Percent as Ratio Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Percent as Ratio.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

A ratio comparing a quantity to 100, written with the % symbol; 'per cent' literally means 'per hundred'.

'Per cent' means 'per hundred'— $25\%$ means 25 out of every 100.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: A percent is a ratio comparing an amount to 100, so $p\%$ means $p$ per hundred.

Common stuck point: The procedure for percent as ratio is the easy part; the trap is using the percent number as the amount. Asking "Is the value a comparison stated per 100 (a rate), not a raw count?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Is the value a comparison stated per 100 (a rate), not a raw count?

Worked Examples

Example 1

easy

A shirt originally costs

\$45

. It is on sale for

20\%

off. Find the sale price.

Answer

The sale price is

\$36.00

First step

Interpret

20\%

as a ratio:

20\% = \dfrac{20}{100} = 0.20

Full solution

2
Calculate the discount: $0.20 \times 45 = \$9.00$ .
3
Sale price $= 45 - 9 = \$36.00$ .

Percent means 'per hundred' — it is a ratio with denominator

100

. Converting the percent to a decimal ratio makes multiplication straightforward. The discount amount is then subtracted from the original price.

Example 2

medium

A student scores

34

out of

40

on a test. Express this as a percentage. Then determine what score out of

40

corresponds to

90\%

Example 3

easy

A pizza has 8 slices and you eat 2. Express the eaten portion as a percent.

Example 4

medium

A team won 14 games out of 20. Express their winning rate as a percent and as a decimal.

Example 5

medium

A car's gas tank holds 16 gallons and currently has 12 gallons. What percent full is it?

Example 6

hard

A salary rose from \$2{,}000 to \$2{,}500 per month. Express the new salary as a percent of the old.

Example 7

challenge

In a class of

50

60\%

are girls. Of the girls,

25\%

play soccer. What percent of the entire class are soccer-playing girls?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

Convert each to the indicated form: (a)

0.045

to percent, (b)

130\%

to decimal, (c)

\dfrac{3}{8}

to percent.

Example 2

medium

A population grew from

8{,}000

9{,}400

. What is the percent increase?

Example 3

easy

Write

25\%

as a fraction out of

100

Example 4

easy

Write

25\%

in lowest terms.

Example 5

easy

Convert

0.35

to a percent.

Example 6

easy

What is

50\%

80

Example 7

easy

Write

\frac{1}{2}

as a percent.

Example 8

easy

What percent is

\frac{3}{4}

Example 9

easy

Convert

7\%

to a decimal.

Example 10

easy

What is

100\%

42

Example 11

medium

30\%

of a class of

40

wear glasses. How many is that?

Example 12

medium

18

out of

24

students passed. What percent passed?

Example 13

medium

\$50

item is

20\%

off. What is the sale price?

Example 14

medium

15\%

of a number is

9

, what is the number?

Example 15

medium

Express the ratio

3:12

as a percent.

Example 16

medium

A price rises from

\$80

\$100

. What is the percent increase?

Example 17

medium

Convert

\frac{5}{8}

to a percent.

Example 18

medium

Which is bigger:

\frac{2}{5}

45\%

Example 19

challenge

A shirt is marked up

25\%

, then put on sale for

20\%

off. Is the final price more, less, or equal to the original?

Example 20

challenge

x\%

y

equals

y\%

x

, prove this holds for all

x,y

Example 21

challenge

A population grows

10\%

per year. By what percent has it grown after 2 years?

Example 22

medium

A tip of

15\%

is added to a

\$40

bill. What is the total?

Example 23

easy

Convert

0.6

to a percent.

Example 24

easy

Write

\dfrac{2}{5}

as a percent.

Example 25

easy

Convert

200\%

to a decimal.

Example 26

easy

Convert

0.005

to a percent.

Example 27

medium

A bag has 15 red and 35 blue marbles. What percent are red?

Example 28

medium

A jacket originally costs \$60 and is on sale for \$45. What percent of the original is the sale price?

Example 29

medium

Convert

\dfrac{7}{20}

to a percent.

Example 30

medium

Out of

250

surveyed shoppers,

40

prefer brand A. What percent prefer brand A?

Example 31

medium

Express

1.25

as a percent.

Example 32

medium

In a survey,

\dfrac{9}{25}

of respondents owned a pet. What percent owned a pet?

Example 33

medium

A test had 50 questions. Mia got 47 right. What percent is correct?

Example 34

hard

A class has boys and girls in the ratio

3:7

. What percent of the class is boys?

Example 35

hard

A solution is

\dfrac{3}{8}

alcohol by volume. What percent alcohol is the solution?

Example 36

hard

A bookstore sold

42

60

copies of a novel. What percent remain unsold?

Example 37

hard

A factory produces

480

widgets per day;

24

are defective. What percent are defective?

Example 38

challenge

A quantity

x

is increased by

20\%

, then decreased by

20\%

. What percent of the original is the final amount?

← Back to Percent as Ratio Formula Explained Practice Mode

Related Concepts

Fractions Decimal Representation Percent Change Probability

Background Knowledge

These ideas may be useful before you work through the harder examples.

fractionsdecimal representation