See the idea
Before you start
Calculate with the four operations and recognise brackets. Powers appear in some examples; if those are new, learn that 3² means 3 × 3 before using the full order.
Words used in this guide
- Expression
- Numbers and operations representing a value.
- Priority
- Which operation is evaluated first under the agreed convention.
- Power
- Repeated multiplication of a base by itself, such as 2³ = 2 × 2 × 2.
Why the method works
Without a shared convention, a string such as 5 + 3 × 4 could be read in different ways. Multiplication has priority, so it is 5 + 12 = 17. Brackets explicitly change the grouping: (5 + 3) × 4 = 32. BODMAS, BIDMAS and PEMDAS describe the same priority levels when read correctly. Multiplication and division share a level, as do addition and subtraction.
Do not read the letters as separate ranks
BODMAS and BIDMAS are reminders. Division does not always happen before multiplication. They have equal priority, so follow their order from left to right. Addition and subtraction also have equal priority.
Brackets change the grouping
3 + 4 × 2 = 11 because multiplication happens before addition. But (3 + 4) × 2 = 14 because the brackets ask you to add first.
Write one clear step at a time
For 18 ÷ 3 × 2, calculate 18 ÷ 3 = 6 and then 6 × 2 = 12. Multiplying 3 × 2 first changes the expression into a different problem.
Worked examples, step by step
Example 1: Calculate 20 − 6 + 2.
- Subtraction and addition have equal priority. Work left to right.
- 20 − 6 + 2 = 14 + 2 = 16.
Example 2: Evaluate 30 ÷ 5 × 2 + 7.
- Division and multiplication share a level. Work left to right: 30 ÷ 5 = 6, then 6 × 2 = 12.
- Now add 7 to obtain 19.
- Multiplying 5 × 2 first would secretly insert brackets that were not in the original expression.
Example 3: Evaluate 2 × (9 − 4)².
- Inside the brackets, 9 − 4 = 5. Next calculate the power: 5² = 25.
- Multiply by 2 to obtain 50.
- Do not square 2 × 5 together: the exponent applies to the bracketed quantity only.
Example 4: A family buys 3 tickets at 8 currency units and pays a booking fee of 2. Write and evaluate the total.
- The ticket cost is 3 × 8. The single fee is added once.
- 3 × 8 + 2 = 24 + 2 = 26 currency units.
- 3 × (8 + 2) would charge the fee three times and describes a different purchase.
Common mistakes and how to repair them
“Always multiply before dividing.”
In 24 ÷ 6 × 3, divide first because the operations share a level and division is leftmost. The result is 12.
“Always add before subtracting.”
In 15 − 4 + 2, calculate 11 + 2 = 13. Addition does not outrank subtraction.
Check your understanding
Choose an answer for each question. You can check again after reading the explanation.
Worked answers
What is 18 ÷ 3 × 2? 12. Division and multiplication share a level: 6 × 2 = 12.
What is 3 + 4 × 2? 11. Multiply first: 3 + 8 = 11.
Practise independently
Work these out on paper. Include a diagram or a sentence where the question asks you to explain. Open each solution after making an attempt.
3. Evaluate 7 + 5 × 3.
Show the reasoning
22, because 5 × 3 = 15 and 7 + 15 = 22.
4. Evaluate (7 + 5) × 3.
Show the reasoning
36, because the brackets make 12 first.
5. Evaluate 36 ÷ 6 × 2 − 5.
Show the reasoning
36 ÷ 6 = 6; 6 × 2 = 12; 12 − 5 = 7.
6. Evaluate 4 + 2³ × 3.
Show the reasoning
2³ = 8; 8 × 3 = 24; 4 + 24 = 28.
If a method still feels uncertain, revisit the closest worked example, then try a fresh problem. A correct answer copied from a solution tells you less than an explanation you can give independently.
Learn it → Try it → Explain it
Take your next practice break
Explore the practice arcade and choose a game whose topic you recognise. Keep using the questions in this guide to practise this specific skill.
Explore the practice arcade →Free guest play has question, level and time limits. Sign in to continue or save progress. A game score is not a mastery assessment.
Questions students and parents ask
Are BODMAS and PEMDAS different rules?
No. The letters use different terms, but multiplication/division have equal priority and addition/subtraction have equal priority in both.
What about nested brackets?
Evaluate the innermost group first, then work outward while applying the usual priorities within each group.
Do calculators always interpret an expression the same way?
Calculator entry styles vary. Use explicit brackets for intended grouping and check that the displayed expression matches your question.
Help at home: Compare a matched pair
Write 6 + 2 × 5 beside (6 + 2) × 5. Ask the child to circle what they will do first, without calculating yet.
If a mnemonic causes confusion, draw three priority levels: grouping and powers in sequence, then multiplication/division, then addition/subtraction. Emphasise the shared levels.
Ask the child to write a short story for one expression. Correct interpretation matters as much as mechanically obtaining the value.
Keep the conversation focused on the reasoning you can hear or see. One short activity cannot establish lasting mastery or diagnose a learning difficulty.
Would a teacher help with the next step?
Bring one example your child found difficult to a free 50-minute session. Tell us their grade, curriculum and time zone when you enquire.
Request a free session