Ross MackellUK-qualified primary teacher · 8 min read

What's 3 + 4 × 2? If you said 14, you're in very good company. It's one of the most argued-about sums on the internet, and it's also a question your child could meet on the Year 6 SATs. The answer is 11.

The reason is a rule called BIDMAS (or BODMAS, depending on when and where you went to school). It tells you which part of a calculation to do first. Once your child knows it, and knows the one detail that the word itself doesn't tell you, these questions become some of the easiest marks on the paper.

I'm Ross, a UK-qualified primary teacher with over ten years in the classroom. In this guide I'll explain what BIDMAS means, how UK schools teach it, worked examples step by step, the mistakes children make most often, and a 10-minute practice routine with answers.

What your child needs first

BIDMAS is a rule about order, not a new method. Your child still has to do every calculation inside it, so they need:

• Quick times tables and division facts. Most BIDMAS questions hide a multiplication or division in the middle. If those are slow, start with how to learn times tables fast.
• Confident mental adding and subtracting, including with bigger numbers, or the written column method when the numbers are too big to hold in their head.
• Square and cube numbers for the "indices" part. Children learn that 5² means 5 × 5 in Year 5.

In the national curriculum, using the order of operations is a Year 6 objective: children should use their knowledge of the order of operations to carry out calculations involving the four operations. It regularly appears on the SATs arithmetic paper, often as a question with brackets or a mix of adding and multiplying.

What do BIDMAS and BODMAS stand for?

Different schools, and different generations, use different words for exactly the same rule:

If you grew up in the US, you might know it as PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). It's the same rule again. Whichever word your child's school uses, use that one at home, so they only have one version in their head.

The detail most children miss

The word BIDMAS makes it look like there are six steps, and that division always comes before multiplication, and addition always before subtraction. That isn't true, and it's the cause of most BIDMAS mistakes.

There are really four steps:

1. Brackets
2. Indices (squared, cubed)
3. Division and multiplication, working from left to right
4. Addition and subtraction, working from left to right

I find it helps to write BIDMAS as B I DM AS, with the pairs grouped together, so children can see the teams.

Why we need an order at all

Children sometimes ask, quite reasonably, why we can't just go left to right like reading. The answer is that maths needs everyone, everywhere, to get the same answer from the same calculation. Without an agreed order, 3 + 4 × 2 could be 14 or 11, and both people would think they were right.

It's a bit like driving on the left in the UK. It doesn't matter which side we agree on, it just matters that everyone agrees. Scientific calculators follow BIDMAS too, which is a fun thing to test with your child: type 3 + 4 × 2 into a calculator and see what comes out.

BIDMAS step by step: 6 worked examples

Example 1: 3 + 4 × 2

1. No brackets, no indices.
2. Multiplication before addition: 4 × 2 = 8.
3. Now 3 + 8 = 11.

Example 2: (3 + 4) × 2

1. Brackets first: 3 + 4 = 7.
2. Now 7 × 2 = 14.

Put these two side by side for your child. Same numbers, same signs, different answers, and the only change is the brackets. It's the clearest way to show why the order matters.

Example 3: 20 − 12 ÷ 4

1. Division before subtraction: 12 ÷ 4 = 3.
2. Now 20 − 3 = 17.

If your child worked left to right, they'd get 20 − 12 = 8, then 8 ÷ 4 = 2. That's the most common wrong answer.

Example 4: 18 ÷ 3 × 2

1. Only division and multiplication here. They're a team, so go left to right.
2. 18 ÷ 3 = 6.
3. 6 × 2 = 12.

A child who thinks "M before D" would do 3 × 2 = 6 first, then 18 ÷ 6 = 3. Wrong answer, and it's the letters in the word that misled them.

Example 5: 10 − 4 + 3

1. Only subtraction and addition. They're a team, so go left to right.
2. 10 − 4 = 6.
3. 6 + 3 = 9.

If you did the addition first (4 + 3 = 7, then 10 − 7), you'd get 3. Same trap as Example 4.

Example 6: 5² + 3 × 4

1. Indices first: 5² means 5 × 5 = 25.
2. Then multiplication: 3 × 4 = 12.
3. Then addition: 25 + 12 = 37.

Watch out for children reading 5² as 5 × 2. It's 5 lots of itself, not 5 lots of 2.

The one-step-per-line habit

The single most useful habit I teach for BIDMAS is this: do one step, then rewrite the whole calculation.

Take 30 − (4 + 2) × 3:

1. Underline the brackets. Work them out: 4 + 2 = 6. Rewrite: 30 − 6 × 3.
2. Underline the multiplication. Work it out: 6 × 3 = 18. Rewrite: 30 − 18.
3. Finish: 12.

It feels slower, but it's much faster than getting it wrong. Each line is a simpler calculation than the one before, and your child can see exactly where a mistake happened if one creeps in. In SATs, it also gives the marker working to look at.

4 common mistakes and how to fix them

Mistake 1: Going straight left to right

Your child reads 3 + 4 × 2 like a sentence and gets 14.

The fix: before calculating anything, get them to scan the whole question and circle the multiplication or division. "Is there a times or a divide? Do that first."

Mistake 2: Always doing multiplication before division

They solve 18 ÷ 3 × 2 as 18 ÷ 6 = 3, doing the multiplication first. Children who learned PEMDAS (where M comes before D) do this a lot, but plenty of BIDMAS children get muddled about which letter "wins" too.

The fix: teach the teams. Write B I DM AS. When two team members appear together, neither wins: read left to right.

Mistake 3: Always doing addition before subtraction

10 − 4 + 3 becomes 10 − 7 = 3.

The fix: same as above, they're a team. A useful check: 10 − 4 + 3 means "start at 10, take away 4, add 3". Walking it on a number line gives 9 every time.

Mistake 4: Rushing the actual calculation

Plenty of children get the order completely right and then write 6 × 3 = 24. The order mark is gone because of a times table slip.

The fix: this is a facts problem, not a BIDMAS problem. If it keeps happening, spend a week on times tables. It will help far more than more BIDMAS questions.

A 10-minute practice routine

Same three steps I use for every skill: watch, copy, practise.

1. Watch: do one yourself, out loud, using one step per line. "Any brackets? No. Any times or divide? Yes, 4 × 2 is 8. Now 3 + 8 is 11."
2. Copy: your child does a very similar one, saying each step out loud.
3. Practise: three or four on their own, then check them on a calculator together.

The pairs in the table are deliberate: 6 + 2 × 5 and (6 + 2) × 5 use the same numbers but give different answers. Ask your child to explain why. Only move on when they're getting three in a row right. Ten minutes, a few times a week, is plenty.

Frequently asked questions

What does BIDMAS stand for?

BIDMAS stands for Brackets, Indices, Division, Multiplication, Addition and Subtraction. It is the order you work out the parts of a calculation in. BODMAS is the same rule, with O standing for Orders instead of Indices.

Is BIDMAS the same as BODMAS?

Yes. BIDMAS and BODMAS describe exactly the same order of operations. The only difference is the second letter: Indices or Orders, which both mean powers such as squared and cubed. PEMDAS, used in the US, is also the same rule.

Do you do division or multiplication first in BIDMAS?

Neither comes first. Division and multiplication have equal priority, so you work them out from left to right in the order they appear. For example, 18 ÷ 3 × 2 = 6 × 2 = 12. Addition and subtraction work the same way.

What is the answer to 3 + 4 × 2?

The answer is 11. Using BIDMAS, multiplication comes before addition, so you work out 4 × 2 = 8 first, then 3 + 8 = 11. If the question were (3 + 4) × 2, the brackets would come first and the answer would be 14.

What year do children learn BIDMAS?

In England, using the order of operations is part of the Year 6 maths curriculum, and it often appears on the KS2 SATs arithmetic paper. Children learn square and cube number notation, which is the indices part, in Year 5.

Sources and further reading

• Department for Education, National curriculum in England: mathematics programmes of study (order of operations in Year 6, square and cube numbers in Year 5)
• Standards and Testing Agency, Key stage 2 mathematics test framework
• Ross Mackell, Teacher's Perspective on YouTube