Multiplying/dividing fractions | Year 7

01 / LEARN

The idea, step by step

Taking part of an amount

A product can mean a fraction of a fraction. Half of three quarters is half the area shaded for three quarters of the same whole. Multiply numerators and denominators, then simplify.

Common factors may be cancelled before multiplying, because this divides numerator and denominator by the same amount. Cancel factors in a product, not separate terms in an addition.

Counting fractional groups

Dividing by a fraction asks how many groups of that size fit. Two metres contains four half-metre groups, so division does not always make a number smaller.

Multiply by the reciprocal of a non-zero divisor. Convert mixed numbers to improper fractions first. If the context asks for complete pieces, interpret the fractional count and then find any leftover amount.

A common trap

Division always makes a quantity smaller.

Instead: Dividing by a positive number below one makes the numerical answer larger because you are counting smaller groups.

02 / WORKED EXAMPLES

See the thinking

Example 1

Take part of a mass

Find $\frac{3}{5}$ of $\frac{10}{9}$ kg.

$\frac{3}{5} \times \frac{10}{9} = \frac{30}{45}$ .
Divide top and bottom by 15: $\frac{30}{45} = \frac{2}{3}$ .

\frac{2}{3}

Example 2

Fill cups

A jug contains $\frac{3}{4}$ L. Each cup holds $\frac{1}{8}$ L. How many full cups can be filled?

$\frac{3}{4} \div \frac{1}{8} = \frac{3}{4} \times 8 = 6$ .
Six one-eighth-litre groups make three quarters of a litre.

6 cups

Check your understanding

Calculate $\frac{2}{3} \div \frac{4}{5}$ .

Show answer

$\frac{5}{6}$

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

03 / WORKSHEET

Your turn

6 questions · 15 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

$\frac{2}{5} \times \frac{3}{4}$
2 marks
$\frac{7}{9} \times \frac{3}{14}$
2 marks
$\frac{5}{6} \div \frac{1}{3}$
2 marks
$1 \frac{1}{2} \times \frac{4}{5}$
2 marks
$2 \frac{1}{4} \div \frac{3}{8}$
3 marks
A $2 \frac{1}{2}$ m ribbon is cut into $\frac{3}{4}$ m pieces. How many complete pieces fit, and what length remains?
4 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

$\frac{2}{5} \times \frac{3}{4}$
2 marks
$\frac{6}{20} = \frac{3}{10}$ .
$\frac{3}{10}$
$\frac{7}{9} \times \frac{3}{14}$
2 marks
Cancel 7 with 14 and 3 with 9 to obtain $\frac{1}{3} \times \frac{1}{2}$ .
$\frac{1}{6}$
$\frac{5}{6} \div \frac{1}{3}$
2 marks
$\frac{5}{6} \times 3 = \frac{15}{6} = \frac{5}{2}$ .
$2 \frac{1}{2}$
$1 \frac{1}{2} \times \frac{4}{5}$
2 marks
$\frac{3}{2} \times \frac{4}{5} = \frac{12}{10} = \frac{6}{5}$ .
$1 \frac{1}{5}$
$2 \frac{1}{4} \div \frac{3}{8}$
3 marks
$\frac{9}{4} \times \frac{8}{3} = \frac{72}{12} = 6$ .
6
A $2 \frac{1}{2}$ m ribbon is cut into $\frac{3}{4}$ m pieces. How many complete pieces fit, and what length remains?
4 marks
$\frac{5}{2} \div \frac{3}{4} = \frac{10}{3} = 3 \frac{1}{3}$ , so only three complete pieces fit.
$\frac{5}{2} - 3 \times \frac{3}{4} = \frac{1}{4}$ m.
3 complete pieces; one quarter of a metre remains.

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Equivalent fractions and mixed numbers; ordering rational numbers on number lines; adding/subtracting fractions; multiplying/dividing fractions; four operations with decimals; converting between fractions and decimals; multi-step problems and checking estimates.

Official curriculum source ↗

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