Practice Dividing Fractions in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Dividing by a fraction means multiplying by its reciprocal: $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}$ . This works because division asks 'how many groups of this size fit?'

Imagine you have 2 cups of flour and each serving of a recipe needs $\frac{1}{3}$ cup. How many servings can you make? You are asking 'how many one-thirds fit into 2?'—that is $2 \div \frac{1}{3} = 6$ servings. Division by a fraction counts how many pieces of that size fit inside the whole.

Showing a random 20 of 50 problems.

Example 1

easy

Divide

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

Example 2

medium

Show that

\frac{a}{b} \div \frac{a}{b} = 1

whenever

a \ne 0

and

b \ne 0

Example 3

challenge

Explain, using a number line, why

\tfrac{3}{4} \div \tfrac{1}{8} = 6

Example 4

easy

Compute

\frac{1}{2} \div 2

Example 5

hard

Compute

2\tfrac{2}{3} \div 1\tfrac{1}{9}

Example 6

medium

Compute

\frac{11}{12} \div \frac{1}{6}

Example 7

easy

Compute

\frac{1}{2} \div \frac{1}{4}

Example 8

medium

A roll of tape is

\frac{15}{4}

m long. Each piece needs to be

\frac{3}{8}

m. How many full pieces?

Example 9

medium

A ribbon is

\frac{7}{8}

of a metre long. It is cut into pieces that are each

\frac{1}{4}

of a metre. How many pieces are there?

Example 10

medium

Compute

\frac{2}{3} \div \frac{4}{9}

Example 11

medium

Compute

\frac{7}{8} \div \frac{14}{16}

Example 12

easy

Compute

\frac{6}{7} \div \frac{2}{7}

Example 13

easy

Compute

\frac{5}{8} \div \frac{1}{4}

Example 14

hard

A construction crew can pour

\tfrac{3}{5}

of a concrete pad per hour. How long does it take to pour

\tfrac{9}{10}

of a pad?

Example 15

medium

Compute

\frac{5}{12} \div \frac{10}{9}

Example 16

easy

Compute

1 \div \frac{3}{5}

Example 17

challenge

Simplify

\frac{\frac{1}{2} + \frac{1}{3}}{\frac{1}{6}}

Example 18

hard

A container holds

\frac{9}{10}

of a litre of juice. Each glass holds

\frac{3}{20}

of a litre. How many full glasses can be filled?

Example 19

challenge

Why does 'invert and multiply' work for fraction division?

Example 20

medium

A board

\frac{7}{8}

m long is cut into

\frac{1}{8}

-m pieces. How many pieces?

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Related Concepts

Multiplying Fractions Inverse Operations Fraction of a Number Proportions