Word problems with fractions
In Year 6 fraction word problems come in three typical shapes. Let's work each one out on an example.
Type 1: part of a whole
Problem. There are 24 pupils in the class. 1/3 of them are absent today. How many are at school? Working:- First find what 1/3 of 24 is: `24 ÷ 3 = 8 absent.`
- The rest are at school: `24 − 8 = 16 pupils.`
Alternative: at school = 2/3 of 24 = `(24 × 2) ÷ 3 = 16`.
Type 2: several fractions together
Problem. Mia spent 1/4 of her money on lunch and 1/3 on a book. How much was left if she had £60? Working:- Lunch: `60 ÷ 4 = £15`.
- Book: `60 ÷ 3 = £20`.
- Spent: `15 + 20 = £35`.
- Left: `60 − 35 = £25`.
Type 3: finding the whole from a part (reverse)
Problem. Tom has read 12 pages, which is 1/5 of the whole book. How many pages does the book have? Working:- If 12 pages is one fifth, the whole book is five such fifths.
- Whole = `12 × 5 = 60 pages.`
This is also rule-of-three: `1/5 → 12, 5/5 → ? → 60`.
Common traps
- A fraction of what? Always check the whole you're taking the fraction of. "1/3 of 60" is different from "1/3 of 24".
- Adding fractions with different denominators — when a problem asks "what's left after 1/4 and 1/3", either compute parts separately, or use a common denominator.
- Watch out for "1/3 less" — that means "whole − 1/3 of whole" = 2/3 of whole, not 1/3.