The idea, step by step
Follow the structure
Brackets show a group that must be calculated first. Next calculate powers such as squares. Multiplication and division come before addition and subtraction. This order makes a written calculation mean the same thing to every reader.
Multiplication and division have equal priority: work from left to right when both occur. Addition and subtraction also have equal priority. A memory word is not a reason to do every addition before every subtraction.
Explain the grouped quantity
In 3×(4+2), the bracket means three groups each containing 4+2. Without the bracket, 3×4+2 means three groups of 4, then two more. A story or a picture can show why the results differ.
Write intermediate calculations on separate lines without changing the value. If your answer seems too large or too small for the context, reread the brackets rather than just repeating the same button presses.
A common trap
Addition always comes before subtraction because its letter comes first in a memory word.
Instead: They have equal priority. For 12−4+3, work left to right: 8+3=11.
See the thinking
Worked example 1
Calculate 6+3×4.
- Multiply first: 3×4=12.
- Then add: 6+12=18.
Worked example 2
Calculate 24÷6×2 and compare it with 24÷(6×2).
- In 24÷6×2, division and multiplication have equal priority: 24÷6=4, then 4×2=8.
- In 24÷(6×2), the bracket is 12, so 24÷12=2.
Check your understanding
Calculate 5×(2+6).
Show answer
40.
The bracket gives 8, then 5×8=40.
Your turn
6 questions · 9 marks · Work at your own pace.
Read the questions online
- Calculate 7+4×3.1 mark
- Calculate (7+4)×3.1 mark
- Calculate 18÷3×2.2 marks
- Calculate 20−6+2.1 mark
- Calculate 4 squared + 3×2.2 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+4×3.1 mark
4×3=12; 7+12=19.
19. - Calculate (7+4)×3.1 mark
The bracket gives 11; 11×3=33.
33. - Calculate 18÷3×2.2 marks
18÷3=6, then 6×2=12.
12. - Calculate 20−6+2.1 mark
Work left to right: 20−6=14, then 14+2=16.
16. - Calculate 4 squared + 3×2.2 marks
4 squared is 16; 3×2=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.
5×3+2=17 dollars.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Growing rational patterns; rules; brackets/order of operations; unknowns; algorithms.
Official curriculum source ↗