Multi-Step Problems
Break it into steps, solve one at a time
Complex problems are just several simpler problems chained together. The skill is identifying each step and labelling your working clearly.
See It in Action
The Problem
A school trip costs $45 per student. There are 32 students, but the school pays a $200 subsidy. How much do the students pay in total?
Common Mistake
45 × 32 = 1,440. Students pay $1,440.
The $200 school subsidy was ignored. The total cost before subsidy is $1,440, but the students only pay the remainder after the school contributes.
Correct Approach
Step 1: Total cost = 45 × 32 = $1,440. Step 2: Students' share = $1,440 − $200 = $1,240.
Answer: $1,240
$1,240 + $200 (school subsidy) = $1,440 total. 45 × 32 = $1,440. ✓
The Core Concept
Multi-step problems look intimidating because they contain several questions in one. The trick is to identify each intermediate question separately, answer it, and label the result before moving to the next step.
Ask yourself: "What do I need to find first to make progress?" Usually the problem has a hidden intermediate question — you can't answer the final question without answering this one first. Write each intermediate answer with a label ("total seats = 180") so you can use it in the next step without confusion.
A common trap is using the wrong intermediate result in a later step — for example, using the number of sold tickets instead of the remaining tickets. Label everything clearly to avoid this.
Common Mistakes to Avoid
Skipping an intermediate step
Multi-step problems are designed so that missing one step gives a plausible but wrong answer (like $1,440). Always identify ALL the steps before starting.
Using an intermediate result in the wrong place
Label every intermediate answer clearly ("total seats = 180") so you don't accidentally use "seats sold" when you need "seats remaining."
Not reading to the end of the problem before starting
Read the full problem first. The final question is often in the last sentence, and it determines which intermediate steps you actually need.
Doing all calculations in one step
Chain calculations are hard to check and easy to get wrong. Break them into separate, labelled steps. Your working shows your understanding, even if the final answer is slightly off.
Try It Yourself
A farmer has 5 crates of oranges, each holding 36 oranges. He sells 3/4 of them and gives 12 to his neighbour. How many oranges does he have left?
Hint: Step 1: total oranges. Step 2: oranges sold. Step 3: subtract sold and given away.
Key Tips
Number your steps (Step 1:, Step 2:...) and label each result before moving on.
Read the whole problem before starting — the last sentence tells you what you're ultimately finding.
Check your final answer makes sense in context (33 oranges from 180 after selling most — reasonable? Yes.)
Ready to practise Multi-Step Problems?
Reading is the start. The Maths Gym has exercises designed around this skill — with instant feedback and progress tracking.