Free worksheet · Australian Curriculum

Dividing fractions worksheets with answers

To divide by a fraction, multiply by its reciprocal. Learn why it works and every type of question, then make a free worksheet with full solutions.

Make a worksheet ↓How to do it and a quick check ↓

Topic guide

Dividing fractions, explained

The rule is quick to learn. Knowing why it works stops it getting mixed up with the other fraction rules.

1. What dividing by a fraction means

$3 \div \frac{1}{2}$ asks how many halves fit into $3$ . There are two halves in each whole, so

$3 \div \frac{1}{2} = 6$

Dividing by a fraction less than one gives a bigger answer.

2. Keep, change, flip

Keep the first fraction, change $\div$ to $\times$ , flip the second fraction, then multiply:

$\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6}$

Only the second fraction is flipped.

3. Dividing by a whole number

Write the whole number as a fraction over $1$ , then flip it:

$\frac{3}{4} \div 6 = \frac{3}{4} \times \frac{1}{6} = \frac{3}{24} = \frac{1}{8}$

4. Mixed numbers

Change mixed numbers to improper fractions first:

$2\frac{1}{2} \div 1\frac{1}{4} = \frac{5}{2} \div \frac{5}{4} = \frac{5}{2} \times \frac{4}{5} = 2$

5. Cancel before you multiply

After flipping, cancel common factors across the multiplication to keep the numbers small:

$\frac{9}{10} \div \frac{3}{5} = \frac{9}{10} \times \frac{5}{3} = \frac{3}{2} \times \frac{1}{1} = \frac{3}{2} = 1\frac{1}{2}$

Here $9$ and $3$ share a factor of $3$ , and $10$ and $5$ share a factor of $5$ .

6. Word problems

How many $\frac{1}{8}$ L cups can be filled from $\frac{3}{4}$ L of juice?

$\frac{3}{4} \div \frac{1}{8} = \frac{3}{4} \times \frac{8}{1} = 6 \text{ cups}$

Questions asking "how many fit" or "how many pieces" are division.

Quick check: 10 questions

Try each one, then open the answer.

Calculate $4 \div \frac{1}{3}$ .
Answer
$12$
Calculate $\frac{1}{2} \div \frac{1}{4}$ .
Answer
$2$
Calculate $\frac{3}{5} \div \frac{3}{10}$ .
Answer
$2$
Calculate $\frac{2}{3} \div \frac{5}{6}$ .
Answer
$\frac{2}{3} \times \frac{6}{5} = \frac{12}{15} = \frac{4}{5}$
Calculate $\frac{5}{8} \div 2$ .
Answer
$\frac{5}{16}$
Calculate $\frac{7}{9} \div \frac{7}{3}$ .
Answer
$\frac{1}{3}$
Calculate $1\frac{1}{2} \div \frac{3}{4}$ .
Answer
$\frac{3}{2} \times \frac{4}{3} = 2$
Calculate $3\frac{1}{3} \div 2\frac{1}{2}$ .
Answer
$\frac{10}{3} \times \frac{2}{5} = \frac{4}{3} = 1\frac{1}{3}$
Calculate $\frac{4}{5} \div 1\frac{1}{5}$ .
Answer
$\frac{4}{5} \times \frac{5}{6} = \frac{2}{3}$
A $6$ m ribbon is cut into pieces $\frac{3}{4}$ m long. How many pieces are there?
Answer
$6 \div \frac{3}{4} = 8$ pieces

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Six questions across Foundation, Standard and Extension, with full worked solutions, written to the Australian Curriculum.

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These topic pages cover this skill, with worked examples, common mistakes and a question to try.

Year 7 worksheetFraction operations Year 7 worksheetFractions and decimals Year 7 worksheetRatios

Questions

How do you divide fractions?

Keep the first fraction, change the division sign to multiplication, and flip the second fraction. Then multiply the numerators and denominators and simplify.

Why do you flip the second fraction?

Dividing by a number is the same as multiplying by its reciprocal. Dividing by one half asks how many halves fit, and that is the same as multiplying by two.

How do you divide mixed numbers?

Change each mixed number to an improper fraction first, then use keep, change, flip. Simplify the answer and change it back to a mixed number if needed.

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