Calculations and order of operations | OCR GCSE Maths Notes

Visual model

BIDMAS keeps calculations in the right order

BID/MA/Sbrackets, indices, divide or multiply, add or subtract

Gold-standard guide

20 mins

What you will learn

Use the four operations confidently and apply BIDMAS correctly.

Use a clear step-by-step method for calculations and order of operations.

Check your answer and avoid the most common exam mistake.

Useful before you start

Core number skillsEarlier number skillsShowing clear working

Core knowledge

Know the rule, then use it

These are the short notes. Read each one, then check you can use it in the worked example below.

Method

BIDMAS: Brackets → Indices → Division/Multiplication (left to right) → Addition/Subtraction (left to right)

Step 1

Brackets first — always

Work out the bracket: 8 − 2 = 6

Step 2

Indices (powers) second

Square the result: 6² = 36

Step 3

Multiplication and Division left to right

3 × 36 = 108, then 108 ÷ 4 = 27

Watch out

Students often work strictly left to right, ignoring priority rules

Order

$Brackets -> indices -> divisio\frac{n}{multiplication} -> additio\frac{n}{subtraction}.$

Equal priority

Division and multiplication go left to right; addition and subtraction go left to right.

Worked example

Work out 5 + 3 × (8 − 2)² ÷ 4

Brackets first — always: Work out the bracket: 8 − 2 = 6.We must do this first because BIDMAS says brackets take highest priority over everything else.

Indices (powers) second: Square the result: 6² = 36.Indices come before multiplication, division, addition, and subtraction.

Multiplication and Division left to right: 3 × 36 = 108, then 108 ÷ 4 = 27.These have equal priority, so work left to right.

Addition last: 5 + 27 = 32. Addition has the lowest priority and is done last.

Final answer

Question ladder

Build up to the hardest questions

Do them in order. If you miss a step, read the solution, then redo the question without looking.

Workedreasoning

Work out 5 + 3 × (8 − 2)² ÷ 4

4 marks4 minscalculations-and-order-of-operations-worked

Show solution

Worked solution

1.Brackets first — always: Work out the bracket: 8 − 2 = 6.We must do this first because BIDMAS says brackets take highest priority over everything else.
2.Indices (powers) second: Square the result: 6² = 36.Indices come before multiplication, division, addition, and subtraction.
3.Multiplication and Division left to right: 3 × 36 = 108, then 108 ÷ 4 = 27.These have equal priority, so work left to right.
4.Addition last: 5 + 27 = 32. Addition has the lowest priority and is done last.

Final answer

Mark points

M1: brackets first — always
M1: indices (powers) second
M1: multiplication and division left to right
M1: addition last
A1: 32

Watch out

Students often work strictly left to right, ignoring priority rules.For example, computing 5 + 3 = 8 first, then 8 × 6 = 48.This is wrong because multiplication must be done before addition. '

Diagnosticrecall

Work out 3 + 4 × 2

1 mark2 minscalculations-and-order-of-operations-q1

Show solution

Worked solution

1.Spot the skill: BIDMAS: Brackets → Indices → Division/Multiplication (left to right) → Addition/Subtraction (left to right).
2.Use the brackets first — always stage first, then indices (powers) second.
3.Keep the final answer visible: 11.

Final answer

Mark points

M1: use the correct bidmas: brackets → indices → division/multiplication (left to right) → addition/subtraction (left to right).think of it as a priority queue: the higher up the list, the sooner you do it.
A1: 11

Watch out

Students often work strictly left to right, ignoring priority rules.For example, computing 5 + 3 = 8 first, then 8 × 6 = 48.This is wrong because multiplication must be done before addition. '

Easyprocedure

Work out (6 + 2) × 3 − 5

2 marks3 minscalculations-and-order-of-operations-q2

Show solution

Worked solution

1.Spot the skill: BIDMAS: Brackets → Indices → Division/Multiplication (left to right) → Addition/Subtraction (left to right).
2.Use the indices (powers) second stage first, then multiplication and division left to right.
3.Keep the final answer visible: 19.

Final answer

Mark points

M1: use the correct bidmas: brackets → indices → division/multiplication (left to right) → addition/subtraction (left to right).think of it as a priority queue: the higher up the list, the sooner you do it.
A1: 19

Watch out

Students often work strictly left to right, ignoring priority rules.For example, computing 5 + 3 = 8 first, then 8 × 6 = 48.This is wrong because multiplication must be done before addition. '

Mediumreasoning

Work out 20 − 4² ÷ 2 + 1

3 marks4 minscalculations-and-order-of-operations-q3

Show solution

Worked solution

1.Spot the skill: BIDMAS: Brackets → Indices → Division/Multiplication (left to right) → Addition/Subtraction (left to right).
2.Use the multiplication and division left to right stage first, then addition last.
3.Keep the final answer visible: 13.

Final answer

Mark points

M1: use the correct bidmas: brackets → indices → division/multiplication (left to right) → addition/subtraction (left to right).think of it as a priority queue: the higher up the list, the sooner you do it.
A1: 13

Watch out

Students often work strictly left to right, ignoring priority rules.For example, computing 5 + 3 = 8 first, then 8 × 6 = 48.This is wrong because multiplication must be done before addition. '

Hardproblem solving

Work out 3 × (2 + 1)² − 4 × 2

3 marks5 minscalculations-and-order-of-operations-q4

Show solution

Worked solution

1.Spot the skill: BIDMAS: Brackets → Indices → Division/Multiplication (left to right) → Addition/Subtraction (left to right).
2.Use the addition last stage first, then brackets first — always.
3.Keep the final answer visible: 19.

Final answer

Mark points

M1: use the correct bidmas: brackets → indices → division/multiplication (left to right) → addition/subtraction (left to right).think of it as a priority queue: the higher up the list, the sooner you do it.
A1: 19

Watch out

Students often work strictly left to right, ignoring priority rules.For example, computing 5 + 3 = 8 first, then 8 × 6 = 48.This is wrong because multiplication must be done before addition. '

Exam-stylemulti-step

Given that the answer to 2 × (x + 3) − 6 is 10, find x. Show all BIDMAS stages.

4 marks6 minscalculations-and-order-of-operations-q5

Show solution

Worked solution

1.Spot the skill: BIDMAS: Brackets → Indices → Division/Multiplication (left to right) → Addition/Subtraction (left to right).
2.Use the brackets first — always stage first, then indices (powers) second.
3.Keep the final answer visible: x = 5.

Final answer

x = 5

Mark points

M1: use the correct bidmas: brackets → indices → division/multiplication (left to right) → addition/subtraction (left to right).think of it as a priority queue: the higher up the list, the sooner you do it.
A1: x = 5

Watch out

Students often work strictly left to right, ignoring priority rules.For example, computing 5 + 3 = 8 first, then 8 × 6 = 48.This is wrong because multiplication must be done before addition. '

Grade 9 stretchproblem solving

Work out 3 - 2[4 - 3(5 - 7)].

4 marks7 minsbidmas-g9

Show solution

Worked solution

1.Calculate the inner bracket first.
2.Continue outwards, keeping the negative sign attached.
3.Complete the subtraction last.

Final answer

-17

Mark points

M1: obtain 5 - 7 = -2
M1: obtain 4 - 3(-2) = 10
A1: -17

Watch out

Do not rush straight into arithmetic. Select the relevant method and show a complete chain of working.

Hard exam-stylemulti-step problem

Work out 48 / (7 - 3) + 5 × (2 - 6).

3 marks6 minsbidmas-paper

Show solution

Worked solution

1.Evaluate each bracket first.
2.Complete the division and multiplication before adding.
3.Keep the negative result from the second bracket.

Final answer

-8

Mark points

M1: use 48 / 4
M1: use 5 × (-4)
A1: obtain -8

Watch out

Read the full question before calculating. Keep each stage of your working visible.

Timed checkpoint

12 mins - 9 marks

Switch between skills

Set a timer and attempt all four questions before opening any answers. This is closer to the way skills appear in a real paper.

1Calculations and order of operations - 2 marksWork out 3 + 4 × 2Mark answer

Answer

2Integers, decimals and place value - 2 marksWork out 10.5 − 3.72Mark answer

Answer

6.78

3Fractions - 2 marksWork out 2⅓ + 1½Mark answer

Answer

3⅚

4Converting decimals, fractions and percentages - 3 marksA student scores 36 out of 48. Write this as a percentage.Mark answer

Answer

75%

Mastery check

I can explain the method for calculations and order of operations.
I can show clear working without skipping key steps.
I can avoid this mistake: Students often work strictly left to right, ignoring priority rules.For example, computing 5 + 3 = 8 first, then 8 × 6 = 48.This is wrong because multiplication must be done before addition. '

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