.}} \\ = \frac{ \cancel{100}}{9} \cdot \frac{1}{ \cancel{100}} ~ & \textcolor{red}{ \text{ Cancel.}} \\ = \frac{1}{9} ~ & \textcolor{red}{ \text{ Simplify.}} \end{aligned}\nonumber \]
Replace \(11 \frac{1}{9} \%\) with 1/9 in the equation and solve for x .
\[ \begin{aligned} \frac{1}{9} x = 20 ~ & ~ \textcolor{red}{11 \frac{1}{9} \% = 1/9/} \\ 9 \left( \frac{1}{9} x \right) = 9(20) ~ & \textcolor{red}{ \text{ Multiply both sides by 9.}} \\ x = 180 \end{aligned}\nonumber \]
Thus, \(11 \frac{1}{9} \%\) of 180 is 20.
\(12 \frac{2}{3} \%\) of what number is 760?
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52. What number is \(79 \frac{1}{6} \%\) of 48?
53. \(59 \frac{1}{2} \%\) of what number is 2.38?
54. \(140 \frac{1}{5} \%\) of what number is 35.05?
55. \(78 \frac{1}{2} \%\) of what number is 7.85?
56. \(73 \frac{1}{2} \%\) of what number is 4.41?
57. What number is \(56 \frac{2}{3} \%\) of 51?
58. What number is \(64 \frac{1}{2} \%\) of 4?
59. What number is \(87 \frac{1}{2} \%\) of 70?
60. What number is \(146 \frac{1}{4} \%\) of 4?
61. It was reported that 80% of the retail price of milk was for packaging and distribution. The remaining 20% was paid to the dairy farmer. If a gallon of milk cost $3.80, how much of the retail price did the farmer receive?
62. At $1.689 per gallon of gas the cost is distributed as follows:
\[ \begin{aligned} \text{Crude oil supplies } & ~ $0.95 \\ \text{Oil Companies } & ~ $0.23 \\ \text{State and City taxes } & ~ $0.23 \\ \text{Federal tax } & ~ $0.19 \\ \text{Service Station } & ~ $0.10 \end{aligned}\nonumber \]
Data is from Money, March 2009 p. 22, based on U. S. averages in December 2008. Answer the following questions rounded to the nearest whole percent.
a) What % of the cost is paid for crude oil supplies?
b) What % of the cost is paid to the service station?
Fractions, Decimals and Percentages Practice Questions
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Unit 4: Percentages
Intro to percents.
- The meaning of percent (Opens a modal)
- Meaning of 109% (Opens a modal)
- Percents from fraction models (Opens a modal)
- Intro to percents Get 5 of 7 questions to level up!
- Percents from fraction models Get 3 of 4 questions to level up!
Visualize percents
- Finding percentages with a double number line (Opens a modal)
- Finding the whole with a tape diagram (Opens a modal)
- Find percents visually Get 5 of 7 questions to level up!
Equivalent representations of percent problems
- Fraction, decimal, and percent from visual model (Opens a modal)
- Converting percents to decimals & fractions example (Opens a modal)
- Percent of a whole number (Opens a modal)
- Ways to rewrite a percentage (Opens a modal)
- Converting between percents, fractions, & decimals (Opens a modal)
- Finding common percentages (Opens a modal)
- Converting percents and fractions review (Opens a modal)
- Converting decimals and percents review (Opens a modal)
- Equivalent representations of percent problems Get 3 of 4 questions to level up!
- Benchmark percents Get 5 of 7 questions to level up!
Percent problems
- Finding a percent (Opens a modal)
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Percent word problems
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Percent Maths Problems
Percentages Worksheets
Welcome to the percentages math worksheet page where we are 100% committed to providing excellent math worksheets. This page includes Percentages worksheets including calculating percentages of a number, percentage rates, and original amounts and percentage increase and decrease worksheets.
As you probably know, percentages are a special kind of decimal. Most calculations involving percentages involve using the percentage in its decimal form. This is achieved by dividing the percentage amount by 100. There are many worksheets on percentages below. In the first few sections, there are worksheets involving the three main types of percentage problems: calculating the percentage value of a number, calculating the percentage rate of one number compared to another number, and calculating the original amount given the percentage value and the percentage rate.
Most Popular Percentages Worksheets this Week
Percentage Calculations
Calculating the percentage value of a number involves a little bit of multiplication. One should be familiar with decimal multiplication and decimal place value before working with percentage values. The percentage value needs to be converted to a decimal by dividing by 100. 18%, for example is 18 ÷ 100 = 0.18. When a question asks for a percentage value of a number, it is asking you to multiply the two numbers together.
Example question: What is 18% of 2800? Answer: Convert 18% to a decimal and multiply by 2800. 2800 × 0.18 = 504. 504 is 18% of 2800.
- Calculating the Percentage Value (Whole Number Results) Calculating the Percentage Value (Whole Number Results) (Percents from 1% to 99%) Calculating the Percentage Value (Whole Number Results) (Select percents) Calculating the Percentage Value (Whole Number Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Whole Number Results) (Percents that are multiples of 25%)
- Calculating the Percentage Value (Decimal Number Results) Calculating the Percentage Value (Decimal Number Results) (Percents from 1% to 99%) Calculating the Percentage Value (Decimal Number Results) (Select percents) Calculating the Percentage Value (Decimal Number Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Decimal Number Results) (Percents that are multiples of 25%)
- Calculating the Percentage Value (Whole Dollar Results) Calculating the Percentage Value (Whole Dollar Results) (Percents from 1% to 99%) Calculating the Percentage Value (Whole Dollar Results) (Select percents) Calculating the Percentage Value (Whole Dollar Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Whole Dollar Results) (Percents that are multiples of 25%)
- Calculating the Percentage Value (Decimal Dollar Results) Calculating the Percentage Value (Decimal Dollar Results) (Percents from 1% to 99%) Calculating the Percentage Value (Decimal Dollar Results) (Select percents) Calculating the Percentage Value (Decimal Dollar Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Decimal Dollar Results) (Percents that are multiples of 25%)
Calculating what percentage one number is of another number is the second common type of percentage calculation. In this case, division is required followed by converting the decimal to a percentage. If the first number is 100% of the value, the second number will also be 100% if the two numbers are equal; however, this isn't usually the case. If the second number is less than the first number, the second number is less than 100%. If the second number is greater than the first number, the second number is greater than 100%. A simple example is: What percentage of 10 is 6? Because 6 is less than 10, it must also be less than 100% of 10. To calculate, divide 6 by 10 to get 0.6; then convert 0.6 to a percentage by multiplying by 100. 0.6 × 100 = 60%. Therefore, 6 is 60% of 10.
Example question: What percentage of 3700 is 2479? First, recognize that 2479 is less than 3700, so the percentage value must also be less than 100%. Divide 2479 by 3700 and multiply by 100. 2479 ÷ 3700 × 100 = 67%.
- Calculating the Percentage a Whole Number is of Another Whole Number Calculating the Percentage a Whole Number is of Another Whole Number (Percents from 1% to 99%) Calculating the Percentage a Whole Number is of Another Whole Number (Select percents) Calculating the Percentage a Whole Number is of Another Whole Number (Percents that are multiples of 5%) Calculating the Percentage a Whole Number is of Another Whole Number (Percents that are multiples of 25%)
- Calculating the Percentage a Decimal Number is of a Whole Number Calculating the Percentage a Decimal Number is of a Whole Number (Percents from 1% to 99%) Calculating the Percentage a Decimal Number is of a Whole Number (Select percents) Calculating the Percentage a Decimal Number is of a Whole Number (Percents that are multiples of 5%) Calculating the Percentage a Decimal Number is of a Whole Number (Percents that are multiples of 25%)
- Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Percents from 1% to 99%) Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Select percents) Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Percents that are multiples of 5%) Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Percents that are multiples of 25%)
- Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Percents from 1% to 99%) Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Select percents) Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Percents that are multiples of 5%) Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Percents that are multiples of 25%)
The third type of percentage calculation involves calculating the original amount from the percentage value and the percentage. The process involved here is the reverse of calculating the percentage value of a number. To get 10% of 100, for example, multiply 100 × 0.10 = 10. To reverse this process, divide 10 by 0.10 to get 100. 10 ÷ 0.10 = 100.
Example question: 4066 is 95% of what original amount? To calculate 4066 in the first place, a number was multiplied by 0.95 to get 4066. To reverse this process, divide to get the original number. In this case, 4066 ÷ 0.95 = 4280.
- Calculating the Original Amount from a Whole Number Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Whole Numbers ) Calculating the Original Amount (Select percents) ( Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 5%) ( Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 25%) ( Whole Numbers )
- Calculating the Original Amount from a Decimal Number Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Decimals ) Calculating the Original Amount (Select percents) ( Decimals ) Calculating the Original Amount (Percents that are multiples of 5%) ( Decimals ) Calculating the Original Amount (Percents that are multiples of 25%) ( Decimals )
- Calculating the Original Amount from a Whole Dollar Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Dollar Amounts and Whole Numbers ) Calculating the Original Amount (Select percents) ( Dollar Amounts and Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 5%) ( Dollar Amounts and Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 25%) ( Dollar Amounts and Whole Numbers )
- Calculating the Original Amount from a Decimal Dollar Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Dollar Amounts and Decimals ) Calculating the Original Amount (Select percents) ( Dollar Amounts and Decimals ) Calculating the Original Amount (Percents that are multiples of 5%) ( Dollar Amounts and Decimals ) Calculating the Original Amount (Percents that are multiples of 25%) ( Dollar Amounts and Decimals )
- Mixed Percentage Calculations with Whole Number Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Whole Numbers ) Mixed Percentage Calculations (Select percents) ( Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Whole Numbers )
- Mixed Percentage Calculations with Decimal Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Decimals ) Mixed Percentage Calculations (Select percents) ( Decimals ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Decimals ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Decimals )
- Mixed Percentage Calculations with Whole Dollar Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Dollar Amounts and Whole Numbers ) Mixed Percentage Calculations (Select percents) ( Dollar Amounts and Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Dollar Amounts and Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Dollar Amounts and Whole Numbers )
- Mixed Percentage Calculations with Decimal Dollar Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Dollar Amounts and Decimals ) Mixed Percentage Calculations (Select percents) ( Dollar Amounts and Decimals ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Dollar Amounts and Decimals ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Dollar Amounts and Decimals )
Percentage Increase/Decrease Worksheets
The worksheets in this section have students determine by what percentage something increases or decreases. Each question includes an original amount and a new amount. Students determine the change from the original to the new amount using a formula: ((new - original)/original) × 100 or another method. It should be straight-forward to determine if there is an increase or a decrease. In the case of a decrease, the percentage change (using the formula) will be negative.
- Percentage Increase/Decrease With Whole Number Percentage Values Percentage Increase/Decrease Whole Numbers with 1% Intervals Percentage Increase/Decrease Whole Numbers with 5% Intervals Percentage Increase/Decrease Whole Numbers with 25% Intervals
- Percentage Increase/Decrease With Decimal Number Percentage Values Percentage Increase/Decrease Decimals with 1% Intervals Percentage Increase/Decrease Decimals with 5% Intervals Percentage Increase/Decrease Decimals with 25% Intervals
- Percentage Increase/Decrease With Whole Dollar Percentage Values Percentage Increase/Decrease Whole Dollar Amounts with 1% Intervals Percentage Increase/Decrease Whole Dollar Amounts with 5% Intervals Percentage Increase/Decrease Whole Dollar Amounts with 25% Intervals
- Percentage Increase/Decrease With Decimal Dollar Percentage Values Percentage Increase/Decrease Decimal Dollar Amounts with 1% Intervals Percentage Increase/Decrease Decimal Dollar Amounts with 5% Intervals Percentage Increase/Decrease Decimal Dollar Amounts with 25% Intervals
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Home / United States / Math Classes / 5th Grade Math / Problem Solving using Fractions
Problem Solving using Fractions
Fractions are numbers that exist between whole numbers. We get fractions when we divide whole numbers into equal parts. Here we will learn to solve some real-life problems using fractions. ...Read More Read Less
Table of Contents
What are Fractions?
Types of fractions.
- Fractions with like and unlike denominators
- Operations on fractions
- Fractions can be multiplied by using
- Let’s take a look at a few examples
Solved Examples
- Frequently Asked Questions
Equal parts of a whole or a collection of things are represented by fractions . In other words a fraction is a part or a portion of the whole. When we divide something into equal pieces, each part becomes a fraction of the whole.
For example in the given figure, one pizza represents a whole. When cut into 2 equal parts, each part is half of the whole, that can be represented by the fraction \(\frac{1}{2}\) .
Similarly, if it is divided into 4 equal parts, then each part is one fourth of the whole, that can be represented by the fraction \(\frac{1}{4}\) .
Proper fractions
A fraction in which the numerator is less than the denominator value is called a proper fraction.
For example , \(\frac{3}{4}\) , \(\frac{5}{7}\) , \(\frac{3}{8}\) are proper fractions.
Improper fractions
A fraction with the numerator higher than or equal to the denominator is called an improper fraction .
Eg \(\frac{9}{4}\) , \(\frac{8}{8}\) , \(\frac{9}{4}\) are examples of improper fractions.
Mixed fractions
A mixed number or a mixed fraction is a type of fraction which is a combination of both a whole number and a proper fraction.
We express improper fractions as mixed numbers.
For example , 5\(\frac{1}{3}\) , 1\(\frac{4}{9}\) , 13\(\frac{7}{8}\) are mixed fractions.
Unit fraction
A unit fraction is a fraction with a numerator equal to one. If a whole or a collection is divided into equal parts, then exactly 1 part of the total parts represents a unit fraction .
Fractions with Like and Unlike Denominators
Like fractions are those in which two or more fractions have the same denominator, whereas unlike fractions are those in which the denominators of two or more fractions are different.
For example,
\(\frac{1}{4}\) and \(\frac{3}{4}\) are like fractions as they both have the same denominator, that is, 4.
\(\frac{1}{3}\) and \(\frac{1}{4}\) are unlike fractions as they both have a different denominator.
Operations on Fractions
We can perform addition, subtraction, multiplication and division operations on fractions.
Fractions with unlike denominators can be added or subtracted using equivalent fractions. Equivalent fractions can be obtained by finding a common denominator. And a common denominator is obtained either by determining a common multiple of the denominators or by calculating the product of the denominators.
There is another method to add or subtract mixed numbers, that is, solve the fractional and whole number parts separately, and then, find their sum to get the final answer.
Fractions can be Multiplied by Using:
Division operations on fractions can be performed using a tape diagram and area model. Also, when a fraction is divided by another fraction then we can solve it by multiplying the dividend with the reciprocal of the divisor.
Let’s Take a Look at a Few Examples
Addition and subtraction using common denominator
( \(\frac{1}{6} ~+ ~\frac{2}{5}\) )
We apply the method of equivalent fractions. For this we need a common denominator, or a common multiple of the two denominators 6 and 5, that is, 30.
\(\frac{1}{6} ~+ ~\frac{2}{5}\)
= \(\frac{5~+~12}{30}\)
= \(\frac{17}{30}\)
( \(\frac{5}{2}~-~\frac{1}{6}\) )
= \(\frac{12~-~5}{30}\)
= \(\frac{7}{30}\)
Examples of Multiplication and Division
Multiplication:
(\(\frac{1}{6}~\times~\frac{2}{5}\))
= (\(\frac{1~\times~2}{6~\times~5}\)) [Multiplying numerator of fractions and multiplying denominator of fractions]
= \(\frac{2}{30}\)
(\(\frac{2}{5}~÷~\frac{1}{6}\))
= (\(\frac{2 ~\times~ 5}{6~\times~ 1}\)) [Multiplying dividend with the reciprocal of divisor]
= (\(\frac{2 ~\times~ 6}{5 ~\times~ 1}\))
= \(\frac{12}{5}\)
Example 1: Solve \(\frac{7}{8}\) + \(\frac{2}{3}\)
Let’s add \(\frac{7}{8}\) and \(\frac{2}{3}\) using equivalent fractions. For this we need to find a common denominator or a common multiple of the two denominators 8 and 3, which is, 24.
\(\frac{7}{8}\) + \(\frac{2}{3}\)
= \(\frac{21~+~16}{24}\)
= \(\frac{37}{24}\)
Example 2: Solve \(\frac{11}{13}\) – \(\frac{12}{17}\)
Solution:
Let’s subtract \(\frac{12}{17}\) from \(\frac{11}{13}\) using equivalent fractions. For this we need a common denominator or a common multiple of the two denominators 13 and 17, that is, 221.
\(\frac{11}{13}\) – \(\frac{12}{17}\)
= \(\frac{187~-~156}{221}\)
= \(\frac{31}{221}\)
Example 3: Solve \(\frac{15}{13} ~\times~\frac{18}{17}\)
Multiply the numerators and multiply the denominators of the 2 fractions.
\(\frac{15}{13}~\times~\frac{18}{17}\)
= \(\frac{15~~\times~18}{13~~\times~~17}\)
= \(\frac{270}{221}\)
Example 4: Solve \(\frac{25}{33}~\div~\frac{41}{45}\)
Divide by multiplying the dividend with the reciprocal of the divisor.
\(\frac{25}{33}~\div~\frac{41}{45}\)
= \(\frac{25}{33}~\times~\frac{41}{45}\) [Multiply with reciprocal of the divisor \(\frac{41}{45}\) , that is, \(\frac{45}{41}\) ]
= \(\frac{25~\times~45}{33~\times~41}\)
= \(\frac{1125}{1353}\)
Example 5:
Sam was left with \(\frac{7}{8}\) slices of chocolate cake and \(\frac{3}{7}\) slices of vanilla cake after he shared the rest with his friends. Find out the total number of slices of cake he had with him. Sam shared \(\frac{10}{11}\) slices from the total number he had with his parents. What is the number of slices he has remaining?
To find the total number of slices of cake he had after sharing we need to add the slices of each cake he had,
= \(\frac{7}{8}\) + \(\frac{3}{7}\)
= \(\frac{49~+~24}{56}\)
= \(\frac{73}{56}\)
To find out the remaining number of slices Sam has \(\frac{10}{11}\) slices need to be deducted from the total number,
= \(\frac{73}{56}~-~\frac{10}{11}\)
= \(\frac{803~-~560}{616}\)
= \(\frac{243}{616}\)
Hence, after sharing the cake with his friends, Sam has \(\frac{73}{56}\) slices of cake, and after sharing with his parents he had \(\frac{243}{616}\) slices of cake left with him.
Example 6: Tiffany squeezed oranges to make orange juice for her juice stand. She was able to get 25 ml from one orange. How many oranges does she need to squeeze to fill a jar of \(\frac{15}{8}\) liters? Each cup that she sells carries 200 ml and she sells each cup for 64 cents. How much money does she make at her juice stand?
First \(\frac{15}{8}\) l needs to be converted to milliliters.
\(\frac{15}{8}\)l into milliliters = \(\frac{15}{8}\) x 1000 = 1875 ml
To find the number of oranges, divide the total required quantity by the quantity of juice that one orange can give.
The number of oranges required for 1875 m l of juice = \(\frac{1875}{25}\) ml = 75 oranges
To find the number of cups she sells, the total quantity of juice is to be divided by the quantity of juice that 1 cup has
= \(\frac{1875}{200}~=~9\frac{3}{8}\) cups
We know that, the number of cups cannot be a fraction, it has to be a whole number. Also each cup must have 200ml. Hence with the quantity of juice she has she can sell 9 cups, \(\frac{3}{8}\) th of a cup cannot be sold alone.
Money made on selling 9 cups = 9 x 64 = 576 cents
Hence she makes 576 cents from her juice stand.
What is a mixed fraction?
A mixed fraction is a number that has a whole number and a fractional part. It is used to represent values between whole numbers.
How will you add fractions with unlike denominators?
When adding fractions with unlike denominators, take the common multiple of the denominators of both the fractions and then convert them into equivalent fractions.
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Basic Problems on Percentage
Basic problems on percentage will help us to get the basic concept to solve any percentage problems. We will learn how to apply the concept of percentage for solving some real-life problems.
Basic problems on percentage:
1. What is 30 % of 80?
= 30/100 × 80
= (30 × 80)/100
2. In a class of 50 students, 40 % are girls. Find the number of girls and number of boys in the class?
Number of girls in the class = 40 % of 50
= 40/100 × 50
= 2000/100
= 20
Number of boys in the class = Total number of students in the class - Number of girls
= 50 – 20
= 30
3. Ron scored 344 marks out of 400 marks and his elder brother Ben scored 582 marks out of 600 marks. Who scored percentage is better?
Percentage of marks scored by Ron = (344/400 × 100) %
= (34400/400) %
= (344/4) %
= 86 %
Percentage of marks scored by Ben = (582/600 × 100) %
= (58200/600) %
= (582/6) %
= 97 %
Hence, the percentage marks scored by Ben is better.
4. In final exam of class IX there are 50 students 10 % students failed. How many students passed to class X?
Percentage of students passed to class X = 100 % - 10 % = 90 %
= 90/100 × 50
Therefore, 45 students passed to class X.
5. Victor gets 92 % marks in examinations. If these are 460 marks, find the maximum marks.
Solution:
Let the maximum marks be m
Then 92 % of m = 460
⇒ 92/100 × m = 460
⇒ m = (460 × 100)/92
⇒ m = 46000/92
Therefore, maximum marks in the examinations are 500.
Fraction into Percentage
Percentage into Fraction
Percentage into Ratio
Ratio into Percentage
Percentage into Decimal
Decimal into Percentage
Percentage of the given Quantity
How much Percentage One Quantity is of Another?
Percentage of a Number
Increase Percentage
Decrease Percentage
Solved Examples on Percentage
Problems on Percentage
Real Life Problems on Percentage
Word Problems on Percentage
Application of Percentage
8th Grade Math Practice From Basic Problems on Percentage to HOME PAGE
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so, you know that (150) is 1/4 of the answer (100%) Add 150 - 4 times (Because we know that 25% X 4 = 100%) And that is equal to: (150 + 150 + 150 + 150) = *600. The method they used in the video is also correct, but i think that this one is easier, and will make it more simple to solve the rest of the question. •.
Using Proportions to Solve Percent Problems. Percent problems can also be solved by writing a proportion. A proportion is an equation that sets two ratios or fractions equal to each other. With percent problems, one of the ratios is the percent, written as \(\ \frac{n}{100}\). The other ratio is the amount to the base.
More Lessons: http://www.MathAndScience.comTwitter: https://twitter.com/JasonGibsonMath In this lesson, you will learn how to solve percent problems using t...
Fractions, Decimals and Percentages - Short Problems. This is part of our collection of Short Problems. You may also be interested in our longer problems on Fractions, Decimals and Percentages. Printable worksheets containing selections of these problems are available here.
Lesson 3: Percent word problems. Solving percent problems. Equivalent expressions with percent problems. Percent word problem: magic club. Percent problems. Percent word problems: tax and discount. Tax and tip word problems. Percent word problem: guavas. Discount, markup, and commission word problems.
Level up on all the skills in this unit and collect up to 900 Mastery points! In these tutorials, we'll explore the number system. We'll convert fractions to decimals, operate on numbers in different forms, meet complex fractions, and identify types of numbers. We'll also solve interesting word problems involving percentages (discounts, taxes ...
Step by step guide to solve percent problems In each percent problem, we are looking for the base, or part or the percent. Use the following equations to find each missing section.
While we are on the topic of percentages, one example will be, the decimal 0.35, or the fraction \(\frac{7}{20}\), which is equivalent to 35 percent, or 35%. Solving Problems Based on Percentages By solving problems based on percentages, we can find the missing values and find the values of various unknowns in a given problem.
Next: Fractions, Decimals and Percentages Practice Questions. The Corbettmaths Practice Questions on Percentages and Fractions.
Solving percent problems When you know the connection between percents and fractions, you can solve a lot of percent problems with a few simple tricks. Other problems, however, require a bit more work. In this section, I show you how to tell an easy percent problem from a tough one, and I give you the tools to solve all of them.
Divide: 15/50 = 0.30. 15 = 50 x Original equation. 15 50 = 50 x 50 Divide both sides by 50. 15 50 = x Simplify right-hand side. x = 0.30 Divide: 15/50 = 0.30. But we must express our answer as a percent. To do this, move the decimal two places to the right and append a percent symbol. Thus, 15 is 30% of 50.
Click here for Answers. equivalent. Practice Questions. Previous: Percentages and Fractions Practice Questions. Next: Ordering Fractions, Decimals and Percentages Practice Questions. The Corbettmaths Practice Questions on Fractions, Decimals and Percentages (FDP)
These percent worksheets are great for practicing multiplying by percents that are powers of ten. You may select from 1%, 10%, 100%, 1000%, or .01% to use in the problems. You may select the range of numbers to work with as well as whole number or decimal numbers. You may vary the format of the problems between numerical or word problems.
The solved examples on percentage will help us to understand how to solve step-by-step different types of percentage problems. Now we will apply the concept of percentage to solve various real-life examples on percentage. Solved examples on percentage: 1. In an election, candidate A got 75% of the total valid votes.
Converting between percents, fractions, & decimals (Opens a modal) Finding common percentages (Opens a modal) Converting percents and fractions review ... Practice. Equivalent representations of percent problems Get 3 of 4 questions to level up! Benchmark percents Get 5 of 7 questions to level up! Quiz 2. Level up on the above skills and ...
Greater Depth Prove whether a statement is true or false when changing fractions to percentages where the denominator is not always a factor of 100. Questions 2, 5 and 8 (Problem Solving) Developing Find the percentage of the white area of the shape where the denominator is 10 or 100. Expected Find the percentage of the white area of the shape ...
Percent math problems with detailed solutions. Problems that deal with percentage increase and decrease as well as problems of percent of quantities. ... y = 30 and solve for x which the original price. x - 0.22 x = 30 0.78 x = 30 x = $38.5 Check the solution to this problem by reducing the origonal price found $38.5 by 22% and see if it gives $30.
First, recognize that 2479 is less than 3700, so the percentage value must also be less than 100%. Divide 2479 by 3700 and multiply by 100. 2479 ÷ 3700 × 100 = 67%. Calculating the Percentage a Whole Number is of Another Whole Number. Calculating the Percentage a Whole Number is of Another Whole Number (Percents from 1% to 99%) Calculating ...
Percentage Questions and Solutions. Q.1: A fruit seller had some apples. He sells 40% apples and still has 420 apples. What is the total number of apples he had originally? Solution: Let the number of apples a fruit seller had be x. As per the given question, (100 - 40%) of x = 420. 60% of x = 420. 60/100 x = 420.
When we divide something into equal pieces, each part becomes a fraction of the whole. For example in the given figure, one pizza represents a whole. When cut into 2 equal parts, each part is half of the whole, that can be represented by the fraction \ (\frac {1} {2}\). Similarly, if it is divided into 4 equal parts, then each part is one ...
Basic problems on percentage will help us to get the basic concept to solve any percentage problems. We will learn how to apply the concept of percentage for solving some real-life problems. Basic problems on percentage: 1. What is 30 % of 80? Solution: 30 % of 80 = 30/100 × 80 = (30 × 80)/100 = 2400/100 = 24
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