Efficient whole-number calculations and order of operations | Year 7

01 / LEARN

The idea, step by step

An expression gives an order

Brackets tell us which calculation to do together. After brackets, evaluate powers, then multiplication and division, then addition and subtraction. Operations at the same level are done from left to right.

A multiplication sign may be hidden beside a bracket: $5 (8 + 2)$ means $5 \times (8 + 2)$ . Copy the unchanged parts when showing each step, so it is clear which calculation has been done.

Efficient does not mean changing the problem

For addition and multiplication, regrouping can make calculations easier. For example, $25 \times 16 = 25 \times 4 \times 4 = 100 \times 4$ . Subtraction and division do not allow arbitrary regrouping.

Check whether an answer is a reasonable size before accepting it. A good method is one you can explain and that keeps the expression equivalent at every step.

A common trap

Addition is always done before subtraction, and multiplication is always done before division.

Instead: Addition/subtraction share one priority level; multiplication/division share another. Work left to right within each level.

02 / WORKED EXAMPLES

See the thinking

Example 1

Multiplication comes before addition

Evaluate $18 + 6 \times 4$ .

Calculate the product first: $6 \times 4 = 24$ .
Then calculate $18 + 24 = 42$ .

Example 2

Brackets and two equal-priority operations

Evaluate $8 (15 - 9) + 12 \div 3$ .

The bracket gives $15 - 9 = 6$ .
Calculate $8 \times 6 = 48$ and $12 \div 3 = 4$ .
Finally, $48 + 4 = 52$ .

Check your understanding

Evaluate $24 \div 6 + 2^{3}$ .

Show answer

The division gives 4 and the power gives 8; $4 + 8 = 12$ .

03 / WORKSHEET

Your turn

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

Worksheet PDF Worked solutions

Read the questions online

Evaluate $72 \div (3 \times 4)$ .
2 marks
Evaluate $30 - 12 \div 3 + 2$ .
2 marks
Evaluate $15 + 4^{2} - 9$ .
2 marks
Evaluate $5 (8 + 6)$ .
2 marks
Evaluate $96 \div 8 \div 3$ .
2 marks
Six cinema tickets cost 9 dollars each. A single booking fee of 4 dollars is added. Find the total cost.
3 marks

Read the worked solutions

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

Evaluate $72 \div (3 \times 4)$ .
2 marks
Calculate the bracket: $3 \times 4 = 12$ .
Then $72 \div 12 = 6$ .
6
Evaluate $30 - 12 \div 3 + 2$ .
2 marks
Division first gives $12 \div 3 = 4$ .
Then work left to right: $30 - 4 + 2 = 26 + 2 = 28$ .
28
Evaluate $15 + 4^{2} - 9$ .
2 marks
The power is $4^{2} = 16$ .
Then $15 + 16 - 9 = 31 - 9 = 22$ .
22
Evaluate $5 (8 + 6)$ .
2 marks
The bracket is $8 + 6 = 14$ .
Multiply: $5 \times 14 = 70$ .
70
Evaluate $96 \div 8 \div 3$ .
2 marks
Both operations have equal priority.
Work left to right: $96 \div 8 = 12$ , then $12 \div 3 = 4$ .
4
Six cinema tickets cost 9 dollars each. A single booking fee of 4 dollars is added. Find the total cost.
3 marks
Ticket cost is $6 \times 9 = 54$ dollars.
Add the one booking fee: $54 + 4 = 58$ dollars.
58 dollars

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum

Place value and powers of ten; efficient whole-number calculations and order of operations; factors, multiples and primes; prime factorisation and exponent notation; square numbers and square roots; estimation and rounding.

Official curriculum source ↗

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