Signed fraction/decimal calculations | Year 8

01 / LEARN

The idea, step by step

Fractions keep their meaning

For addition and subtraction, first write equivalent fractions with a common denominator. The sign belongs to the whole fraction. For multiplication, multiply numerators and denominators, simplify, and apply the sign rule. For division, multiply by the reciprocal of the nonzero divisor. Cancelling is useful in multiplication, but never cancels terms across an addition sign.

Decimals and negative amounts

Line up decimal places for addition and subtraction. Think about direction before calculating: a temperature fall from a negative starting point moves farther below zero. In multiplication and division, calculate the magnitude and then the sign. Extra trailing zeros can help align places, but they do not change a number.

A common trap

A negative sign can be ignored while adding the numerators.

Instead: Keep the signs in the numerator calculation. $- 8 + 3$ is -5, not 11.

02 / WORKED EXAMPLES

See the thinking

Example 1

Add unlike signed fractions

Calculate $- \frac{3}{4} + \frac{5}{6}$ .

The common denominator is 12: $- \frac{3}{4} = - \frac{9}{12}$ and $\frac{5}{6} = \frac{10}{12}$ .
Add numerators: $\frac{- 9 + 10}{12} = \frac{1}{12}$ .

\frac{1}{12}

Example 2

Combine decimal operations

Calculate $- 1.2 \div 0.3 - (- 0.5)$ .

$- 1.2 \div 0.3 = - 4$ .
Subtracting $- 0.5$ adds $0.5$ .
$- 4 + 0.5 = - 3.5$ .

-3.5

Check your understanding

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

Show answer

$- \frac{3}{4}$

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

03 / WORKSHEET

Your turn

6 questions · 13 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Calculate $- \frac{2}{3} + \frac{1}{4}$ .
2 marks
Calculate $\frac{1}{2} - (- \frac{3}{5})$ .
2 marks
Calculate $(- \frac{5}{6}) (- \frac{9}{10})$ .
2 marks
Calculate $- \frac{3}{4} \div \frac{1}{8}$ .
2 marks
Calculate $- 2.4 + 0.75$ .
2 marks
The temperature is -1.5°C. It falls by 2.75°C, then rises by 0.5°C. Find the final temperature.
3 marks

Read the worked solutions

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

Calculate $- \frac{2}{3} + \frac{1}{4}$ .
2 marks
$- \frac{8}{12} + \frac{3}{12} = - \frac{5}{12}$ .
$- \frac{5}{12}$
Calculate $\frac{1}{2} - (- \frac{3}{5})$ .
2 marks
$\frac{1}{2} + \frac{3}{5} = \frac{5}{10} + \frac{6}{10} = \frac{11}{10}$ .
$\frac{11}{10}$
Calculate $(- \frac{5}{6}) (- \frac{9}{10})$ .
2 marks
The product is positive.
$\frac{45}{60} = \frac{3}{4}$ .
$\frac{3}{4}$
Calculate $- \frac{3}{4} \div \frac{1}{8}$ .
2 marks
$- \frac{3}{4} \times 8 = - 6$ .
-6
Calculate $- 2.4 + 0.75$ .
2 marks
$- 2.40 + 0.75 = - 1.65$ .
-1.65
The temperature is -1.5°C. It falls by 2.75°C, then rises by 0.5°C. Find the final temperature.
3 marks
$- 1.5 - 2.75 + 0.5 = - 4.25 + 0.5 = - 3.75$ .
-3.75°C

Checking saved progress…

Continue learning

Order of operations

Next lesson

Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Four operations with integers; signed fraction/decimal calculations; order of operations; terminating and recurring decimals; rational and irrational numbers; estimating square roots and recognising pi; choosing efficient exact/decimal representations.

Official curriculum source ↗

Back to Integers and rational numbers