Order of Operations: BIDMAS Explained for KS3 Maths

BIDMAS stands for Brackets, Indices, Division, Multiplication, Addition, Subtraction. It is the agreed order in which mathematical operations must be carried out. Without it, the expression 2 + 3 × 4 would give different answers depending on who calculated it — BIDMAS ensures everyone gets the same result: 14, not 20.

What does BIDMAS stand for?

Letter | Operation | Example
B | Brackets | (2 + 3) is calculated first
I | Indices (powers and roots) | 3², √16
D | Division | 12 ÷ 4
M | Multiplication | 3 × 5
A | Addition | 7 + 2
S | Subtraction | 9 − 4

BODMAS (where the O stands for "Order" — another name for indices/powers) means exactly the same thing. Both acronyms describe the same rule. UK schools most commonly use BIDMAS or BODMAS; you may see either on an exam paper.

Why does the order matter?

Mathematics needs one agreed set of rules so that every person — and every computer — reaches the same answer. Without an order of operations, 2 + 3 × 4 could be calculated two ways:

Left to right: (2 + 3) × 4 = 5 × 4 = 20

Multiplication first: 2 + (3 × 4) = 2 + 12 = 14

The correct answer is 14 because multiplication is performed before addition. BIDMAS is a universal convention, not an arbitrary rule.

How to apply BIDMAS: step-by-step worked examples

Work through each expression by identifying the highest-priority operation and calculating it first, then moving to the next.

Worked example 1 — simple expression

Calculate 5 + 3 × 2.

Step 1 — Brackets? None. Step 2 — Indices? None. Step 3 — Division/Multiplication: 3 × 2 = 6. Step 4 — Addition/Subtraction: 5 + 6 = 11.

Answer: 11

Worked example 2 — brackets change everything

Calculate (5 + 3) × 2.

Step 1 — Brackets: 5 + 3 = 8. Step 2 — No indices. Step 3 — Multiplication: 8 × 2 = 16.

Answer: 16

Compare examples 1 and 2: the brackets moved the answer from 11 to 16. This is why placing brackets in the right place is critical.

Worked example 3 — indices (powers)

Calculate 2 + 3².

Step 1 — Brackets? None. Step 2 — Indices: 3² = 9. Step 3 — No division or multiplication. Step 4 — Addition: 2 + 9 = 11.

Answer: 11

Common mistake: students sometimes calculate (2 + 3)² = 5² = 25. The absence of brackets means the index applies only to the 3, not to the whole expression.

Worked example 4 — full BIDMAS expression

Calculate 4 + (6 ÷ 2)² − 1.

Step 1 — Brackets: 6 ÷ 2 = 3, so the expression becomes 4 + 3² − 1. Step 2 — Indices: 3² = 9, giving 4 + 9 − 1. Step 3 — No standalone multiplication or division. Step 4 — Addition and subtraction left to right: 4 + 9 = 13, then 13 − 1 = 12.

Answer: 12

Worked example 5 — division and multiplication at the same level

Calculate 12 ÷ 4 × 3.

Division and multiplication share the same tier in BIDMAS, so work left to right.

12 ÷ 4 = 3, then 3 × 3 = 9.

Answer: 9

If you did multiplication first: 4 × 3 = 12, then 12 ÷ 12 = 1 — wrong. Left to right is the rule when operations share a tier.

Worked example 6 — addition and subtraction at the same level

Calculate 10 − 3 + 2.

Addition and subtraction are at the same tier. Work left to right.

10 − 3 = 7, then 7 + 2 = 9.

Answer: 9

If you added first: 3 + 2 = 5, then 10 − 5 = 5 — wrong again.

Worked example 7 — multi-step problem common in Year 7 tests

Calculate 3 × (2 + 5)² ÷ 7.

Step 1 — Brackets: 2 + 5 = 7. Expression: 3 × 7² ÷ 7. Step 2 — Indices: 7² = 49. Expression: 3 × 49 ÷ 7. Step 3 — Division and multiplication left to right: 3 × 49 = 147, then 147 ÷ 7 = 21.

Answer: 21

What happens inside nested brackets?

When you have brackets inside brackets, work from the innermost pair outward.

Calculate 2 × [(3 + 1)² − 6].

Inner brackets: 3 + 1 = 4. Expression: 2 × [4² − 6]. Indices: 4² = 16. Expression: 2 × [16 − 6]. Outer brackets: 16 − 6 = 10. Expression: 2 × 10. Multiplication: 2 × 10 = 20.

Answer: 20

BIDMAS on a calculator

Scientific calculators (including those used in GCSE exams) follow BIDMAS automatically. However, basic calculators process operations left to right as you enter them. If you type 2 + 3 × 4 = on a basic calculator it returns 20 (wrong). On a scientific calculator it returns 14 (correct). In exams you will always have a scientific calculator — but knowing BIDMAS means you can check your calculator's output makes sense.

How BIDMAS fits the national curriculum

The DfE's KS3 mathematics programme of study (Department for Education) explicitly requires pupils to use conventional notation for priority of operations, including brackets, powers, roots and reciprocals. According to BBC Bitesize's KS3 maths resources, BIDMAS is introduced in Year 7 and tested directly in calculator and non-calculator papers throughout KS3 and GCSE, often embedded within algebra and number problems rather than as a stand-alone question.

Common mistakes at KS3

Mistake | Incorrect working | Correct working
Ignoring BIDMAS, working left to right | 2 + 3 × 4 = 5 × 4 = 20 | 2 + 3 × 4 = 2 + 12 = 14
Applying index to the wrong number | 2 + 3² = 5² = 25 | 2 + 3² = 2 + 9 = 11
Division before multiplication when M comes first | In 3 × 12 ÷ 4, doing 12 ÷ 4 first | Work left to right: 3 × 12 = 36, then 36 ÷ 4 = 9
Subtraction before addition when A comes first | In 10 − 3 + 2, doing 3 + 2 = 5 first | Work left to right: 10 − 3 = 7, then 7 + 2 = 9

Frequently asked questions

What is the difference between BIDMAS and BODMAS?

There is no mathematical difference. Both describe the same order of operations. BODMAS uses "O" for "Order" (meaning powers and roots); BIDMAS uses "I" for "Indices" (same thing). UK schools use both terms. You may also see PEMDAS in American resources, where "E" stands for Exponents and the acronym lists Parentheses (brackets) first.

Does division always come before multiplication in BIDMAS?

No. Division and multiplication share the same priority level. When both appear in the same expression, work left to right. For example, 8 ÷ 2 × 4: do 8 ÷ 2 = 4 first (it appears first reading left to right), then 4 × 4 = 16. Treating the D as always before M is one of the most common BIDMAS errors.

How do I know when to use brackets to change the answer?

Add brackets around any operation you want to perform first. Without brackets, BIDMAS determines the order. With brackets, you override it. For example, to make 2 + 3 × 4 equal 20, write (2 + 3) × 4. Brackets are the most powerful tool for controlling calculation order.

Do indices apply before or after brackets?

Brackets always come first. Evaluate whatever is inside the brackets first, and then apply any index to the result. For example, (2 + 3)²: brackets give 5, then indices give 5² = 25. Compare with 2 + 3² (no brackets): indices give 3² = 9 first, then addition gives 2 + 9 = 11.

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