GCSE — mathsFoundation2 min read

Order of Operations (BIDMAS)

Master the order of operations using BIDMAS for GCSE Maths. Learn how to evaluate expressions with brackets, indices, and mixed operations.

Tutor AI Team2026-02-25T01:42:18.587Z

BIDMAS (Brackets, Indices, Division, Multiplication, Addition, Subtraction) tells you the order in which to carry out operations when evaluating a mathematical expression. Without BIDMAS, different people would get different answers for the same calculation.

The BIDMAS Rules

Priority	Operation	Example
1st	Brackets	$(3 + 2) \times 4 = 20$
2nd	Indices (powers/roots)	$2^3 = 8$
3rd	Division and Multiplication (left to right)	$12 \div 3 \times 2 = 8$
4th	Addition and Subtraction (left to right)	$5 + 3 - 1 = 7$

Key Points

Division and Multiplication have equal priority — work left to right.
Addition and Subtraction have equal priority — work left to right.
Nested brackets — work from the innermost bracket outward.

Worked Example: Example 1

Problem

$3 + 4 \times 2$

Multiplication first: $4 \times 2 = 8$ . Then: $3 + 8 = 11$ .

Not $3 + 4 = 7$ , then $7 \times 2 = 14$ .

Solution

Worked Example: Example 2

Problem

$(5 + 3)^2 - 10 \div 2$

Brackets: $5 + 3 = 8$ . Indices: $8^2 = 64$ . Division: $10 \div 2 = 5$ . Subtraction: $64 - 5 = 59$ .

Solution

Worked Example: Example 3

Problem

$\frac{6 + 4}{2} + 3^2$

The fraction bar acts as brackets: $\frac{10}{2} = 5$ . Indices: $3^2 = 9$ . Addition: $5 + 9 = 14$ .

Solution

Worked Example: Example 4

Problem

$2 \times (3 + 4 \times 5)$

Inside the bracket: $4 \times 5 = 20$ , then $3 + 20 = 23$ . Outside: $2 \times 23 = 46$ .

Solution

Common Mistakes

Working left to right ignoring priorities. Always check for × and ÷ before + and −.
Forgetting that the fraction bar acts as brackets. Evaluate top and bottom separately.
Mishandling nested brackets. Start from the innermost.

Practice Problems

1. $(7 - 3)^2 + 6 \div 3$
1. $4 \times (2 + 3) - 1$
1. $\frac{12 + 8}{4} - 1$
1. $2^3 + 3 \times 4 - 10$

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Key Takeaways

✓
BIDMAS gives the correct order: Brackets → Indices → Division/Multiplication → Addition/Subtraction.
✓
D and M are equal priority (left to right). A and S are equal priority (left to right).
✓
Fraction bars and square-root signs act like invisible brackets.

Tags:

#gcse#maths#number#bidmas#order-of-operations

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The BIDMAS Rules

Key Points

Worked Example: Example 1

Worked Example: Example 2

Worked Example: Example 3

Worked Example: Example 4

Common Mistakes

Practice Problems

Key Takeaways

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