Multiplying Fractions Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Multiplying Fractions.

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

Concept Recap

To multiply fractions, multiply the numerators together and the denominators together: $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$ . Simplify the result by cancelling common factors.

$\frac{2}{3} \times \frac{3}{4}$ means 'two-thirds of three-quarters.' Take $\frac{3}{4}$ of something, then take $\frac{2}{3}$ of that result.

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: Multiplying fractions multiplies the tops and the bottoms — it means taking a fraction of a fraction.

Common stuck point: The procedure for multiplying fractions is the easy part; the trap is finding a common denominator before multiplying. Asking "Am I taking a part of a part, multiplying tops and bottoms straight across?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Am I taking a part of a part, multiplying tops and bottoms straight across?

Worked Examples

Example 1

easy

Multiply

\frac{2}{3} \times \frac{5}{7}

Answer

\frac{10}{21}

First step

Multiply the numerators:

2 \times 5 = 10

Full solution

2
Multiply the denominators: $3 \times 7 = 21$ .
3
The product is $\frac{10}{21}$ , which is already in simplest form since $\gcd(10, 21) = 1$ .

To multiply fractions, multiply numerator by numerator and denominator by denominator. No common denominator is needed, unlike addition.

Example 2

medium

Compute

\frac{4}{9} \times \frac{3}{8}

4/9 × 3/8 simplifies to 1/6

Example 3

easy

Multiply

\frac{2}{7} \times \frac{3}{4}

and simplify if possible.

2/7 × 3/4 = 3/14 of the whole

Example 4

medium

Compute

3\frac{1}{3} \times \frac{3}{5}

Example 5

medium

Compute

2\frac{1}{4} \times 1\frac{1}{3}

Example 6

hard

Solve for

x

\frac{3}{5} \times x = \frac{9}{20}

Practice Problems

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

Example 1

easy

Multiply

\frac{3}{5} \times \frac{2}{9}

3/5 × 2/9 = 2/15 of the whole

Example 2

medium

A tank is

\frac{3}{4}

full. If

\frac{2}{5}

of the water is used, what fraction of the tank is still full?

Tank 3/4 full; 2/5 used — 9/20 of the tank remains

Example 3

easy

Compute

\frac{1}{2} \times \frac{1}{3}

1/2 × 1/3: the product is 1 out of 6 equal parts

Example 4

easy

Compute

\frac{2}{3} \times \frac{4}{5}

2/3 × 4/5 = 8/15 of the whole

Example 5

easy

Compute

\frac{3}{4} \times \frac{2}{3}

3/4 × 2/3: start with 3/4, take 2/3 of it — result is 1/2

Example 6

easy

Compute

\frac{1}{4} \times 8

Example 7

easy

Compute

\frac{2}{5} \times \frac{5}{2}

Example 8

easy

Compute

\frac{1}{2} \times \frac{1}{2}

1/2 × 1/2: half of a half equals one quarter

Example 9

easy

Compute

\frac{3}{10} \times \frac{5}{6}

Example 10

easy

Compute

\frac{0}{5} \times \frac{7}{8}

Example 11

medium

Compute

2\frac{1}{2} \times \frac{3}{4}

Example 12

medium

Compute

\frac{6}{8} \times \frac{4}{9}

6/8 × 4/9 simplifies to 1/3

Example 13

medium

Compute

\frac{2}{3}

\$45

Example 14

medium

Compute

\frac{3}{5} \times \frac{10}{9}

Example 15

medium

Compute

\frac{1}{2} \times \frac{2}{3} \times \frac{3}{4}

Example 16

medium

Compute

\left(\frac{2}{3}\right)^3

Example 17

medium

A recipe calls for

\frac{3}{4}

cup flour. If you make

\frac{2}{3}

of the recipe, how much flour?

Recipe: 3/4 cup flour; 2/3 of the recipe needs only 1/2 cup

Example 18

medium

Compute

\frac{4}{5} \times \frac{15}{16}

4/5 × 15/16 = 3/4

Example 19

medium

Compute

\frac{3}{8} \div \frac{1}{4}

Example 20

challenge

Compute

\frac{1}{2} \times \frac{3}{4} \times \frac{5}{6} \times \frac{7}{8}

Example 21

challenge

What is the product of the first

50

terms:

\frac{1}{2} \cdot \frac{2}{3} \cdot \frac{3}{4} \cdots \frac{50}{51}

Example 22

challenge

Find

\frac{a}{b}

such that

\frac{a}{b} \times \frac{3}{5} = \frac{1}{10}

where

\gcd(a, b) = 1

Example 23

easy

Compute

\frac{1}{3} \times \frac{1}{5}

1/3 × 1/5 = 1/15 of the whole

Example 24

easy

Compute

\frac{3}{4} \times \frac{1}{2}

3/4 × 1/2: taking half of 3/4 gives 3/8

Example 25

easy

Compute

\frac{5}{6} \times \frac{0}{7}

Example 26

easy

Compute

\frac{4}{5} \times 1

Example 27

medium

Compute

\frac{8}{9} \times \frac{3}{4}

8/9 × 3/4 simplifies to 2/3

Example 28

medium

Compute

\frac{7}{10} \times \frac{5}{14}

7/10 × 5/14 simplifies to 1/4

Example 29

medium

Find

\frac{3}{8}

\$64

Example 30

medium

Compute

\frac{5}{12} \times \frac{8}{15}

5/12 × 8/15 = 2/9 of the whole

Example 31

medium

Compute

\left(\frac{3}{4}\right)^2

(3/4)²: squaring 3/4 produces 9/16 — a smaller fraction

Example 32

medium

A pitcher holds

\frac{5}{6}

L of juice. If

\frac{3}{5}

of it is poured out, how much was poured?

3/5 of 5/6 L poured out equals 1/2 L

Example 33

medium

Compute

\frac{2}{9} \times \frac{9}{2}

Example 34

hard

Compute

\frac{7}{8} \times \frac{16}{21}

Example 35

hard

A garden is

\frac{3}{4}

acre.

\frac{2}{5}

of it is planted with corn, and

\frac{1}{3}

of that corn area is sweet corn. What fraction of the garden is sweet corn?

Example 36

hard

Compute

\frac{2}{3} \times \frac{3}{4} \times \frac{4}{5} \times \frac{5}{6}

Example 37

hard

A recipe makes

\frac{4}{5}

kg of cookies and you want to make

\frac{2}{3}

of the recipe. How many kg of cookies?

2/3 × 4/5 kg = 8/15 kg of cookies

Example 38

hard

Compute

\frac{15}{16} \times \frac{8}{25}

15/16 × 8/25 = 3/10 of the whole

Example 39

challenge

Compute the product

\prod_{k=2}^{10} \frac{k-1}{k}

(that is,

\frac{1}{2}\cdot\frac{2}{3}\cdots\frac{9}{10}

Example 40

challenge

Find positive integers

a, b

in lowest terms with

\gcd(a,b)=1

so that

\frac{a}{b} \times \frac{7}{12} = \frac{1}{3}

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Related Concepts

Fractions Multiplication Dividing Fractions Fraction of a Number

Background Knowledge

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

fractionsmultiplication