Multi-step word problems
In grade 7 the word problems start to chain together — a single story may use a fraction, a percent and a ratio. The key to success is splitting the problem into separate steps and writing down every intermediate result.
Type 1: fraction → percent
Problem. A school has 300 pupils. 1/3 of them signed up for the art club. Of those, 40 % chose painting. How many pupils chose painting?
Working:
- Signed up: `300 · 1/3 = 100` pupils.
- Painting: `100 · 40 / 100 = 40` pupils.
Type 2: ratio → percent
Problem. £200 is split in the ratio 2 : 3. The bigger share then donates 25 % of what it received. How many £ are donated?
Working:
- Sum of parts: `2 + 3 = 5`. One part: `200 / 5 = £40`.
- Bigger share: `3 · 40 = £120`.
- Donated: `120 · 25 / 100 = £30`.
Type 3: percent → fraction
Problem. The budget is £400. 25 % goes to category A. Of that money, 1/4 is kept for next month. How much is kept?
Working:
- Category A: `400 · 25 / 100 = £100`.
- Kept: `100 · 1/4 = £25`.
Practical tips
- Always plan the steps and underline what is to be found.
- Write every intermediate value with its unit (£, kg, pupils…).
- For fractions, think about "fraction of what" — the whole can change between steps.
- After the final answer, estimate: does it make sense? More or less than the starting value?