Addition and subtraction of fractions | Year 6

01 / LEARN

The idea, step by step

Make the pieces match

Counts can be combined only when they count the same-sized pieces. Rename fractions with different denominators before adding or subtracting them.

For 1/3+1/4, use twelfths: 4/12+3/12=7/12. Only the numerator counts change when adding. The denominator stays 12 because the pieces are still twelfths.

Simplify and check

Simplify the result where possible. If the numerator is at least the denominator, the amount is at least one whole and can also be written as a mixed number.

Adding a positive amount must increase the starting amount. Subtracting a positive amount must decrease it. Use these checks to detect a wrong denominator or a missed whole.

A common trap

$\frac{1}{2} + \frac{1}{3} = \frac{2}{5}$ because both top and bottom numbers are added.

Instead: Halves and thirds have different sizes. Rename as sixths to get 3/6+2/6=5/6.

02 / WORKED EXAMPLES

See the thinking

Example 1

Worked example 1

Calculate $\frac{2}{3} + \frac{1}{4}$ .

Use twelfths: 2/3=8/12 and 1/4=3/12.
8/12+3/12=11/12. It is below 1 but above 2/3.

\frac{11}{12}

Example 2

Worked example 2

Calculate $1 \frac{1}{4} - \frac{2}{3}$ .

Rename 1 1/4 as 5/4.
5/4−2/3=15/12−8/12=7/12.

\frac{7}{12}

Check your understanding

Calculate $\frac{5}{6} - \frac{1}{3}$ .

Show answer

$\frac{1}{2}$ .

1/3=2/6, so 5/6−2/6=3/6=1/2.

03 / WORKSHEET

Your turn

6 questions · 11 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Calculate $\frac{3}{8} + \frac{1}{8}$ .
1 mark
Calculate $\frac{1}{2} + \frac{1}{5}$ .
2 marks
Calculate $\frac{5}{6} - \frac{1}{4}$ .
2 marks
Calculate $\frac{3}{4} + \frac{2}{3}$ .
2 marks
Calculate $2 - \frac{3}{5}$ .
2 marks
A ribbon is $\frac{7}{8}$ metre long. A $\frac{1}{4}$ metre piece is removed. What remains?
2 marks

Read the worked solutions

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

Calculate $\frac{3}{8} + \frac{1}{8}$ .
1 mark
4/8 simplifies to 1/2.
$\frac{1}{2}$ .
Calculate $\frac{1}{2} + \frac{1}{5}$ .
2 marks
5/10+2/10=7/10.
$\frac{7}{10}$ .
Calculate $\frac{5}{6} - \frac{1}{4}$ .
2 marks
10/12−3/12=7/12.
$\frac{7}{12}$ .
Calculate $\frac{3}{4} + \frac{2}{3}$ .
2 marks
9/12+8/12=17/12.
$\frac{17}{12} = 1 \frac{5}{12}$ .
Calculate $2 - \frac{3}{5}$ .
2 marks
2=10/5; 10/5−3/5=7/5.
$1 \frac{2}{5}$ .
A ribbon is $\frac{7}{8}$ metre long. A $\frac{1}{4}$ metre piece is removed. What remains?
2 marks
1/4=2/8; 7/8−2/8=5/8.
$\frac{5}{8}$ metre.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Equivalence; comparing/ordering; addition/subtraction; practical quantities.

Official curriculum source ↗

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