Do brackets, indices, division and multiplication, then addition and subtraction — in the right order. It is a Foundation topic, aimed at grade 1. Free questions with answers are on this page. Worked examples show each line before you try the questions.
BIDMAS (or BODMAS) is the order everyone has agreed so that 18÷3+2×4 has one answer, not three. Brackets first, then indices (powers and roots), then division and multiplication working left to right, then addition and subtraction left to right. Division is not 'more important' than multiplication — they share a rung.
5×(8−3)2 is 5×52=5×25=125, not 52. The bracket is squared, not the 5. If a question asks you to insert brackets to make a statement true, try wrapping the addition or subtraction that needs to happen before a multiply.
On the calculator, what you type is what you get. A fraction bar is a hidden pair of brackets: 23+5 is (3+5)÷2, not 3+5÷2.
Objectives
Do brackets before other operations.
Do multiplication and division before addition and subtraction.
Work left to right when two operations are at the same level.
Key points
Evaluate calculations with mixed operations in the correct order.
Deal with brackets and powers first.
Treat division and multiplication as equal priority, working left to right (same for + and −).
Insert brackets to make a calculation give a target answer.
Worked examples
Example 1
Work out 4 + 6 × 3.
2 marks
6 × 3 = 18.
4 + 18 = 22.
4 + 6 × 3 = 22.
Answer: 22
Common slips
Slip: 4 + 6 = 10. Addition does not go first.
Slip: 10 × 3 = 30. 30 is what you get by working strictly left to right.
Slip: 4 + 6 × 3 = 30. The product is added on afterwards.
Example 2
Work out (9 − 4) × 5.
2 marks
Bracket first: 9 − 4 = 5.
5 × 5 = 25.
(9 − 4) × 5 = 25.
Answer: 25
Common slips
Slip: 9 − 20. Without the bracket the multiplication would go first.
Slip: 9 − 4 × 5 = −11. −11 ignores the bracket.
Slip: (9 − 4) × 5 = 9. The 5 outside the bracket still has to be used.
Example 3
Work out 30 − 4 × 2².
3 marks
2² = 4, and only the 2 is squared.
4 × 4 = 16.
30 − 16 = 14.
Answer: 14
Common slips
Slip: 4 × 2 is squared as a pair. There is no bracket around 4 × 2.
Slip: 30 − 4 = 26 first. Subtraction waits.
Slip: 30 − 16 = 46. Subtracting 16 from 30 makes a smaller number.
Questions and answers
GCSE Maths bidmas questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
Work out 7 + 3 × 2.
Show answer
Answer: 13
3 × 2 = 6.
7 + 6 = 13.
M1 — 3 × 2 = 6.
A1 — Answer 13
Question 2 Easy2 marks
Work out 20 − 4 × 3.
Show answer
Answer: 8
4 × 3 = 12.
20 − 12 = 8.
M1 — 4 × 3 = 12.
A1 — Answer 8
Question 3 Medium2 marks
Work out 5 × 4 − 6.
Show answer
Answer: 14
5 × 4 = 20.
20 − 6 = 14.
M1 — 5 × 4 = 20.
A1 — Answer 14
Question 4 Medium2 marks
Work out 16 ÷ 4 × 3.
Show answer
Answer: 12
16 ÷ 4 = 4.
4 × 3 = 12.
M1 — 16 ÷ 4 = 4.
A1 — Answer 12
Question 5 Hard2 marks
Work out 40 − (2 + 3) × 4.
Show answer
Answer: 20
2 + 3 = 5.
5 × 4 = 20, then 40 − 20 = 20.
M1 — 2 + 3 = 5.
A1 — Answer 20
Question 6 Hard2 marks
Work out 6 + 12 ÷ 3 × 2.
Show answer
Answer: 14
12 ÷ 3 = 4.
4 × 2 = 8, then 6 + 8 = 14.
M1 — 12 ÷ 3 = 4.
A1 — Answer 14
Question 7 Exam-style3 marks
Work out 6 × (8 − 3) + 4.
Show answer
Answer: 34
8 − 3 = 5.
6 × 5 = 30, then 30 + 4 = 34.
M1 — Does the bracket
M1 — Multiplies, then adds
A1 — Answer 34
Common mistakes
Most lost marks on this topic are one slip.
Working strictly left to right when a multiplication comes second.
Do the multiplication or division before you add or subtract.
Doing the later multiplication first in a chain such as 24 ÷ 6 × 2.
Division and multiplication share a level, so go left to right.
Squaring more than the number that carries the power.
In 4 × 2² only the 2 is squared, unless a bracket includes the 4.
Spot the slip
In 2 + 3 × 4, what is worked out first?
3 × 4
2 + 3
The first number
Show the slip
3 × 4 Multiplication comes before addition when there are no brackets.
Exam tips
Be ready to do this without a calculator. Paper 1 is the non-calculator paper.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Write each new line in full. Examiners can follow your order and award method marks even if the last step slips.
Circle or underline the operation you are about to do; it keeps you honest about the order.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.