Related-denominator addition/subtraction | Year 5

01 / LEARN

The idea, step by step

Use the same unit before calculating

We can add three apples and two apples because both amounts use apples. Fractions work in the same way: $\frac{3}{8} + \frac{2}{8} = \frac{5}{8}$ . The denominator stays eight because the pieces are still eighths.

If the denominators are related, rename one fraction. For $\frac{1}{4} + \frac{3}{8}$ , each quarter is two eighths. Now $\frac{2}{8} + \frac{3}{8} = \frac{5}{8}$ . Draw equal-sized wholes if the renaming is difficult to see.

Subtract, simplify and check

For $\frac{5}{6} - \frac{1}{3}$ , write the third as two sixths. Then subtract $\frac{5}{6} - \frac{2}{6} = \frac{3}{6} = \frac{1}{2}$ . A subtraction answer should be smaller than the starting amount when a positive amount is removed.

Adding proper fractions can pass one whole: $\frac{3}{4} + \frac{1}{2} = \frac{3}{4} + \frac{2}{4} = \frac{5}{4} = 1 \frac{1}{4}$ . When mixed numbers occur, keep track of whole parts as well as fraction parts. Use a model if regrouping is needed.

\frac{5}{6} - \frac{1}{3} = \frac{5}{6} - \frac{2}{6} = \frac{3}{6} = \frac{1}{2}

A common trap

Adding denominators: $\frac{1}{3} + \frac{1}{6} = \frac{2}{9}$ .

Instead: Rename thirds as sixths first. $\frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2}$ . The shared denominator names the size of the pieces.

02 / WORKED EXAMPLES

See the thinking

Example 1

Add thirds and sixths

Calculate $\frac{2}{3} + \frac{1}{6}$ .

Rename $\frac{2}{3}$ as $\frac{4}{6}$ .
Add the numerators: $\frac{4}{6} + \frac{1}{6} = \frac{5}{6}$ .
Five and six have no common factor greater than one.

\frac{5}{6}

Example 2

Subtract ribbon lengths

A ribbon is $1 \frac{1}{2}$ metres long. Cut off $\frac{3}{4}$ metre. How much remains?

Write $1 \frac{1}{2}$ as $\frac{6}{4}$ .
Subtract $\frac{6}{4} - \frac{3}{4} = \frac{3}{4}$ .
The remainder is less than the original length, as expected.

\frac{3}{4}

metre.

Check your understanding

Calculate $\frac{3}{5} + \frac{1}{10}$ .

Show answer

$\frac{7}{10}$

$\frac{3}{5} = \frac{6}{10}$ , so $\frac{6}{10} + \frac{1}{10} = \frac{7}{10}$ .

03 / WORKSHEET

Your turn

6 questions · 10 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Calculate $\frac{2}{7} + \frac{3}{7}$ .
1 mark
Calculate $\frac{1}{2} + \frac{1}{4}$ .
1 mark
Calculate $\frac{7}{8} - \frac{1}{4}$ .
2 marks
Calculate $\frac{5}{6} - \frac{1}{2}$ . Simplify your answer.
2 marks
For a picnic, Sam fills $\frac{2}{5}$ of a jug with juice and $\frac{3}{10}$ with water. What fraction of the jug is filled?
2 marks
A bag holds $1 \frac{3}{4}$ kilograms of rice. A cook uses $\frac{1}{2}$ kilogram. How much rice remains?
2 marks

Read the worked solutions

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

Calculate $\frac{2}{7} + \frac{3}{7}$ .
1 mark
Both fractions use sevenths. Add two and three.
$\frac{5}{7}$
Calculate $\frac{1}{2} + \frac{1}{4}$ .
1 mark
$\frac{1}{2} = \frac{2}{4}$ , so $\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$ .
$\frac{3}{4}$
Calculate $\frac{7}{8} - \frac{1}{4}$ .
2 marks
$\frac{1}{4} = \frac{2}{8}$ . Subtract $\frac{7}{8} - \frac{2}{8} = \frac{5}{8}$ .
$\frac{5}{8}$
Calculate $\frac{5}{6} - \frac{1}{2}$ . Simplify your answer.
2 marks
$\frac{1}{2} = \frac{3}{6}$ . Then $\frac{5}{6} - \frac{3}{6} = \frac{2}{6} = \frac{1}{3}$ .
$\frac{1}{3}$
For a picnic, Sam fills $\frac{2}{5}$ of a jug with juice and $\frac{3}{10}$ with water. What fraction of the jug is filled?
2 marks
$\frac{2}{5} = \frac{4}{10}$ .
$\frac{4}{10} + \frac{3}{10} = \frac{7}{10}$ .
$\frac{7}{10}$
A bag holds $1 \frac{3}{4}$ kilograms of rice. A cook uses $\frac{1}{2}$ kilogram. How much rice remains?
2 marks
$\frac{1}{2} = \frac{2}{4}$ .
$1 \frac{3}{4} - \frac{2}{4} = 1 \frac{1}{4}$ .
$1 \frac{1}{4}$ kilograms

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Curriculum reference & lesson scope

Australian Curriculum v9.0; SA Curriculum Mathematics 2026

Equivalence; mixed numbers; ordering; related-denominator addition/subtraction.

Official curriculum source ↗

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