Is BIDMAS included in GCSE Maths Foundation?

Yes. Order of operations is Foundation content. You need to apply the conventional priority of operations when working with brackets, powers, roots and calculations involving several operations.

Does division always come before multiplication in BIDMAS?

No. Division and multiplication have equal priority, so evaluate them from left to right. For example, $12\times2\div3=24\div3=8$.

Does addition always come before subtraction?

No. Addition and subtraction have equal priority. Work from left to right, so $10-4+2=6+2=8$.

What is the difference between BIDMAS and BODMAS?

They describe the same order of operations. In BIDMAS, I stands for indices; in BODMAS, O stands for orders. Both refer to evaluating powers and roots before multiplication and division.

How does BIDMAS work with a fraction bar?

A fraction bar groups the entire numerator and denominator. Evaluate each group using the order of operations, then divide the numerator by the denominator.

BIDMAS (Order of Operations): GCSE Maths Foundation

BIDMAS tells you the correct order for working out a calculation: brackets first, then indices, then multiplication and division, then addition and subtraction. Multiplication and division have equal priority, as do addition and subtraction. Within each pair, work from left to right.

This BIDMAS (order of operations) GCSE Maths Foundation guide explains each stage, shows worked examples and gives you exam-style practice questions with answers. The aim is to help you choose the correct next step, rather than simply remember six letters.

What does BIDMAS mean?

BIDMAS is a memory aid for the order of operations. An operation is a mathematical action, such as adding, multiplying or squaring.

Letter	Meaning	What to do
B	Brackets	Work out calculations inside brackets first.
I	Indices	Evaluate powers and roots.
D and M	Division and multiplication	Work from left to right, giving both equal priority.
A and S	Addition and subtraction	Work from left to right, giving both equal priority.

The most important point is that BIDMAS describes four priority levels, not six separate stages. The position of D before M does not mean that division always comes before multiplication.

You may also hear BODMAS, where O stands for orders, meaning powers and roots. It describes the same rules.

Why does the order matter?

Consider:

6+4\times3

Multiplication has priority over addition, so the calculation means:

6 + 12 = 18

Adding first would give a different answer. If the intention were to add first, brackets would be needed:

(6+4)\times3=10\times3=30

Brackets therefore change the meaning of a calculation. They are instructions, not decoration.

BIDMAS (order of operations) at GCSE Maths Foundation

Order of operations is part of Foundation content. Both AQA and Pearson Edexcel include conventional notation for the priority of operations, including brackets, powers, roots and reciprocals, in their specifications.

You need this skill for direct number calculations and when evaluating expressions, substituting into formulae or calculating with fractions. It is worth securing early because an order-of-operations mistake can affect otherwise accurate work.

Check your wider revision coverage using the GCSE maths topics by exam board and tier guide. The examples below focus on calculations suitable for Foundation revision.

How to apply BIDMAS step by step

Use the same routine each time:

Check the whole expression. Identify brackets, powers, roots and fraction bars before calculating.
Evaluate brackets. Start with the innermost brackets if there is more than one set.
Evaluate powers and roots. Keep track of exactly which number or expression they apply to.
Multiply and divide from left to right. Complete these before addition or subtraction.
Add and subtract from left to right. Finish the remaining calculation.

BIDMAS also applies inside brackets. You do not automatically work from left to right just because an expression is inside them.

Rewrite the whole expression after each stage. This makes it easier to preserve signs and avoid accidentally leaving out a number.

BIDMAS (order of operations) worked examples

Example 1: Multiplication before addition

Work out:

8+5\times4

Multiply first:

5\times4=20

Then add:

8 + 20 = 28

The answer is $28$ . Starting with $8 + 5$ would ignore the priority of multiplication.

Example 2: Operations inside brackets

Work out:

3\times(4+2\times5)

The brackets come first, but multiplication still has priority inside them:

3\times(4+10)

Complete the brackets, then multiply:

3\times14=42

The answer is $42$ . The instruction “brackets first” means evaluate the bracketed expression correctly, using the same order-of-operations rules.

Example 3: Powers before multiplication

Work out:

5+2\times3^2

Evaluate the power:

3^2=3\times3=9

Then multiply and finally add:

5+2\times9=5+18=23

The answer is $23$ . Remember that $3^2$ means $3×33\times3$ , not $3×23\times2$ . If this stage needs more practice, use the Powers and Roots questions.

Example 4: Multiplication and division have equal priority

Work out:

24\div6\times2

Work from left to right:

24\div6\times2=4\times2=8

The answer is $8$ . Multiplying $6×26\times2$ first would incorrectly treat those numbers as a group. There are no brackets telling you to do that.

The same rule applies to addition and subtraction:

15 - 6 + 2 = 9 + 2 = 11

Do not add $6 + 2$ first just because A appears before S in BIDMAS.

Example 5: A fraction bar groups calculations

Work out:

\frac{7+5}{8-4}

A fraction bar groups the whole numerator and the whole denominator. Evaluate both before dividing:

\frac{12}{4}=3

The answer is $3$ . Treating a fraction bar as a division sign without preserving these groups can change the calculation.

Example 6: Negative numbers and brackets

Work out:

(-3)^2+4\times(-2)

First evaluate the square:

(-3)^2=(-3)\times(-3)=9

Then multiply:

4\times(-2)=-8

Finally, add:

9 + (- 8) = 1

The answer is $1$ . Notice that $3)^2=9$ , whereas $3^2=-9$ : without brackets, the square applies to $3$ before the negative sign is applied. Use the Negative Numbers questions if sign errors are affecting your answers.

Common BIDMAS mistakes and how to avoid them

Common mistake	Why it goes wrong	Better habit
Working through everything from left to right	Some operations have higher priority.	Identify the highest-priority operation first.
Always dividing before multiplying	Division and multiplication have equal priority.	Work through these operations from left to right.
Always adding before subtracting	Addition and subtraction have equal priority.	Keep each sign attached to its number and work left to right.
Treating a square as multiplication by two	A square means multiplying a number by itself.	Write the power as repeated multiplication if unsure.
Ignoring grouping in a fraction	The fraction bar groups the numerator and denominator.	Evaluate each group before dividing.
Dropping a negative sign while rewriting	This changes the value of the expression.	Copy all unchanged numbers and signs carefully.

An answer can be arithmetically accurate but still wrong because the operations were performed in the wrong order. When checking, examine your choice of first step as well as your number work.

Try an exam-style BIDMAS question

Work out:

30-2\times(4+3)

Write down an intermediate step before checking the answer below.

Answer: Start with the brackets, then multiply:

30-2\times7=30-14=16

If you reached $196$ , you probably subtracted before multiplying. The subtraction must wait until the multiplication is complete.

Try 4 more using MathsGenie's BIDMAS practice questions. Work through four questions and check the solutions after attempting them yourself.

BIDMAS (order of operations) exam questions

These are original Foundation-level exam-style questions, not quotations from an exam paper. Attempt them without a calculator first so that your method tests your understanding of the order of operations.

Question	Task
A	Work out $18−3×418-3\times4$ .
B	Work out $(18−3)×4(18-3)\times4$ .
C	Work out $32÷4×232\div4\times2$ .
D	Work out $6+23×36+2^3\times3$ .
E	Work out $15+99−3\frac{15+9}{9-3}$ .
F	Work out $20−(3+2×4)20-(3+2\times4)$ .
G	Insert one pair of brackets into $8+4×38+4\times3$ to make the answer $36$ .
H	A student writes $20 - 8 + 3 = 9$ . Explain the mistake and give the correct answer.

Answers and checking steps

Question	Answer and method
A	$18 - 12 = 6$ . Multiply first.
B	$15×4=6015\times4=60$ . Evaluate the brackets first.
C	$8×2=168\times2=16$ . Divide and multiply from left to right.
D	$6+8×3=6+24=306+8\times3=6+24=30$ . Evaluate the power before multiplying.
E	$246=4\frac{24}{6}=4$ . Evaluate the numerator and denominator separately.
F	$20 - (3 + 8) = 20 - 11 = 9$ . Multiply inside the brackets before adding.
G	$(8+4)×3=36(8+4)\times3=36$ . The brackets make addition happen first.
H	The student added $8 + 3$ before subtracting. Addition and subtraction have equal priority, so $20 - 8 + 3 = 12 + 3 = 15$ .

Questions A and B show why brackets matter: the numbers and operations are the same, but the grouping changes the answer.

How to revise BIDMAS effectively

Start by checking your first step before doing any arithmetic. Ask yourself which operation has priority and whether any brackets or fraction bars group parts of the calculation.

Use a short, focused routine:

Attempt a few questions independently.
Compare your working with the solution.
Identify whether each error involved priority, arithmetic or a copied sign.
Redo incorrect questions without looking at the answer.
Return later to check that you can still choose the correct order.

On calculator questions, enter the expression with its grouping preserved. Use brackets where needed, especially around a numerator or denominator, and check the display before evaluating. Calculator layouts vary, so practise using your own model.

Showing intermediate working is sensible exam technique, particularly in longer calculations. Any method marks depend on the question's mark scheme; writing a step does not automatically earn a mark.

Build confidence with the order of operations

The essential rule is to work through brackets, powers and roots, multiplication and division, then addition and subtraction. Equal-priority operations are evaluated from left to right, and grouping symbols must be preserved throughout.

If you still hesitate over the next step, revisit the MathsGenie BIDMAS revision guide. Then use the BIDMAS exam-style booklet with answers for a focused practice session, checking your method as carefully as your final answer.

Sources and referenced URLs

What does BIDMAS mean?

BIDMAS is a memory aid for the order of operations. An operation is a mathematical action, such as adding, multiplying or squaring.

Letter	Meaning	What to do
B	Brackets	Work out calculations inside brackets first.
I	Indices	Evaluate powers and roots.
D and M	Division and multiplication	Work from left to right, giving both equal priority.
A and S	Addition and subtraction	Work from left to right, giving both equal priority.

The most important point is that BIDMAS describes four priority levels, not six separate stages. The position of D before M does not mean that division always comes before multiplication.

You may also hear BODMAS, where O stands for orders, meaning powers and roots. It describes the same rules.