Sheet № 10 · Foundation + Higher · AQA · Edexcel · OCR
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
§Key definitions
Question:
Work out 5 + 3 × (8 − 2)².
Answer:
4 × (3 + 5) − 1 = 31
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.
§Formulas to memorise
Brackets first, then Indices, then Division and Multiplication (left to right), then Addition and Subtraction (left to right)
Division and Multiplication have equal priority. — Work through them from left to right.
Addition and Subtraction have equal priority. — Again, work left to right.
Brackets first. — Evaluate everything inside brackets, starting with the innermost brackets if they are nested.
Indices next. — Calculate any powers or roots.
Division and Multiplication. — Work from left to right, doing whichever comes first.
Addition and Subtraction. — Work from left to right, doing whichever comes first.
−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
Work out 5 + 3 × (8 − 2)².
Working:
⚠ 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.