Brackets/order of operations | Year 6

01 / LEARN

Understand the idea.

Follow the structure

Calculate inside brackets first, then powers, then multiplication and division, and finally addition and subtraction. This shared order makes an expression give the same result to every reader. Do not simply perform every operation from left to right.

Multiplication and division have equal priority, so work from left to right between them. Addition and subtraction also have equal priority. A memory word lists groups of priority; it does not put multiplication ahead of every division or addition ahead of subtraction.

Explain the grouped quantity

Brackets describe a grouped quantity. In $3 \times (4 + 2)$ , each of three groups contains six. In $3 \times 4 + 2$ , there are three groups of four followed by two extra units. The different structures explain the different answers.

Keep each line equal to the original expression while replacing one completed part at a time. When checking, look at the structure and brackets as well as the arithmetic; repeating an incorrect operation order will repeat the same error.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Worked example 1

Calculate 6+3×4.

Worked solution

1
Identify the operation with higher priority.
$3 \times 4 = 12$
Multiplication is completed before addition when no brackets change the order.
2
Replace the product and add.
$6 + 3 \times 4 = 6 + 12 = 18$
The remaining operation adds six to the product, giving 18.

Answer

18.

EXAMPLE 02

Worked example 2

Calculate 24÷6×2 and compare it with 24÷(6×2).

Worked solution

1
Start the unbracketed expression on the left.
$24 \div 6 = 4$
Division and multiplication have equal priority, so the leftmost operation comes first.
2
Complete the unbracketed calculation.
$4 \times 2 = 8$
The multiplication uses the result of the preceding division.
3
Evaluate the bracketed product first.
$6 \times 2 = 12$
The bracket makes the whole product the divisor.
4
Complete and compare the bracketed calculation.
$24 \div (6 \times 2) = 24 \div 12 = 2$
Without brackets the result is 8; with this grouped divisor it is 2.

Answer

8 without the bracket; 2 with it.

03 / YOUR TURN

Try it yourself.

Check your understanding

Calculate 5×(2+6).

Show answer & reasoning

40.

The brackets give $2 + 6 = 8$ . Then $5 \times 8 = 40$ .

Keep practising

6 worksheet questions · 9 marks

Open worksheet Worked solutions

Read the questions online

Calculate $7 + 4 \times 3$ .
1 mark
Calculate $(7 + 4) \times 3$ .
1 mark
Calculate $18 \div 3 \times 2$ .
2 marks
Calculate $20 - 6 + 2$ .
1 mark
Calculate $4^{2} + 3 \times 2$ .
2 marks
Five notebooks cost 3 dollars each. A pen costs 2 dollars. Write and evaluate a calculation for the total.
2 marks

Read the worked solutions

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

Calculate $7 + 4 \times 3$ .
1 mark
$4 \times 3 = 12$ ; $7 + 12 = 19$ .
19.
Calculate $(7 + 4) \times 3$ .
1 mark
The bracket gives 11; $11 \times 3 = 33$ .
33.
Calculate $18 \div 3 \times 2$ .
2 marks
$18 \div 3 = 6$ , then $6 \times 2 = 12$ .
12.
Calculate $20 - 6 + 2$ .
1 mark
Work left to right: $20 - 6 = 14$ , then $14 + 2 = 16$ .
16.
Calculate $4^{2} + 3 \times 2$ .
2 marks
$4^{2}$ is 16; $3 \times 2 = 6$ ; $16 + 6 = 22$ .
22.
Five notebooks cost 3 dollars each. A pen costs 2 dollars. Write and evaluate a calculation for the total.
2 marks
Find the notebook cost first, then add the pen.
$5 \times 3 + 2 = 17$ dollars.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Growing rational patterns; rules; brackets/order of operations; unknowns; algorithms.

Official curriculum source ↗

In this lesson

Understand the idea.

Follow the structure

Explain the grouped quantity

See the method in action.

Worked example 1

Identify the operation with higher priority.

Replace the product and add.

Worked example 2

Start the unbracketed expression on the left.

Complete the unbracketed calculation.

Evaluate the bracketed product first.

Complete and compare the bracketed calculation.

Try it yourself.

Check your understanding

Keep practising