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Fractions, Decimals and Percentages - Short Problems

fraction percentage problem solving

Bouncing Ball

A ball is dropped from a height, and every time it hits the ground, it bounces to 3/5 of the height from which it fell.

Percentage Mad

Weekly Problem 43 - 2013 What is 20% of 30% of 40% of £50?

Information Display

The information display on a train shows letters by illuminating dots in a rectangular array. What fraction of the dots in this array is illuminated?

Mean Sequence

Weekly Problem 38 - 2009 This sequence is given by the mean of the previous two terms. What is the fifth term in the sequence?

Ordering Fractions

Weekly Problem 46 - 2014 Which of these fractions has greatest value?

Jacob's Flock

How many sheep are in Jacob's flock?

Farthest Fraction

Which of these fractions is the largest?

Tommy's Tankard

Weekly Problem 4 - 2017 Tommy's tankard holds 480ml when it is one quarter empty. How much does it hold when it is one quarter full?

Multiplication Magic Square

Weekly Problem 32 - 2015 Can you work out the missing numbers in this multiplication magic square?

Smashing Time

Weekly Problem 58 - 2012 Once granny has smashed some of her cups and saucers, how many cups are now without saucers?

Talulah's Tulips

Weekly Problem 10 - 2017 Talulah plants some tulip bulbs. When they flower, she notices something interesting about the colours. What fraction of the tulips are white?

Better Spelling

Weekly Problem 12 - 2010 Can Emily increase her average test score to more than $80$%? Find out how many more tests she must take to do so.

Valuable Percentages

Weekly Problem 23 - 2010 These numbers have been written as percentages. Can you work out which has the greatest value?

Can you find a number that is halfway between two fractions?

Pride of Place

Two fractions have been placed on a number line. Where should another fraction be placed?

Second Half Score

Boarwarts Academy played their annual match against Range Hill School. What fraction of the points were scored in the second half?

Between a Sixth and a Twelfth

The space on a number line between a sixth and a twelfth is split into 3 equal parts. Find the number indicated.

Magical Products

Can you place the nine cards onto a 3x3 grid such that every row, column and diagonal has a product of 1?

Smallest Fraction

Which of these is the smallest?

Three Blind Mice

Each of the three blind mice in turn ate a third of what remained of a piece of cheese. What fraction of the cheese did they eat in total?

Charlie's Money

How much money did Charlie have to begin with?

Tricky Fractions

Use this series of fractions to find the value of x.

Too Close to Call

Weekly Problem 24 - 2012 Can you put these very close fractions into order?

Slightly Outnumbered

If this class contains between $45$% and $50$% girls, what is the smallest possible number of girls in the class?

What fraction of this triangle is shaded?

Peanut Harvest

A group of monkeys eat various fractions of a harvest of peanuts. What fraction is left behind?

Test Scores

Ivan, Tibor and Alex sat a test and achieved 85%, 90% and 95% respectively. Tibor scored just one more mark than Ivan. How many marks did Alex get?

Tennis Club

Three-quarters of the junior members of a tennis club are boys and the rest are girls. What is the ratio of boys to girls among these members?

The Grand Old Duke of York

What percentage of his 10,000 men did the Grand Old Duke of York have left when he arrived back at the bottom of the hill?

Meeting Point

Malcolm and Nikki run at different speeds. They set off in opposite directions around a circular track. Where on the track will they meet?

How many rats did the Pied Piper catch?

To make porridge, Goldilocks mixes oats and wheat bran..... what percentage of the mix is wheat?

Petrol Station

Andrea has just filled up a fraction of her car's petrol tank. How much petrol does she now have?

A Drink of Water

Weekly Problem 43 - 2015 Rachel and Ross share a bottle of water. Can you work out how much water Rachel drinks?

Entrance Exam

Dean finishes his exam strongly. Can you work out how many questions are on the paper if he gets an average of 80%?

Which of the cities shown had the largest percentage increase in population?

Weekly Problem 11 - 2013 A shop has "Everything half price", and then "15% off sale prices". What is the overall reduction in cost?

What percentage of the truck's final mass is coal?

Percentage Unchanged

If the base of a rectangle is increased by 10% and the area is unchanged, by what percentage is the width decreased by ?

What fraction of customers buy Kleenz after the advertising campaign?

2011 Digits

Weekly Problem 10 - 2014 What is the sum of the first $2011$ digits when $20 \div 11$ is written as a decimal?

Pineapple Juice

What percentage of this orange drink is juice?

After playing 500 games, my success rate at Solitare is 49%. How many games do I need to win to increase my success rate to 50%?

Percentage of a Quarter

What percentage of a quarter is a fifth?

Fractions of 1000

Find a simple way to compute this long fraction.

Breakfast Time

Four hobbits each eat one quarter of the porridge remaining in the pan. How much is left?

Percentage Swap

What is 50% of 2007 plus 2007% of 50?

Recurring Mean

What is the mean of 1.2 recurring and 2.1 recurring?

Itchy's Fleas

Itchy the dog has a million fleas. How many fleas might his shampoo kill?

Antiques Roadshow

Last year, on the television programme Antiques Roadshow... work out the approximate profit.

Squeezed In

Weekly Problem 9 - 2017 What integer x makes x/9 lie between 71/7 and 113/11?

Producing an Integer

Multiply a sequence of n terms together. Can you work out when this product is equal to an integer?

Elephants and Geese

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?

The Property Market

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.

How to Solve Percent Problems? (+FREE Worksheet!)

Related Topics

  • How to Find Percent of Increase and Decrease
  • How to Find Discount, Tax, and Tip
  • How to Do Percentage Calculations
  • How to Solve Simple Interest Problems

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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Mathematics LibreTexts

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.

Screen Shot 2019-09-23 at 2.55.59 PM.png

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

\[10 = 80x.\nonumber \]

\[ \begin{aligned} 10 = 80x ~ & \textcolor{red}{ \text{ Original equation.}} \\ \frac{10}{80} = \frac{80x}{80} ~ & \textcolor{red}{ \text{ Divide both sides by 80.}} \\ \frac{1}{8} = x ~ & \textcolor{red}{ \text{ Reduce: } 10/80 = 1/8.} \\ 0.125 = x ~ & \textcolor{red}{ \text{ Divide: } 1/8 = 0.125.} \end{aligned}\nonumber \]

Screen Shot 2019-09-23 at 3.00.38 PM.png

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?

1. What number is 22.4% of 125?

2. What number is 159.2% of 125?

3. 60% of what number is 90?

4. 25% of what number is 40?

5. 200% of what number is 132?

6. 200% of what number is 208?

7. 162.5% of what number is 195?

8. 187.5% of what number is 90?

9. 126.4% of what number is 158?

10. 132.5% of what number is 159?

11. 27 is what percent of 45?

12. 9 is what percent of 50?

13. 37.5% of what number is 57?

14. 162.5% of what number is 286?

15. What number is 85% of 100?

16. What number is 10% of 70?

17. What number is 200% of 15?

18. What number is 50% of 84?

19. 50% of what number is 58?

20. 132% of what number is 198?

21. 5.6 is what percent of 40?

22. 7.7 is what percent of 35?

23. What number is 18.4% of 125?

24. What number is 11.2% of 125?

25. 30.8 is what percent of 40?

26. 6.3 is what percent of 15?

27. 7.2 is what percent of 16?

28. 55.8 is what percent of 60?

29. What number is 89.6% of 125?

30. What number is 86.4% of 125?

31. 60 is what percent of 80?

32. 16 is what percent of 8?

33. What number is 200% of 11?

34. What number is 150% of 66?

35. 27 is what percent of 18?

36. 9 is what percent of 15?

37. \(133 \frac{1}{3} \%\) of what number is 80?

38. \(121 \frac{2}{3} \%\) of what number is 73?

39. What number is \(54 \frac{1}{3} \%\) of 6?

40. What number is \(82 \frac{2}{5} \%\) of 5?

41. What number is \(62 \frac{1}{2} \%\) of 32?

42. What number is \(118 \frac{3}{4} \%\) of 32?

43. \(77 \frac{1}{7} \%\) of what number is 27?

44. \(82 \frac{2}{3} \%\) of what number is 62?

45. What number is \(142 \frac{6}{7} \%\) of 77?

46. What number is \(116 \frac{2}{3} \%\) of 84?

47. \(143 \frac{1}{2} \%\) of what number is 5.74?

48. \(77 \frac{1}{2} \%\) of what number is 6.2?

49. \(141 \frac{2}{3} \%\) of what number is 68?

50. \(108 \frac{1}{3} \%\) of what number is 78?

51. What number is \(66 \frac{2}{3} \%\) of 96?

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?

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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!

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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

Calculating the Percent Value of Whole Number Currency Amounts and Select Percents

Percentage Calculations

fraction percentage problem solving

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

fraction percentage problem solving

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

Copyright © 2005-2024 Math-Drills.com You may use the math worksheets on this website according to our Terms of Use to help students learn math.

fraction percentage problem solving

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

fraction percentage problem solving

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 \(\frac{1}{4}\) .

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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 .

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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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The Sunday Read: ‘Sure, It Won an Oscar. But Is It Criterion?’

How the criterion collection became the film world’s arbiter of taste..

Narrated by Shaun Taylor-Corbett

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By Joshua Hunt

Produced by Aaron Esposito and Jack D’Isidoro

Edited by John Woo

Original music by Aaron Esposito

Engineered by Daniel Farrell and Andrea Vancura

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In October 2022, amid a flurry of media appearances promoting their film “Tàr,” the director Todd Field and the star Cate Blanchett made time to visit a cramped closet in Manhattan. This closet, which has become a sacred space for movie buffs, was once a disused bathroom at the headquarters of the Criterion Collection, a 40-year-old company dedicated to “gathering the greatest films from around the world” and making high-quality editions available to the public on DVD and Blu-ray and, more recently, through its streaming service, the Criterion Channel. Today Criterion uses the closet as its stockroom, housing films by some 600 directors from more than 50 countries — a catalog so synonymous with cinematic achievement that it has come to function as a kind of film Hall of Fame. Through a combination of luck, obsession and good taste, this 55-person company has become the arbiter of what makes a great movie, more so than any Hollywood studio or awards ceremony.

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Additional production for The Sunday Read was contributed by Isabella Anderson, Anna Diamond, Sarah Diamond, Elena Hecht, Emma Kehlbeck, Tanya Pérez and Krish Seenivasan.

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COMMENTS

  1. Solving percent problems (video)

    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. •.

  2. 5.2.1: Solving Percent Problems

    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.

  3. Calculate Percents Using Fractions (Solve Percent Problems ...

    More Lessons: http://www.MathAndScience.comTwitter: https://twitter.com/JasonGibsonMath In this lesson, you will learn how to solve percent problems using t...

  4. Fractions, Decimals and Percentages

    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.

  5. Percent problems (practice)

    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.

  6. Fractions, decimals, & percentages

    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 ...

  7. How to Solve Percent Problems? (+FREE Worksheet!)

    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.

  8. How to Solve Percentage Problems with Examples?

    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.

  9. Percentages and Fractions Practice Questions

    Next: Fractions, Decimals and Percentages Practice Questions. The Corbettmaths Practice Questions on Percentages and Fractions.

  10. How to Calculate Percentages to Solve Math Problems

    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.

  11. 7.3: Solving Basic Percent Problems

    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.

  12. Fractions, Decimals and Percentages Practice Questions

    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)

  13. Percent Worksheets

    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.

  14. Different Types of Percentage 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.

  15. Percentages

    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 ...

  16. PDF Year 6 Fractions to Percentages Reasoning and Problem Solving

    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 ...

  17. Percent Maths Problems

    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.

  18. Percentages Worksheets

    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 ...

  19. Percentage Questions (with Answers)

    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.

  20. Problem Solving using Fractions (Definition, Types and Examples

    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 ...

  21. 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? Solution: 30 % of 80 = 30/100 × 80 = (30 × 80)/100 = 2400/100 = 24

  22. The Sunday Read: 'Sure, It Won an Oscar. But Is It Criterion?'

    How the Criterion Collection became the film world's arbiter of taste.