BIDMAS GCSE Questions and Worked Answers

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Start with the meaning

What you need to know about bidmas

You buy one £5 notebook and three £4 pens. The pens cost £12, so the total is £17. The calculation 5 + 3 × 4 records those purchases: 3 × 4 is one part of the total. Adding 5 and 3 first would describe a different purchase. We use an agreed order so everyone reads the same calculation the same way.

See the idea first

The brackets change what belongs together

Compare the shopping total with four copies of a whole £5 + £3 bundle. A bracket groups its contents into one amount.

Separate purchase5 + 3 × 4three £4 pens, plus a £5 notebook

Multiply first5 + 12 = 17the pens form one part of the total

A different purchase(5 + 3) × 4 = 32four complete £8 bundles

From problem to method

Typical problems you need to be able to solve

These are the main kinds of question in this topic. Each card first states the problem, then explains how to solve it.

Evaluate a mixed calculation

What the problem asks: Work out 8 + 2 × 7.

How to solve it: Multiply 2 by 7, then add 8: 8 + 14 = 22. Keep the part you have not yet calculated on the next line.

Evaluate brackets and a power

What the problem asks: Work out 2 × (3 + 4)².

How to solve it: The bracket gives 7. Squaring means multiplying 7 by itself, so the result is 2 × 49 = 98.

Handle multiplication and division together

What the problem asks: Work out 24 ÷ 6 × 2.

How to solve it: These operations have equal priority. Move left to right: 24 ÷ 6 = 4, then 4 × 2 = 8. The D before M in the acronym does not make division stronger.

Read a fraction bar

What the problem asks: Evaluate (9 + 7) divided by (6 − 2).

How to solve it: A fraction bar groups everything above it and everything below it. Calculate 16 and 4 separately, then divide: 16 ÷ 4 = 4.

A reliable routine

Evaluate an expression containing several operations

An expression is a written calculation. This routine follows its grouping and the standard priority rules; it is a convention for interpreting the expression, not a rule for changing the question.

Calculate inside brackets, starting with the innermost pair. Apply the same order inside them.
Evaluate powers and roots. An index is the small raised number, such as the 2 in 7².
Do multiplication and division from left to right.
Do addition and subtraction from left to right. After each step, copy everything you have not yet calculated.

Check: BODMAS, BIDMAS and PEMDAS describe the same hierarchy. Do not do all divisions before all multiplications, or all additions before subtractions.

Fully worked

BIDMAS GCSE worked examples

Each solution explains the clue, why the method fits and how to check the result.

Example 1

Multiplication before addition

2 marks

Question

Work out 7 + 5 × 6.

The multiplication is one term of the sum.

7+5\times6=7+30

=37

Tip: do not turn the first line into 12 × 6.

Example 2

Equal priority, left to right

2 marks

Question

Work out $36\div9\times3$ .

Division and multiplication have equal priority.

36\div9\times3=4\times3

=12

Doing 9 × 3 first would add grouping that is not there.

Example 3

Subtraction before a later addition

2 marks

Question

Work out 20 − 7 + 2.

Addition and subtraction share one level.

20-7+2=13+2

=15

Tip: it is not 20 − (7 + 2).

Example 4

Brackets, then a square

3 marks

Question

Work out $3(8-5)^2+4$ .

The adjacent 3 means multiplication. Work inside the bracket first.

3(8-5)^2+4=3\times3^2+4

=3\times9+4

=27+4

=31

Squaring 3 gives 9, not 6.

Example 5

The whole numerator and denominator

3 marks

Question

Work out $\dfrac{18+6}{7-3}$ .

The fraction bar groups 18 + 6 above it and 7 − 3 below it.

\frac{18+6}{7-3}=\frac{24}{7-3}

=\frac{24}{4}

=6

Tip: enter (18 + 6) ÷ (7 − 3) on a calculator.

Example 6

A negative base needs brackets

3 marks

Question

Work out $(-4)^2$ and $-4^2$ . Explain the difference.

In the first expression, the whole negative number is squared.

(-4)^2=(-4)\times(-4)=16

In the second, the square applies only to 4; the minus sign remains outside.

-4^2=-(4\times4)=-16

Tip: a calculator needs the same grouping as the written expression.

10 original questions · total 21 marks

BIDMAS GCSE exam-style questions

Try each question before opening its fully worked answer. The difficulty rises through the set.

Before you startAllow about 26 minutes · Show your working. Give exact answers unless a question asks you to round, and include units where needed. · answers start collapsed

1

Multiply first

1 mark

Work out 6 + 4 × 5.

Show worked answer

6+4\times5=6+20

=26

The product comes before the addition.

2

Divide first

1 mark

Work out $19-12\div3$ .

Show worked answer

19-12\div3=19-4

=15

Divide before subtracting.

3

A bracket changes the result

2 marks

Work out $(6+4)\times5$ .

Show worked answer

(6+4)\times5=10\times5

=50

The whole bracket is multiplied by 5.

4

Read left to right

2 marks

Work out $48\div8\times2$ .

Show worked answer

48\div8\times2=6\times2

=12

Do not multiply 8 by 2 first.

5

Addition and subtraction

2 marks

Work out 14 − 9 + 6.

Show worked answer

14-9+6=5+6

=11

Work left to right at this priority level.

6

Powers

2 marks

Work out $2+3^2\times4$ .

Show worked answer

2+3^2\times4=2+9\times4

=2+36

=38

Evaluate the square before multiplication.

7

Nested brackets

3 marks

Work out $5[2+(9-6)]$ .

Show worked answer

5[2+(9-6)]=5[2+3]

=5\times5

=25

Square brackets group calculations just like round brackets.

8

Fraction and power

3 marks

Work out $\dfrac{5^2-1}{2+4}$ .

Show worked answer

\frac{5^2-1}{2+4}=\frac{25-1}{6}

=\frac{24}{6}

=4

Keep all of the numerator over the denominator.

9

Spot the mistake

2 marks

Sam says $30\div5\times2=3$ . Explain the error and correct it.

Show worked answer

Sam has calculated 5 × 2 first. With no brackets, use left to right.

30\div5\times2=6\times2

=12

The answer 3 would belong to 30 ÷ (5 × 2).

10

Explain a negative square

3 marks

Work out $(-3)^2-2^3$ and explain why the answer is not −17.

Show worked answer

(-3)^2-2^3=9-8

=1

The bracket makes −3 the base of the square, giving +9 rather than −9. The answer −17 comes from incorrectly using −9 − 8. A cube means three factors: 2 × 2 × 2 = 8.

Examiner-style feedback

Common bidmas mistakes

Following every letter in strict order

D and M share a level, as do A and S. Read left to right within a level.

Dropping untouched terms

Copy the rest of the expression after each step so a later +4 or minus sign is not lost.

Treating a square as ×2

6² means 6 × 6, not 6 × 2.

30-second recap

Choose, carry out, check

Translate the wording before you reach for a rule.

Brackets specify a group.
Powers come before products.
Equal-priority operations go left to right.
Keep fraction-bar grouping and negative-base brackets.

Quick answers

BIDMAS FAQ

Are BIDMAS and BODMAS different?

No. Indices and orders both refer to powers and roots; the priority rules are the same.

Why does my calculator give a different answer?

Check how you entered brackets, fraction bars and negative powers. The calculator evaluates the expression entered, which may not match the one on the page.

Build connected skills

What to revise next

Use the order

Indices

Understand powers and index laws.

Revise indices

Check a result

Estimation

Use simpler values to check the size of an answer.

Revise estimation

Content standards

Curriculum and rights review

N3: priority of operations, brackets, powers, roots and inverse operations across tiers. Questions, suggested marks, solutions and diagrams are original practice material, not official past-paper questions.

Official specification references

AQA GCSE Maths subject content