Order of Operations (BIDMAS) –

The order of operations — commonly remembered as BIDMAS (or BODMAS) — is a rule that tells you which parts of a calculation to do first. It underpins every numerical and algebraic question in GCSE Maths, from straightforward arithmetic to complex expressions with brackets and powers. Both Foundation and Higher tier students need to apply BIDMAS fluently, and examiners regularly set questions designed to catch those who work left to right without thinking. This page breaks down each level of priority, walks through worked examples, and highlights the traps you must avoid. For advice on structuring your revision, see our how to revise GCSE Maths guide.

What Is BIDMAS?

BIDMAS is a mnemonic for the order in which mathematical operations should be performed:

Key Points

• Division and Multiplication have equal priority. Work through them from left to right.
• Addition and Subtraction have equal priority. Again, work left to right.
• The mnemonic is sometimes written as BODMAS, where "O" stands for "Orders" (another word for indices/powers). They mean exactly the same thing.

Why It Matters

Without a universal order, the expression 3 + 4 × 2 could give either 14 (if you add first) or 11 (if you multiply first). The correct answer is 11, because multiplication takes priority over addition.

Step-by-Step Method

Evaluating a Numerical Expression

1. Brackets first. Evaluate everything inside brackets, starting with the innermost brackets if they are nested.
2. Indices next. Calculate any powers or roots.
3. Division and Multiplication. Work from left to right, doing whichever comes first.
4. Addition and Subtraction. Work from left to right, doing whichever comes first.

Inserting Brackets to Make a Statement True

Some exam questions give you a calculation and a target answer, then ask you to insert brackets. To solve these:

1. Try placing brackets around different pairs of operations.
2. Evaluate each version using BIDMAS.
3. Check which placement gives the target answer.

Using BIDMAS with Negative Numbers

When negative numbers appear:

• −3² means −(3²) = −9 (the square applies only to the 3).
• (−3)² means (−3) × (−3) = 9 (the brackets tell you to square the negative number).

Worked Example 1 — Foundation Level

Question: Work out 5 + 3 × (8 − 2)².

Working:

Step 1 — Brackets: 8 − 2 = 6. The expression becomes 5 + 3 × 6².

Step 2 — Indices: 6² = 36. The expression becomes 5 + 3 × 36.

Step 3 — Multiplication: 3 × 36 = 108. The expression becomes 5 + 108.

Step 4 — Addition: 5 + 108 = 113.

Answer: 113

Worked Example 2 — Higher Level

Question: Insert one pair of brackets to make this statement true: 4 × 3 + 5 − 1 = 31.

Working:

Without brackets, BIDMAS gives: 4 × 3 + 5 − 1 = 12 + 5 − 1 = 16. That is not 31.

Try brackets around (3 + 5): 4 × (3 + 5) − 1 = 4 × 8 − 1 = 32 − 1 = 31. That works.

Answer: 4 × (3 + 5) − 1 = 31

Common Mistakes

• Working strictly left to right without considering priority. In 10 − 2 × 3, some students calculate 10 − 2 = 8, then 8 × 3 = 24. The correct answer is 10 − 6 = 4, because multiplication comes before subtraction.
• Thinking D always comes before M (or A before S). Division and multiplication have equal priority — do whichever appears first from left to right. The same applies to addition and subtraction. The mnemonic can be misleading here.
• Forgetting that a fraction bar acts as a bracket. In the expression (6 + 4) ÷ 2, the fraction bar groups 6 + 4 together. Evaluate the top (and bottom if applicable) before dividing.
• Misapplying indices with negative signs. −5² = −25, not 25. If you want the square of negative five, you need (−5)² = 25. Always check whether the negative sign is inside or outside the brackets.
• Ignoring implied multiplication. In expressions like 2(3 + 4), the 2 is multiplied by the result of the bracket. This is the same as 2 × (3 + 4) = 14.

Exam Tips

• Show each step on a separate line. This makes your working clear and earns method marks. Write the expression, then rewrite it after each operation.
• On calculator papers, use the bracket keys. Modern scientific calculators follow BIDMAS, but entering a complex expression in one go can lead to input errors. Use brackets to be safe.
• BIDMAS applies inside brackets too. If you have (3 + 2 × 5), work inside the bracket using BIDMAS: 2 × 5 = 10 first, then 3 + 10 = 13.
• Practise "insert the brackets" questions. These are popular on Foundation and Higher papers and are easy marks once you are confident with the order. See our formulas guide for more on exam technique.

Practice Questions

Q1 (Foundation): Work out 12 ÷ 4 + 2 × 5.

Q2 (Foundation): Work out (7 + 3)² ÷ 5.

Q3 (Higher): Insert brackets to make this true: 2 + 6 ÷ 2 + 1 = 2.

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Related Topics

• Powers and Roots
• Fractions
• Simplifying Expressions
• Indices and Index Laws

Summary

• BIDMAS stands for Brackets, Indices, Division, Multiplication, Addition, Subtraction.
• Division and Multiplication share equal priority — work left to right.
• Addition and Subtraction share equal priority — work left to right.
• A fraction bar acts as an invisible bracket grouping the numerator and denominator.
• Negative signs and indices interact differently depending on bracket placement.
• Show every step of your working clearly on separate lines for maximum method marks.
• BIDMAS rules apply inside brackets as well as outside them.