Percentages
Percentage of an amount, percentage change, fraction-decimal-percentage triangle.
Per cent means "out of 100". You do not need to multiply by scary decimals — nearly every percentage question can be built out of easy 10% blocks.
Build from 10% — what is 35% of 240?
Step 1 · find 10%
240 ÷ 10 = 24
Step 2 · build 30%
24 × 3 = 72
Step 3 · add 5% (half of 10%)
72 + 12 = 84
Remember it like this
“Find 10% first — everything builds from it.”
10% is just ÷10. Then 5% is half of that, 1% is a tenth of it, 20% is double it.
⚠ Watch out
Percentage change is always compared with the ORIGINAL price. A £60 jacket reduced to £45 saves £15, and 15 out of 60 is 25% off. Dividing by the new price (£45) instead is the single most common lost mark on this topic.
The reverse one (harder)
After a 30% discount, a coat costs £24.50. What was the original price?
- After 30% off, you are paying 70% of the original
- So £24.50 = 70% of the original
- Divide by what is left: 24.50 ÷ 0.7
£35
⚠ Watch out
In reverse-percentage questions, do not add the 30% back on — £24.50 × 1.3 gives £31.85, which is wrong (and is always one of the trap options). Divide by what is left instead.
✏ Your turn
What is 15% of 80?
Show the answerHide the answer
- 10% of 80 = 8
- 5% is half of that: 4
- 15% = 8 + 4
12
For parents — the full topic guide
Fractions, Decimals & Percentages — 11+ Topic Guide
Part of the GrammarMock topic guides. Read with your child, then drill with the Fractions mini-tests.
Why this topic decides marks
Roughly a quarter of GL maths questions involve fractions, decimals or percentages in some form — either directly ("what is 5/6 of 144?") or hidden inside word problems ("a coat is reduced by 20%..."). It's also the topic Year 5 children most commonly lose marks on, because school coverage varies and the three formats (fraction, decimal, percentage) are really one idea wearing three outfits.
The one idea
A fraction, a decimal and a percentage are three ways to write the same thing:
3/4 = 0.75 = 75%
If your child can move fluently between the three forms, most questions become easy. If they can't, every question is a fresh struggle. So the first two weeks of practice should be conversion drills, not word problems.
Conversions your child should know by heart:
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 1/3 | 0.333... | 33⅓% |
| 1/10 | 0.1 | 10% |
The four question types GL asks
1. Fraction of an amount
"What is 5/8 of 96?"
Method: divide by the bottom, multiply by the top. 96 ÷ 8 = 12, then 12 × 5 = 60.
2. Adding/subtracting fractions
"What is 5/6 − 1/4?"
Method: common denominator first, always. 5/6 = 10/12, 1/4 = 3/12, so 10/12 − 3/12 = 7/12. The exam's wrong-answer options are built from the classic mistake of subtracting tops and bottoms separately (5−1)/(6−4) = 4/2 — teach your child to laugh at that trap.
3. Percentage of an amount
"What is 35% of 240?"
Method: build from 10%. 10% of 240 = 24. So 30% = 72, and 5% = 12. Total 84. The 10% building-block method beats formal multiplication for exam speed every time.
4. Percentage change (the hard one)
"A £60 jacket is reduced to £45. What percentage discount is that?"
Method: change ÷ original × 100. Saving is £15. 15/60 = 1/4 = 25%. The trap: dividing by the NEW price instead of the original. This single error accounts for a big share of lost marks on this question type.
The reverse version is harder still: "After a 30% discount, a coat costs £24.50. What was the original price?" Here £24.50 is 70% of the original, so original = 24.50 ÷ 0.7 = £35. Children want to add 30% back on (£24.50 × 1.3 = £31.85 — wrong). Practise until the "divide by what's left" instinct is automatic.
Common mistakes to drill out
- Adding denominators (1/4 + 1/4 = 2/8 ✗). It's 2/4 = 1/2.
- Percentage of wrong base (discount as % of the sale price rather than original).
- Decimal place slips in ×/÷ by 10, 100 (0.7 × 0.6 = 4.2 ✗; it's 0.42 — count decimal places).
- Not simplifying (12/16 left as-is when the answer options show 3/4).
Two-week practice plan
- Days 1-4: conversion drills, 10 a day (make flashcards from the table above)
- Days 5-8: fraction-of-amount and percentage-of-amount, 8 questions a day
- Days 9-11: adding/subtracting fractions with different denominators
- Days 12-14: percentage change and reverse percentage word problems
Then take the Fractions mini-test on GrammarMock. 12+/15 = move on. Below that, repeat days 9-14.
Ready to practise this topic?
Try a full paper — questions on percentages show up in most 11+ maths and VR papers.