Addition and subtraction of fractions | Year 6

01 / LEARN

Understand the idea.

Make the pieces match

Addition and subtraction combine counts of the same kind of piece. Rename unlike fractions with a common denominator first. For thirds and quarters, twelfths let you count all the pieces using a single unit.

Once the pieces match, add or subtract only the numerators. In $\frac{4}{12} + \frac{3}{12} = \frac{7}{12}$ , the answer is still measured in twelfths. Adding denominators would invent a different piece size instead of combining the given amounts.

Simplify and check

Convert a mixed number to an improper fraction when that makes subtraction clearer. Count the parts in the whole number as well as the fractional part. Then rename both fractions, calculate, and simplify if a common factor remains.

Check the result’s size. Adding a positive fraction must increase the starting value; subtracting one must decrease it. A numerator at least as large as its denominator represents at least one whole and may be written as a mixed number.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Worked example 1

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

Worked solution

1
Rename both fractions in twelfths.
$\frac{2}{3} = \frac{8}{12}, \frac{1}{4} = \frac{3}{12}$
Twelve is a common multiple of both denominators.
2
Add the counts of twelfths.
$\frac{8}{12} + \frac{3}{12} = \frac{8 + 3}{12} = \frac{11}{12}$
The pieces stay the same size while their counts are added.
3
Check the answer’s size and form.
$\frac{2}{3} < \frac{11}{12} < 1$
The sum is greater than the starting fraction and has no common factor to simplify.

Answer

$\frac{11}{12}$ .

EXAMPLE 02

Worked example 2

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

Worked solution

1
Convert the mixed number.
$1 \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4}$
The whole contributes four quarters.
2
Rename both amounts in twelfths.
$\frac{5}{4} = \frac{15}{12}, \frac{2}{3} = \frac{8}{12}$
A common denominator makes the parts suitable for subtraction.
3
Subtract the counts.
$\frac{15}{12} - \frac{8}{12} = \frac{7}{12}$
Taking away eight of the fifteen twelfths leaves seven.
4
Check by adding back.
$\frac{7}{12} + \frac{8}{12} = \frac{15}{12} = 1 \frac{1}{4}$
Restoring the subtracted amount gives the original value.

Answer

$\frac{7}{12}$ .

03 / YOUR TURN

Try it yourself.

Check your understanding

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

Show answer & reasoning

$\frac{1}{2}$ .

$\frac{1}{3} = \frac{2}{6}$ , so $\frac{5}{6} - \frac{2}{6} = \frac{3}{6} = \frac{1}{2}$ . Three of the six equal parts make half the whole.

Keep practising

6 worksheet questions · 11 marks

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

Addition/subtraction

In this lesson

Understand the idea.

Make the pieces match

Simplify and check

See the method in action.

Worked example 1

Rename both fractions in twelfths.

Add the counts of twelfths.

Check the answer’s size and form.

Worked example 2

Convert the mixed number.

Rename both amounts in twelfths.

Subtract the counts.

Check by adding back.

Try it yourself.

Check your understanding

Keep practising