Dividing Fractions Examples: 48 Problems with Answers

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

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.

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: Dividing by a fraction asks how many of that size fit, so you multiply by its reciprocal.

Common stuck point: The procedure for dividing fractions is the easy part; the trap is flipping the first fraction instead of the divisor. Asking "Am I asking how many of a fractional size fit into another amount?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Am I asking how many of a fractional size fit into another amount?

Worked Examples

Example 1

easy

Divide

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

Answer

\frac{15}{8} = 1 \frac{7}{8}

First step

Take the reciprocal of the divisor:

\frac{2}{5}

becomes

\frac{5}{2}

Full solution

2
Multiply: $\frac{3}{4} \times \frac{5}{2} = \frac{15}{8}$ .
3
Convert to a mixed number if desired: $\frac{15}{8} = 1\frac{7}{8}$ .

Dividing by a fraction is equivalent to multiplying by its reciprocal. This 'keep-change-flip' rule works because division asks 'how many groups of the divisor fit into the dividend.'

Example 2

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 3

medium

Show that

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

whenever

a \ne 0

and

b \ne 0

Example 4

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 5

challenge

Explain, using a number line, why

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

Practice Problems

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

Example 1

easy

Compute

\frac{5}{6} \div \frac{5}{12}

Example 2

hard

A container holds

\frac{9}{10}

of a litre of juice. Each glass holds

\frac{3}{20}

\frac{1}{4}

-cup servings are in

3

cups?

Example 13

medium

Compute

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

Example 14

medium

Compute

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

Example 15

medium

A board

\frac{7}{8}

m long is cut into

\frac{1}{8}

-m pieces. How many pieces?

Example 16

medium

Compute

\frac{3}{5} \div \frac{6}{25}

Example 17

medium

Simplify the complex fraction

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

Example 18

medium

Compute

\frac{7}{10} \div \frac{7}{10}

and explain quickly.

Example 19

medium

\frac{3}{4}

of a pizza is split among

3

people. How much pizza each?

Example 20

challenge

Simplify

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

Example 21

challenge

Solve for

x

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

Example 22

How many

\frac{1}{3}

-cup servings are in

\frac{5}{6}

cup?

Example 33

medium

Compute

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

Example 34

medium

Compute

1\tfrac{1}{2} \div \frac{3}{8}

Example 35

medium

A roll of tape is

\frac{15}{4}

m long. Each piece needs to be

\frac{3}{8}

x

\frac{3}{4} \div x = \frac{9}{8}

Example 42

hard

Compute

\frac{14}{15} \div \frac{7}{10}

Example 43

challenge

\frac{a}{b} \div \frac{c}{d} = \frac{c}{d} \div \frac{a}{b}

and both fractions are positive, what must be true about

\frac{a}{b}

and

\frac{c}{d}

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Related Concepts

Multiplying Fractions Inverse Operations Fraction of a Number Proportions

Background Knowledge

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

multiplying fractionsinverse operations