Adding/subtracting fractions | Year 7

01 / LEARN

The idea, step by step

Rename before combining

Adding fractions combines counts of the same-sized part. If the denominators differ, rewrite the fractions using a common denominator. The least common multiple usually keeps the numbers small, but any common denominator will work.

Once the pieces match, add or subtract numerators and keep the denominator. Simplify the final fraction. Adding the denominators changes the piece size and does not describe the original amounts.

Mixed numbers and a size check

Converting mixed numbers to improper fractions gives a dependable method when a whole must be regrouped. You can also separate whole and fractional parts if no regrouping is needed.

Estimate first. A sum of two positive fractions below one must be below two. A positive subtraction should be less than the starting amount. These checks help spot an incorrect common denominator or regrouping step.

A common trap

Adding $\frac{1}{3} + \frac{1}{4}$ gives $\frac{2}{7}$ .

Instead: Rename thirds and quarters as twelfths: $\frac{4}{12} + \frac{3}{12} = \frac{7}{12}$ .

02 / WORKED EXAMPLES

See the thinking

Example 1

Add different parts

Calculate $\frac{3}{8} + \frac{1}{4}$ .

Rename $\frac{1}{4}$ as $\frac{2}{8}$ .
$\frac{3}{8} + \frac{2}{8} = \frac{5}{8}$ .
5 and 8 have no common factor greater than 1.

\frac{5}{8}

Example 2

Subtract from a mixed number

Calculate $2 \frac{1}{4} - \frac{5}{6}$ .

$2 \frac{1}{4} = \frac{9}{4}$ .
$\frac{9}{4} - \frac{5}{6} = \frac{27}{12} - \frac{10}{12} = \frac{17}{12}$ .
$\frac{17}{12} = 1 \frac{5}{12}$ .

1 \frac{5}{12}

Check your understanding

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

Show answer

$\frac{1}{2}$

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

03 / WORKSHEET

Your turn

6 questions · 14 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

$\frac{2}{7} + \frac{3}{7}$
2 marks
$\frac{1}{6} + \frac{1}{4}$
2 marks
$\frac{7}{8} - \frac{1}{4}$
2 marks
$1 \frac{2}{3} + \frac{5}{6}$
2 marks
$3 \frac{1}{5} - 1 \frac{3}{4}$
3 marks
A bottle holds $\frac{3}{4}$ L. You pour out $\frac{2}{5}$ L. What remains?
3 marks

Read the worked solutions

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

$\frac{2}{7} + \frac{3}{7}$
2 marks
The denominators match; add the counts of sevenths.
$\frac{5}{7}$
$\frac{1}{6} + \frac{1}{4}$
2 marks
$\frac{2}{12} + \frac{3}{12} = \frac{5}{12}$ .
$\frac{5}{12}$
$\frac{7}{8} - \frac{1}{4}$
2 marks
$\frac{7}{8} - \frac{2}{8} = \frac{5}{8}$ .
$\frac{5}{8}$
$1 \frac{2}{3} + \frac{5}{6}$
2 marks
$\frac{5}{3} + \frac{5}{6} = \frac{15}{6} = \frac{5}{2}$ .
$2 \frac{1}{2}$
$3 \frac{1}{5} - 1 \frac{3}{4}$
3 marks
$\frac{16}{5} - \frac{7}{4} = \frac{64}{20} - \frac{35}{20} = \frac{29}{20}$ .
$1 \frac{9}{20}$
A bottle holds $\frac{3}{4}$ L. You pour out $\frac{2}{5}$ L. What remains?
3 marks
$\frac{3}{4} - \frac{2}{5} = \frac{15}{20} - \frac{8}{20} = \frac{7}{20}$ .
$\frac{7}{20}$ L

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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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