Order of operations | Year 8

01 / LEARN

The idea, step by step

A consistent calculation order

Brackets decide which groups are evaluated first. Next calculate powers. Multiplication and division have equal priority and are handled left to right; addition and subtraction are also equal-priority operations handled left to right. The rule does not mean division must always be done before multiplication. Write a new line after each useful stage so the expression remains clear.

Powers and negative signs

In $- 3^{2}$ , the exponent applies to 3 before the outside negative sign, giving -9. In ${(- 3)}^{2}$ , the base is the bracketed number -3, so the product is positive 9. Brackets are mathematical instructions, not decoration. Estimating the likely sign or size first helps detect an order mistake.

A common trap

Multiplication must be finished before every division, even when it is farther right.

Instead: Multiplication and division have equal priority: $24 \div 6 \times 2 = 4 \times 2 = 8$ .

02 / WORKED EXAMPLES

See the thinking

Example 1

A power and a bracket

Calculate $- 2^{2} + 3 (5 - 8)$ .

Bracket: $5 - 8 = - 3$ .
Power: $- 2^{2} = - 4$ ; product: $3 (- 3) = - 9$ .
Add: $- 4 - 9 = - 13$ .

-13

Example 2

Group a denominator

Calculate $36 \div (3 \times 4) + 2^{2}$ .

Inside the bracket, $3 \times 4 = 12$ .
$36 \div 12 = 3$ and $2^{2} = 4$ .
$3 + 4 = 7$ .

Check your understanding

Calculate $6 + 2 \times (- 5)$ .

Show answer

-4

$2 \times (- 5) = - 10$ , then $6 - 10 = - 4$ .

03 / WORKSHEET

Your turn

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

Worksheet PDF Worked solutions

Read the questions online

Calculate $8 - 3 \times 5$ .
2 marks
Calculate $(8 - 3) \times 5$ .
2 marks
Calculate $- 3^{2} + 4$ .
2 marks
Calculate ${(- 3)}^{2} + 4$ .
2 marks
Calculate $24 \div 6 \times 2$ .
2 marks
Calculate $18 - 2 [3 + (- 1)]$ .
3 marks

Read the worked solutions

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

Calculate $8 - 3 \times 5$ .
2 marks
$3 \times 5 = 15$ , so $8 - 15 = - 7$ .
-7
Calculate $(8 - 3) \times 5$ .
2 marks
$8 - 3 = 5$ , then $5 \times 5 = 25$ .
25
Calculate $- 3^{2} + 4$ .
2 marks
$- 3^{2} = - 9$ , then $- 9 + 4 = - 5$ .
-5
Calculate ${(- 3)}^{2} + 4$ .
2 marks
${(- 3)}^{2} = 9$ , then $9 + 4 = 13$ .
13
Calculate $24 \div 6 \times 2$ .
2 marks
Work left to right: $24 \div 6 = 4$ , then $4 \times 2 = 8$ .
8
Calculate $18 - 2 [3 + (- 1)]$ .
3 marks
$3 + (- 1) = 2$ .
$2 \times 2 = 4$ , so $18 - 4 = 14$ .
14

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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.

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