"What is 4 + 6 × 2?" The wrong answer is 20 (working left to right). The right answer is 16 — because of BIDMAS, the order of operations. Every 11+ maths paper tests this rule somewhere, and getting it wrong is one of the most common avoidable mark-losers. The good news is that BIDMAS is a set of fixed steps: once your child follows them in the same order every single time, these questions become some of the easiest marks on the paper. This guide breaks the rule down in plain English, works through the exact traps that catch 11+ pupils, and shows you how to drill it until it is automatic.
What BIDMAS (and BODMAS) actually stands for
BIDMAS is a memory aid for the order you must carry out the different parts of a calculation. Each letter tells you what to do next:
- B — Brackets: work out anything inside brackets first.
- I — Indices: powers and roots, such as 5² or the square root of 9.
- D — Division.
- M — Multiplication.
- A — Addition.
- S — Subtraction.
BODMAS is exactly the same rule with different wording — the O stands for "Orders", which is just another name for indices. Whether your child's school teaches BIDMAS, BODMAS or BIDMAS's American cousin PEMDAS, the maths is identical. Pick one word and stick with it so your child never has to translate between versions under exam pressure.
The rule most children get wrong: D-M and A-S are tied
This is the single most important idea on the page, and it is the one competitors often skate over. Division and multiplication have equal priority. You do not always do division before multiplication — you do whichever comes first when reading left to right. The same is true for addition and subtraction: they are tied, so you work through them left to right too.
- 12 ÷ 3 × 2 = 4 × 2 = 8 (not 2 — you do not multiply first).
- 10 − 3 + 2 = 7 + 2 = 9 (not 5 — you do not add first).
- 20 ÷ 4 ÷ 5 = 5 ÷ 5 = 1 (left to right again).
A useful way to explain this to a child: think of BIDMAS as four levels, not six. Brackets, then indices, then the "× and ÷ level", then the "+ and − level". Inside each of the bottom two levels, you simply read from left to right like a book.
A full worked example, step by step
Take the expression 2 + 3 × (4 − 1)². Here is exactly how a pupil should lay it out, one operation per line:
- Brackets first: (4 − 1) = 3, so the expression becomes 2 + 3 × 3².
- Indices next: 3² = 9, so it becomes 2 + 3 × 9.
- Multiplication: 3 × 9 = 27, so it becomes 2 + 27.
- Addition last: 2 + 27 = 29.
The discipline of writing one line per step is what separates confident pupils from careless ones. It is slower on question one and far faster over a whole paper, because it stops the "brain skip" where a child jumps straight to adding the first two numbers they see.
The wrong answer versus the right answer
11+ questions are usually multiple choice, and the wrong options are chosen deliberately to match the mistakes children make. Look at 5 + 2 × 3:
| Method | Working | Answer |
|---|---|---|
| Wrong (left to right) | 5 + 2 = 7, then 7 × 3 | 21 |
| Correct (BIDMAS) | 2 × 3 = 6, then 5 + 6 | 11 |
Both 21 and 11 will appear in the answer options. That is why "read the letters in order" is not enough advice on its own — your child has to spot which numbers are attached to the multiplication or division and deal with those before touching the addition.
The BIDMAS traps that catch 11+ pupils
Once the basic rule is secure, marks are lost on a small set of predictable traps. Teach these explicitly:
- Implied multiplication. A number next to a bracket means "multiply". So 3(2 + 1) = 3 × 3 = 9, not 3 + 2 + 1.
- Negatives and squaring. (−2)² = 4 because the whole of −2 is squared, but −2² = −4 because only the 2 is squared and the minus stays outside. This distinction appears in tougher independent-school and CSSE papers.
- Nested brackets. Work from the innermost bracket outwards: in 2 × (3 + (4 − 1)), do 4 − 1 first, then 3 + 3, then double it.
- Division written as a fraction. A fraction line acts like a bracket. In (6 + 4) ÷ 5 the top must be worked out before dividing.
- Long expressions. Don't try to do it all in one leap. One operation, one line, every time.
How BIDMAS appears in the real 11+ exam
Order-of-operations questions are a staple of the maths and, in some regions, the numerical-reasoning sections. Since GL Assessment now sets the tests in most areas (following the phasing out of CEM's separate 11+ papers around 2022–2023), most pupils meet BIDMAS as tightly timed, multiple-choice questions — roughly 50 questions in 50 minutes, about a minute each, answered A–E on a separate answer sheet, and no calculator. In Essex CSSE and many independent papers the same skill can appear as free-response working, where showing each step earns method marks. Either way, the underlying rule is identical; only the answer format changes. For a full breakdown of the paper styles, see our exam guides and the region-by-region notes in the GL 11+ papers overview.
Because the raw score is converted into an age-adjusted Standard Age Score (SAS, roughly 69–141 with 100 as average and many grammars needing around 111+), fast, error-free BIDMAS answers are worth chasing: they are near-guaranteed marks that free up thinking time for the harder problem-solving questions later in the paper.
A quick-reference method your child can memorise
Have your child say this checklist under their breath on every calculation question:
- Are there brackets? Clear them first, innermost first.
- Any indices (powers or roots)? Do those next.
- Now sweep left to right doing × and ÷ as you meet them.
- Finally sweep left to right doing + and −.
- Check: does the answer match one of the options, and did I respect the tied levels?
Year 4 and 5 pupils can start with two-operation questions like 6 + 4 × 2, then progress to Year 6 exam-level expressions with brackets, indices and negatives combined. Building difficulty gradually is far more effective than throwing hard questions at a child who has not yet made the basic rule automatic.
Practice that locks BIDMAS in
The trick is volume of short questions, not a handful of long ones. Ten quick BIDMAS calculations a day for a fortnight will embed the rule far better than one exhausting worksheet. Quest Arena is completely free, so you can drill this as much as you like without a paywall. Our maths worksheets include dedicated BIDMAS drill sheets, and you can then test the skill against the clock in a timed mock paper to build the exam-day speed. When your child is ready to see how the topic sits alongside the rest of the syllabus — fractions, ratio, algebra and geometry — the revision hub maps out the whole maths programme, and the centre-specific mocks match the exact style of 52 selective centres.
Frequently asked questions
Is a calculator allowed for BIDMAS questions in the 11+?
No. Standard GL 11+ maths papers are non-calculator, and pupils must work through the order of operations by hand. That is why laying out one step per line matters so much — it keeps mental arithmetic accurate under time pressure.
What is the difference between BIDMAS and BODMAS?
None mathematically. They are two names for the same rule; the "O" (Orders) and the "I" (Indices) both mean powers and roots. Choose one version and use it consistently so your child is never confused mid-exam.
Do you really always do division before multiplication?
No — this is the biggest misconception. Division and multiplication are equal in priority, so you do whichever appears first reading left to right. The same applies to addition and subtraction. Treat BIDMAS as four levels rather than six.