Fraction of a Number Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Fraction of a Number.

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

Concept Recap

Finding a fraction of a number means multiplying that number by the fraction: $\frac{a}{b}$ of $n$ equals $\frac{a}{b} \times n = \frac{a \times n}{b}$ . It answers 'what is this part of the whole amount?'

$\frac{3}{4}$ of 20 means split 20 into 4 equal groups (5 each), then take 3 groups: $3 \times 5 = 15$ .

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 fraction of a number splits the number into equal groups and takes some of them.

Common stuck point: The procedure for fraction of a number is the easy part; the trap is dividing the number by the fraction instead of multiplying. Asking "Does the problem ask for a fraction 'of' a given amount?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Does the problem ask for a fraction 'of' a given amount?

Worked Examples

Example 1

easy

Find

\frac{3}{4}

28

3 out of 4 equal parts are shaded — this is what 3/4 of a whole looks like

Answer

21

First step

Divide by the denominator first:

28 \div 4 = 7

Full solution

2
Multiply by the numerator: $7 \times 3 = 21$ .
3
Alternatively: $\frac{3}{4} \times 28 = \frac{3 \times 28}{4} = \frac{84}{4} = 21$ .

Finding a fraction of a number is multiplication: 'of' means multiply. A practical two-step method is to divide by the denominator first (to find one equal part) and then multiply by the numerator (to count the required parts).

Example 2

medium

A school has

360

students.

\frac{5}{9}

of them play a sport. How many students play a sport?

5 of 9 equal shares are shaded — representing the students who play a sport

Example 3

easy

A pizza has

12

slices. Mia eats

\frac{1}{4}

of it. How many slices did Mia eat?

Example 4

medium

Find

\frac{5}{12}

96

Example 5

medium

Find

\frac{2}{3}

\frac{9}{10}

Example 6

medium

Find

\frac{3}{4}

\$120

Example 7

hard

Lily spent

\frac{1}{3}

of her money on books and

\frac{1}{4}

of what was left on snacks. She has

\$30

remaining. How much did she start with?

Practice Problems

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

Example 1

easy

A bag holds

45

marbles.

\frac{2}{5}

of them are red. How many marbles are red?

2 of 5 equal shares are shaded — the red marbles out of the total

Example 2

hard

A shop has

\$2400

in sales.

medium

What is

\frac{2}{3}

\frac{3}{4}

medium

\frac{2}{5}

of a number is 14. Find the number.

Example 18

medium

Find

\frac{5}{8}

of 64.

Example 19

medium

Find

\frac{3}{4}

\frac{8}{9}

Example 20

challenge

A tank is

\frac{3}{5}

full. After adding 12 L it is

\frac{4}{5}

full. What is the tank's capacity?

Example 21

challenge

Two thirds of the books on a shelf are fiction. Of the fiction,

\frac{1}{4}

are mysteries. If there are 6 mysteries, how many books total?

Example 22

challenge

\frac{3}{8}

A book has

240

pages. Sam read

\frac{5}{8}

of it. How many pages has Sam read?

Example 29

medium

Find

\frac{7}{12}

84

Example 30

medium

A garden has

48

tomato plants.

\frac{3}{4}

have ripe fruit. How many plants have ripe fruit?

Example 31

medium

\frac{5}{6}

of a number is

25

. Find the number.

Example 32

medium

A piece of ribbon is

72

cm long. Cut off

\frac{2}{9}

of it. How long is the piece cut off?

Example 33

medium

Find

\frac{4}{9}

108

Example 34

hard

300

tickets sold,

\frac{2}{5}

went to adults and

\frac{1}{4}

of the rest went to seniors. How many seniors bought tickets?

Example 35

hard

\frac{3}{7}

of a number is

24

more than

\frac{1}{7}

of the number. Find the number.

Example 36

hard

A jar has

96

candies.

\frac{3}{8}

are red and half of the non-red are blue. How many blue candies are in the jar?

Example 37

hard

A farmer harvests

560

kg of apples.

\frac{3}{8}

go to market and

\frac{2}{5}

of the rest are juiced. How many kg are juiced?

Example 38

hard

Three friends share a prize. Andy gets

\frac{1}{3}

, Beth gets

\frac{2}{5}

of the rest, and Chen gets the remaining

\$36

. What was the total prize?

Example 39

challenge

\frac{5}{8}

of a class voted yes and

\frac{1}{4}

voted no; the remaining

6

students abstained. How many students are in the class?

Example 40

challenge

A pool drains

\frac{1}{6}

of its water each hour. After

3

hours,

1000

L remain. How much water did the pool start with? (Round to the nearest liter.)

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Related Concepts

Multiplying Fractions Percent of a Number Decimal-Fraction Conversion

Background Knowledge

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

multiplying fractions