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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 )

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7.3: Solving Basic Percent Problems

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  • 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?

Percent Maths Problems

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Course: 7th grade   >   Unit 2

  • 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
  • Multi-step ratio and percent problems
  • Your answer should be
  • an integer, like 6 ‍  
  • a simplified proper fraction, like 3 / 5 ‍  
  • a simplified improper fraction, like 7 / 4 ‍  
  • a mixed number, like 1   3 / 4 ‍  
  • an exact decimal, like 0.75 ‍  
  • a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  

Percents (%)

When we say "percent" we are really saying "per 100".

One percent ( 1% ) means 1 per 100.

Try it Yourself:

Using Percent

Use the slider and try some different numbers (What is 40% of 80? What is 10% of 200? What is 90% of 10?)

Because "Percent" means "per 100" think:

"this should be divided by 100"

So 75% really means 75 100

And 100% is 100 100 , or exactly 1 (100% of any number is just the number, unchanged)

And 200% is 200 100 , or exactly 2 (200% of any number is twice the number)

A Percent can also be expressed as a Decimal or a Fraction

Read more about this at Decimals, Fractions and Percentages .

Some Worked Examples

Example: calculate 25% of 80.

25% = 25 100

And   25 100 × 80 = 20

So 25% of 80 is 20

Example: 15% of 200 apples are bad. How many apples are bad?

15% = 15 100

30 apples are bad

Example: if only 10 of the 200 apples are bad, what percent is that?

As a fraction, 10 200 = 0.05

As a percentage it is: 10 200 x 100 = 5%

5% of those apples are bad

skateboard

Example: A Skateboard is reduced 25% in price. The old price was $120. Find the new price.

First, find 25% of $120:

And   25 100  × $120 = $30

25% of $120 is $30

So the reduction is $30

Take the reduction from the original price

$120 − $30 = $90

The Price of the Skateboard in the sale is $90

Calculation Trick

This little rule can make some calculations easier:

x% of y = y% of x

Example: 8% of 50

8% of 50 is the same as 50% of 8

And 50% of 8 is 4

So 8% of 50 is also 4

Percent vs Percentage

My Dictionary says "Percentage" is the "result obtained by multiplying a quantity by a percent". So 10 percent of 50 apples is 5 apples: the 5 apples is the percentage .

But in practice people use both words the same way.

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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 Amounts and Multiples of 5 Percents

Percentage Calculations

solve math problems percent

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

solve math problems percent

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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Solving problems with percentages

  • Price difference I
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  • How many students?

To solve problems with percent we use the percent proportion shown in "Proportions and percent".

$$\frac{a}{b}=\frac{x}{100}$$

$$\frac{a}{{\color{red} {b}}}\cdot {\color{red} {b}}=\frac{x}{100}\cdot b$$

$$a=\frac{x}{100}\cdot b$$

x/100 is called the rate.

$$a=r\cdot b\Rightarrow Percent=Rate\cdot Base$$

Where the base is the original value and the percentage is the new value.

47% of the students in a class of 34 students has glasses or contacts. How many students in the class have either glasses or contacts?

$$a=r\cdot b$$

$$47\%=0.47a$$

$$=0.47\cdot 34$$

$$a=15.98\approx 16$$

16 of the students wear either glasses or contacts.

We often get reports about how much something has increased or decreased as a percent of change. The percent of change tells us how much something has changed in comparison to the original number. There are two different methods that we can use to find the percent of change.

The Mathplanet school has increased its student body from 150 students to 240 from last year. How big is the increase in percent?

We begin by subtracting the smaller number (the old value) from the greater number (the new value) to find the amount of change.

$$240-150=90$$

Then we find out how many percent this change corresponds to when compared to the original number of students

$$90=r\cdot 150$$

$$\frac{90}{150}=r$$

$$0.6=r= 60\%$$

We begin by finding the ratio between the old value (the original value) and the new value

$$percent\:of\:change=\frac{new\:value}{old\:value}=\frac{240}{150}=1.6$$

As you might remember 100% = 1. Since we have a percent of change that is bigger than 1 we know that we have an increase. To find out how big of an increase we've got we subtract 1 from 1.6.

$$1.6-1=0.6$$

$$0.6=60\%$$

As you can see both methods gave us the same answer which is that the student body has increased by 60%

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solve math problems percent

Home / United States / Math Classes / 6th Grade Math / Solving Problems Based on Percentage

Solving Problems Based on Percentage

Percent is an alternate method of representing fractions and decimals. Here we will learn different methods of calculati ng the percent and the steps involved in each method. We will also look at some examples that will help you gain a better understanding of the concept. ...Read More Read Less

Table Of Contents

solve math problems percent

What is meant by percentage?

Solving problems based on percentages, finding the percentage of a number, finding the whole number from the percent, finding the whole using the ratio method, solved examples.

  • Frequently Asked Questions

In mathematics, a percentage is a number or ratio that represents a fraction of 100. The symbol “ % ” is frequently used to represent it, and it has a few hundred years of history. 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%.

By solving problems based on percentages, we can find the missing values and find the values of various unknowns in a given problem.

Find 40% of 200.

\(\frac{40}{100}\times 200\)              Write the percentage as a fraction

\(\frac{2}{5}\times 200=800\)            Simplify

percent 1

First, write the percentage as a fraction or decimal. Then, divide the fraction or decimal by the part. This method applies to any situation in which a percentage and its value are given. 

If 2 percent equals 80, multiply 80 by 100 and divide it by 2 to get 4000.

Prove that 20% of 120 is 24. 

20% =\(\frac{20}{100}\)       Write the percent as a fraction or decimal.

Using multiplication equation:

\(\frac{20}{100}\times 120=24\)      Simplify

To prove the reverse of this solution we use the  division equation:

\(\frac{24}{\frac{20}{100}}\)      Simplify

\(\frac{2400}{20}=120\)    

A ratio table is the table that shows the comparison between two units and shows the relationship between them.

Example 1: What is 25% of 50?

We have 25% of 50.

So, 25% of 50 = \(\frac{1}{4}\times 50\) Write the percentage as a fraction or decimal.

                       = \(\frac{50}{4}\)     Simplify.

                       = 12.5  

Example 2: Using the ratio table, answer the following question:

What is 60% of 200?

We have 60% of 200.

Now, we have to use the ratio table to find the part. Let one row represent the part and the other row represent the whole row in the table and find the equivalent ratio of 200.

percent 2

The first column represents the percentage = \(\frac{60}{100}\)

percent 3

So, 60% of 200 is 120.

Example 3: Find the whole of the number.

                  50% of what number is 45.

We have: 50% of what number is 45?

Use division equation

\(\frac{45}{50%}\)    Write the percentage as a fraction or decimal

\(=\frac{45}{\frac{1}{2}}\)  Simplify

So, \(45\times 2=90\)

Hence, 50% of 90 is 45

Example 4: Find the whole of the number using the ratio table.

140% of what number is 84

We have to find 140% of what number is 84.

Use the ratio table to find the part. Let one be the part and the other be the whole row in the table. Now, find the equivalent ratio of 200.

percent 4

So, 140% of 60 is 84.

Example 5: A rectangular hall’s width is 60 percent of its length.

What are the room’s dimensions?

percent 7

Solution:  

Calculate the width of the room by taking 60% of 15 feet.

\(60%\times 15\) Write the percentage as a fraction or decimal.

= \(0.6\times 15\)      Simplify

We can al so understand it with the help of a diagram:

percent 8

The width is 9 feet.

Area of the rectangle = \(\text{length}\times \text{width}\)

                                    = \(15\times 9\)

                                    = 135

Hence, the area of the given room is 135 \(feet^2\).

Example 6: You have won a camping trip at an auction at your school fair that cost $80. Your bid is 40% of your maximum bid for the price of the camping trip. How much more would you be willing to pay for the trip if you hadn’t already paid the full price?

women

You are given the winning camping bid that represents the maximum bid as well as the percentage of your maximum bid. You must calculate how much more you would have paid for the camping trip if you had known how much more you were willing to pay.

Your winning bid is the part, and your maximum bid is the whole.

Create a model based on the fact that 40% of the total is $80 to determine the highest bid. Then divide the winning bid by the maximum bid to find out how much more you were willing to pay.

percent10

The maximum bid is $200 and the winning bid is $80. So, you would be willing to bid $200 – $80 = $120 more for the tickets.

How do you calculate a percentage?

To calculate a percentage, divide the given value by the total value and multiply the result by 100. That is “(value/total value) x 100%”. This is the formula for calculating percentages.

In mathematics, a percentage is a number or ratio that represents a fraction of 100 in mathematics. Percentage is usually represented by the symbol “%”. It is also written simply as “percent” or “pct”. For example, the decimal 0.35, or the fraction \(\frac{35}{100}\), is equivalent to 0.35.

What is the purpose of percentages?

Percentages are used to figure out “how much” or “how many” of something is to be taken from a given value. Percentage makes it easier to calculate the exact amount or figure being discussed. In order to determine whether a percentage increase or decrease has occurred, a comparison of fractions is done. This aids in calculating percentages of profit and loss, for example in real life situations.

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IMAGES

  1. Solving percent equations

    solve math problems percent

  2. Worksheet on Percent Problems

    solve math problems percent

  3. Solving Percent Problems (examples, solutions, worksheets, videos

    solve math problems percent

  4. Solving Percent Problems Using a Percent Proportion

    solve math problems percent

  5. Solve Percent Problems using the Proportion Method

    solve math problems percent

  6. Revisit Percentages

    solve math problems percent

VIDEO

  1. CRAZY MATH TRICK

  2. PERCENT TRICK

  3. PERCENT

  4. A Nice Math Percents Problem

  5. Solving Percent Question 1

  6. A Nice Math Problem With Percent

COMMENTS

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

    Solution: 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\)? Solution: In this problem, we are looking for the percent. Use the following equation:

  2. How to Solve Percent Problems

    Solve simple percent problems Some percents are easy to figure. Here are a few. Finding 100% of a number: Remember that 100% means the whole thing, so 100% of any number is simply the number itself: 100% of 5 is 5 100% of 91 is 91 100% of 732 is 732

  3. Solving percent problems (video)

    Do you want to learn how to solve percent problems in math? Watch this video from Khan Academy, a nonprofit that offers free, world-class education for anyone, anywhere. You will see how to use proportions, equations, and mental math to find the missing values in percent problems. You will also get to practice with some interactive exercises and quizzes.

  4. Percentage Calculator

    1. How to calculate percentage of a number. Use the percentage formula: P% * X = Y Example: What is 10% of 150? Convert the problem to an equation using the percentage formula: P% * X = Y P is 10%, X is 150, so the equation is 10% * 150 = Y Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10

  5. Calculate percentages with Step-by-Step Math Problem Solver

    Welcome to Quickmath Solvers! Enter the value (s) for the required question and click the adjacent Go button. What is % of ? is what percent of ? is % of what number? What is the fraction / as a percentage? What is the decimal or integer as a percentage? What is % as a fraction? What is % as a decimal? What is the percentage change when becomes ?

  6. Solving percent problems

    Solving Percent Problems: IS/OF

  7. 5.2.1: Solving Percent Problems

    To solve percent problems, you can use the equation, Percent ⋅ Base = Amount , and solve for the unknown numbers. Or, you can set up the proportion, Percent = amount base , where the percent is a ratio of a number to 100. You can then use cross multiplication to solve the proportion. Percents are a ratio of a number and 100, so they are ...

  8. Percentage Calculator with detailed explanation

    This online calculator solves the four basic types of percent problems and percentage increase/decrease problem. The calculator will generate a step-by-step explanation for each type of percentage problem. Percentage Calculator Four types of percentage problems + steps. show help ↓↓ examples ↓↓ 0 1 2 3 4 5 6 7 8 9. / del What is % of ?

  9. How to Calculate Percentages to Solve Math Problems

    Percentage = (Value/Total Value) x 100 As an example, suppose that in a group of 40 cats and dogs, 10 of the animals are dogs. What percentage is that? Solution: The number of dogs = 10

  10. 7.3: Solving Basic Percent Problems

    7.3: Solving Basic Percent Problems

  11. Percentages

    Quiz Unit test Intro to percents Learn The meaning of percent Meaning of 109% Percents from fraction models Practice Up next for you: Intro to percents Get 5 of 7 questions to level up! Start Not started

  12. Percent Maths Problems

    Solution to Problem 1 The absolute decrease is 20 - 15 = $5 The percent decrease is the absolute decrease divided by the the original price (part/whole). percent decease = 5 / 20 = 0.25 Multiply and divide 0.25 to obtain percent. percent decease = 0.25 = 0.25 * 100 / 100 = 25 / 100 = 25% Problem 2 Mary has a monthly salary of $1200.

  13. Percent problems (practice)

    Solving percent problems Math > 7th grade > Rates and percentages > Percent word problems Percent problems Google Classroom A brand of cereal had 1.2 milligrams ( mg) of iron per serving. Then they changed their recipe so they had 1.8 mg of iron per serving. What was the percent increase in iron? % Stuck?

  14. Solving Percent Problems

    1.4K 74K views 1 year ago 6th Grade Course - Unit 3 View more at www.MathAndScience.com. In this lesson, you will learn how to solve percent problems that you are likely to encounter in...

  15. Percent Word Problems Calculator

    Free Percent Word Problems Calculator - solve percent word problems step by step

  16. Introduction to Percents

    A Percent can also be expressed as a Decimal or a Fraction : A Half can be written... As a percentage: 50%. As a decimal: 0.5. As a fraction: 1 / 2. Read more about this at Decimals, Fractions and Percentages. Some Worked Examples. Example: Calculate 25% of 80. 25% = 25100. And 25100 × 80 = 20.

  17. Step-by-Step Math Problem Solver

    QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students. The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and ...

  18. Solving Percent Problems

    Math Worksheets. Examples, solutions, and videos that will help GMAT students review how to solve percent word problems. The following diagram shows some examples of solving percent problems using the part, base, rate formula. Scroll down the page for more examples and solutions of solving percent problems. Solving Percent Problems.

  19. Step-by-Step Calculator

    To solve math problems step-by-step start by reading the problem carefully and understand what you are being asked to find. Next, identify the relevant information, define the variables, and plan a strategy for solving the problem.

  20. 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.

  21. Solving problems with percentages

    To solve problems with percent we use the percent proportion shown in "Proportions and percent". a b = x 100. a b ⋅ b = x 100 ⋅ b. a = x 100 ⋅ b. x/100 is called the rate. a = r ⋅ b ⇒ P e r c e n t = R a t e ⋅ B a s e. Where the base is the original value and the percentage is the new value.

  22. How to Solve Percentage Problems with Examples?

    If 2 percent equals 80, multiply 80 by 100 and divide it by 2 to get 4000. Prove that 20% of 120 is 24. 20% =\ (\frac {20} {100}\) Write the percent as a fraction or decimal. Using multiplication equation: \ (\frac {20} {100}\times 120=24\) Simplify. To prove the reverse of this solution we use the division equation:

  23. IXL

    Spanish. Recommendations. Skill plans. IXL plans. Virginia state standards. Textbooks. Test prep. Awards. Improve your math knowledge with free questions in "Solve percent problems" and thousands of other math skills.

  24. ‎MathPix

    Recognize math problems quickly and accurately. The homework solver is like a teacher on the spot. Use canvas tools to write your own problem on the phone and get the results step-by-step. Get detailed step-by-step solutions for solving math problems to understand better. Keep historical solving records and review them at any time.

  25. ‎Math Solver

    Download Math Solver - Nerd AI and enjoy it on your iPhone, iPad, and iPod touch. ‎Powered by the latest AI technology, Nerd AI is here to help you breeze through your studies. With a range of powerful features, Nerd AI transforms the way you approach writing, problem-solving, language learning, summarizing, coding, and expanding your ...

  26. Save 30% on CRASH MATH on Steam

    CRASH MATH You must solve math problems while trying to drive a car and avoid traps. This driving game has a lot of possibilities. The physics engine simulates every component of a vehicle in real-time, resulting in a funny behavior. While creating the excitement of solving math problems.