BIDMAS and the order of operations: why multiplication before addition? An explanation for children

Your child comes home with a calculation like 2 + 3 × 4 and asks: where do you start? The answer is not obvious — and behind it stands an international agreement, centuries old, that is worth knowing about.

The problem: the same calculation, two different answers

Imagine your child brings home the following calculation: 2 + 3 × 4. One friend of theirs works out 2 + 3 = 5, and then 5 × 4 = 20. Your child works out 3 × 4 = 12 and then 2 + 12 = 14. The two of them keep arguing — who is right?

The real problem is not who is cleverer, but that without an agreed rule, everyone can get a different answer to the same mathematical expression. For maths to work as a universal language — from space scientists to bridge engineers — everyone has to get the same answer. That is exactly why the rules for the order of operations were created.

The international agreement: why is there a rule at all?

For hundreds of years, mathematicians in different countries wrote formulae in different ways. As trade, science and engineering began to spread between countries, the confusion caused expensive mistakes. In the nineteenth century mathematicians began to agree on uniform rules. The agreement that was settled says: not all operations are equal — there is a clear hierarchy between them.

It is important to stress: this is not a law of nature. Mathematicians chose this rule because it is logical, convenient and lets you write physics and chemistry formulae compactly without a sea of brackets. It is a convention — and that is why all of us have to respect it.

The full order: brackets, indices, multiplication and division, addition and subtraction

The order of operations can be set out in a clear table. The higher the priority, the earlier you do the operation:

In English schools this rule is called BIDMAS (or sometimes BODMAS) — an acronym that helps you remember the order: Brackets, Indices, Division and Multiplication, Addition and Subtraction. In the United States the same rule is called PEMDAS.

Why is multiplication 'stronger' than addition?

The most logical explanation for children comes from everyday life. Suppose you go to the supermarket and buy 2 packs of chocolate bars, with 3 bars in each pack. You also buy one single bar.

How many bars altogether? The obvious answer: first work out how many bars are in the packs (2 × 3 = 6), then add the single one (+ 1). Total: 7 bars.

If we did it from left to right — 2 + 3 = 5, then 5 × 1 = 5 — we would get a wrong answer that does not match the real question. Multiplication represents repeated quantities, and it is 'heavier' than simple addition. That is why it comes first.

When you go to buy 2 packs with 3 bars in each, plus one extra bar — first you multiply, then you add.

Guided examples, step by step

Example A: 2 + 3 × 4

1. No brackets and no indices — skip.
2. Multiplication first: 3 × 4 = 12.
3. Now addition: 2 + 12 = 14.
4. The correct answer: 14.

Example B: (2 + 3) × 4

1. There are brackets — work them out first: 2 + 3 = 5.
2. Now multiplication: 5 × 4 = 20.
3. The correct answer: 20.

Example C: 10 − 2 × 3 + 1

1. No brackets and no indices.
2. Multiplication first: 2 × 3 = 6.
3. Now the rest of the expression: 10 − 6 + 1.
4. Addition and subtraction from left to right: 10 − 6 = 4, then 4 + 1 = 5.
5. The correct answer: 5.

Look at Example C: when there are only additions and subtractions (no multiplication or division) — you work from left to right. The same rule applies to multiplication and division when they are at the higher level: 12 ÷ 4 × 2 = (12 ÷ 4) × 2 = 3 × 2 = 6.

The classic problem: 6 ÷ 2(1 + 2) = ?

This is one of the hottest arguments on the internet. The calculation 6 ÷ 2(1 + 2) circulates all over the world and gets different answers — 1 and 9. Who is right?

1. Brackets first: (1 + 2) = 3.
2. Now the expression is: 6 ÷ 2 × 3.
3. Multiplication and division have the same priority — work from left to right.
4. 6 ÷ 2 = 3, then 3 × 3 = 9.
5. The answer by the standard rules: 9.

Common pupil mistakes

• Working from left to right without checking for multiplication or division — the most common mistake.
• Forgetting to work out the brackets first — 2 + (3 × 4) is written that way even though the brackets are unnecessary, but (2 + 3) × 4 changes the answer completely.
• Treating subtraction as though it always comes after multiplication — subtraction is at the same level as addition, and you work from left to right.
• Forgetting that division and multiplication have equal priority — multiplication does not always come before division.
• Expressions with indices — sometimes children work out indices after multiplication and before brackets, when indices come after brackets and before multiplication.

Tips for remembering the rule easily

• Ask yourself before every calculation: are there brackets here? Indices? — Start there.
• Underline in pencil the operation that needs doing first — a powerful visual aid.
• Say out loud: 'first brackets, then indices, then divide and multiply, and finally add and subtract.'
• Check the answer by substituting back — does it make sense?
• Use everyday examples: shopping, sharing sweets, working out quantities.
• Practise with flashcards: write a calculation on one side, and the correct order on the back.

A digital tool like MathsUK lets pupils practise the order of operations interactively — the tool shows the steps one by one and explains where the mistake was. It is the fastest way to build confidence.

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