FREE LESSON · Maths Foundations
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Learn the order to work in. Then use it on word problems, where your first answer might only be halfway.
Do the brackets first, then multiply, then add. So 6 + 4 × (8 − 3) is 26. In word problems, you also choose the number sentence. Then check your final number answers the question.
BODMAS tells you which part to do first. Brackets, then Orders (like 2 squared), then Divide and Multiply, then Add and Subtract. Inside brackets, use the same order. Then swap the brackets for their answer. In 6 + 4 × (8 − 3), start with 8 − 3 = 5. That gives 6 + 4 × 5.
Divide and multiply are equal, so do them left to right. 24 ÷ 3 × 2 is 8 × 2 = 16. It isn't 24 ÷ 6 = 4. Add and subtract are equal too: 15 − 6 + 2 is 9 + 2 = 11. BODMAS doesn't mean you always divide before you multiply.
Write the whole calculation again after each step. Keep the other numbers and signs the same. 6 + 4 × (8 − 3) = 6 + 4 × 5 = 6 + 20 = 26. One step on each line makes it easy to spot a missing number, or adding too early.
Check the size with a quick estimate. 8 − 3 is 5, and four lots of 5 is 20. Add about 5 more, and you expect about 25. The exact answer, 26, is close. 50 is much too big. An estimate warns you, but it doesn't prove the answer. If it doesn't match, work it out again in order.
Now try a story. Six boxes hold 24 counters each. Four games use 15 counters each. The rest are shared among seven tables. The number sentence is (6 × 24 − 4 × 15) ÷ 7. That's 144 − 60 = 84 left, and 84 ÷ 7 = 12 each. 84 is the trap. It's how many are left, not how many each table gets.
BODMAS
Brackets, Orders (powers), Division/Multiplication, Addition/Subtraction.It tells you which part to do first, even if another sign comes first.Equal signs
divide and multiply are equal. Add and subtract are equal too.When two are equal, work left to right: 24 ÷ 3 × 2 = 16.Brackets
a small calculation to finish first. Then use its answer in the rest.8 − 3 becomes 5 in 6 + 4 × (8 − 3).Estimate
a quick, rounded calculation to check the size of your answer.About 25 fits 26. It warns you that 50 is wrong.Halfway answer
a number you need on the way, but not the final answer.84 counters left still have to be shared among seven tables.The moveKeep what the question asks in mind all the way. Don't stop at the first number you get.
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Watch how to solve it, one step at a time.
Read the problem, then follow the steps. You'll see the answer, the trap, and what to do next time.
Full problem: find each table's share
Question: How many counters does each table receive?A school club has six boxes of 24 counters each. Four games use 15 counters each. The club shares the remaining counters equally among seven tables.
How many counters does each table receive?
A. 12
B. 24
C. 60
D. 84
E. 144
Work out what kind of answer you need.
The question asks how many each table gets. So 84 left over can't be my answer. I need the total, take away what's used, then share what's left among 7. First I estimate. Six boxes of about 25 is about 150. Four games use 60, so about 90 are left. 90 shared by 7 is about 13 each. Then I write (6 × 24 − 4 × 15) ÷ 7.
Follow the steps from the facts to the answer.
Keep what the question asks in mind.
See why a tempting answer is wrong.
Common wrong answer: D, 84.
Why it tempts you: 6 × 24 − 4 × 15 = 84 is correct maths, so 84 looks right.
Why it's wrong: 84 is how many counters are left. The question asks how many each table gets.
Fix: divide the 84 by 7 to get 12 each table. The words 'each table' show the missing step.
Say the answer and the shortest proof.
A. 12 counters each table. (6 × 24 − 4 × 15) ÷ 7 = (144 − 60) ÷ 7 = 84 ÷ 7 = 12. Check backwards: 12 × 7 = 84, and 84 + 60 = 144. That's all the counters.
What to remember for questions like this.
The story tells you where the brackets go. All the counters left must be shared by 7. Without brackets, 6 × 24 − 4 × 15 ÷ 7 only divides the game counters. That's because you divide before you take away. So first turn the story into (start − used) ÷ number of tables. Then use BODMAS. 84 is useful, but it's only halfway. An estimate of about 13 and a check backwards both support 12.
What to do on your next question.
| In this question | Next time | Why it helps |
|---|---|---|
| 'Left' and 'each table' meant take away, then divide. | Underline what the question asks. Turn each action into a sign. | This stops a halfway number becoming your answer. |
| Wrote (6 × 24 − 4 × 15) ÷ 7 before calculating. | Put brackets around everything that gets shared. | Without them, only the last part is divided. |
| Found 144, 60, 84, then 12. | Write what each number means, with its unit. | Labels show which number answers the question. |
| Estimated about 13 and checked 7 × 12 + 60 = 144. | Estimate first, then check backwards. | Two different checks catch different slips. |
compare
The last operation matters as much as the first three.
Two students answered the same question. One followed the facts all the way. The other didn't.
The whole response
Stopped at what's left
Five packs give 90. Three posters use 36. So 90 − 36 = 54. I choose 54.
Answered for each table
(5 × 18 − 3 × 12) ÷ 6 = (90 − 36) ÷ 6 = 9 stickers each. Check: 6 × 9 + 36 = 90.
guide
One small step with help before you go solo.
Look back at the worked problem. Now try one like it.
Four stalls raise $24 each. There's also $12 in extra donations. Three activities cost $16 each. The money left is shared equally among five clubs. How much does each club get? Write one number sentence, show your working, and include the unit.
Want feedback on your own answer? Get started to practise with instant marking.
A museum has 5 trays of 18 tokens and 12 loose tokens. It uses 3 sets of 14 tokens. The rest is put equally into 6 bags.
Which expression finds the number of tokens in each bag?
Four players each answer 6 questions correctly and 3 incorrectly. Each correct answer earns 5 points; each incorrect answer loses 2 points.
Which expression gives the team's total score?
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