Page 1 · Introduction
Percentages the easy way
Percentages look scary, but the test rarely wants long division. Almost every percentage question can be cracked with a few clever shortcuts — and this module hands them all to you.
The single most useful idea: 10% is easy (just move the decimal point / divide by 10), and almost every other percentage is built from 10%.
The big ideaFind 10% first — then add, halve or scale to reach the percentage you actually want.
💡We build from easy to challenging. By the end you'll do percentages in your head faster than most people can reach for a calculator.
On the real testWhere this appearsPercentages come up throughout the Mathematical Reasoning section (25% of your mark, no calculator from 2025). Mental shortcuts are exactly what save you time.
Page 2 · The foundation
10% is your best friend
To find 10% of any number, just divide by 10 (move the decimal point one place left).
10% examples
- 10% of 80 = 8
- 10% of 250 = 25
- 10% of 45 = 4.5
Once you have 10%, you can build almost anything:
20% = 10% × 2 · 5% = 10% ÷ 2 · 30% = 10% × 3
✅Whenever you see a percentage question, your first move is: "what's 10% of this?" Everything flows from there.
Page 3 · Building blocks
Making any percentage from 10%
Break the percentage you want into easy pieces:
Find 30% of 90.
10% of 90 = 9. So 30% = 9 × 3 = 27.
27
Find 15% of 40.
10% of 40 = 4, and 5% = half of that = 2. So 15% = 4 + 2 = 6.
6
Find 25% of 40.
25% is just a quarter. 40 ÷ 4 = 10.
10
💡Handy quarters & halves: 25% = ÷4, 50% = ÷2, 75% = half then add half again. Learn these and skip the working.
Page 4 · The star trick
The "flip it around" trick
This one feels like magic. For any two numbers:
x% of y = y% of x
So if one way is hard, flip it — the other way is often easy!
Find 4% of 50.
4% of 50 is awkward. Flip it: 50% of 4 = half of 4 = 2. Same answer, far easier!
2
Find 8% of 25.
Flip it: 25% of 8 = a quarter of 8 = 2.
2
Why it worksBoth are the same multiplication (x × y ÷ 100) — just in a different order. Flipping never changes the answer, only the difficulty.
Page 5 · Increase & decrease
Discounts and increases
For "25% off" or "20% more", find the percentage, then add or subtract.
A $40 shirt has 25% off. New price?
25% of 40 = 10 (a quarter). Take it off: 40 − 10 = 30.
$30
The even-faster way
25% off means you pay 75%. 75% of 40 = 30 in one step. Thinking "what's left" often beats "what's removed".
✅For a discount, you can find the new price directly: 20% off → pay 80%; 30% off → pay 70%. One calculation instead of two.
Page 6 · Worth memorising
Percentages, fractions & the quick ones
Learn these by heart
- 50% = ½ · 25% = ¼ · 75% = ¾
- 10% = 1/10 · 20% = ⅕ · 33⅓% = ⅓
- 1% = 1/100 (divide by 100)
When you see these percentages, switch straight to the fraction — it's usually faster.
💡Spotting "25%" and instantly thinking "÷ 4" saves precious seconds on every question it appears in.
Page 7 · Practice
Level 1 · Easy
Warm up
Use 10%, halves and quarters. Tap to check.
1. What is 10% of 80?
Divide by 10: 80 ÷ 10 = 8.
2. What is 50% of 60?
50% = half. 60 ÷ 2 = 30.
3. What is 25% of 40?
25% = a quarter. 40 ÷ 4 = 10.
🎉The easy ones are just halves, quarters and dividing by 10. Now let's build bigger percentages.
Page 8 · Practice
Level 2 · Medium
Building from 10%
Find 10% first, then scale or add.
1. What is 20% of 150?
10% of 150 = 15. 20% = 15 × 2 = 30.
2. What is 15% of 40?
10% = 4, 5% = 2. 15% = 4 + 2 = 6.
3. What is 30% of 90?
10% of 90 = 9. 30% = 9 × 3 = 27.
💪See how everything grows from 10%? That one anchor handles most percentages you'll meet.
Page 9 · Practice
Level 3 · Hard
The flip-it trick
These look awkward — until you flip them around. Remember: x% of y = y% of x.
1. What is 8% of 25?
Flip it: 25% of 8 = a quarter of 8 = 2. Much easier than 8% of 25.
2. What is 12% of 50?
Flip it: 50% of 12 = half of 12 = 6.
3. What is 5% of 80?
Flip it: 80% of 5 = 4. (Or: 10% of 80 = 8, then halve = 4.)
💡The flip-it trick turns "hard" percentages into easy ones. Once you spot it, these become some of the fastest questions on the paper.
Page 10 · Challenge
Level 4 · Challenge
Think smart
These combine ideas or work backwards. Take your time — and reach for a shortcut before doing it the long way.
1. A $40 jacket has 25% off, then $2 more off at the till. Final price?
25% off means pay 75%: 75% of 40 = 30. Then − $2 = $28. Finding "what's left" (75%) is faster than removing 25% separately.
2. After a 20% increase, a number becomes 60. What was it before?
After +20%, the new number is 120% of the old. So 120% = 60, meaning 10% = 5, so 100% = 50. Working back from the percentage is the key.
3. Which is bigger: 20% of 60, or 60% of 20?
A They are equal
B 20% of 60
C 60% of 20
D Can't tell
By the flip-it rule, x% of y = y% of x — so they're exactly equal (both are 12). A question designed to catch anyone who doesn't know the trick!
🌟You now have a whole toolkit of percentage shortcuts — the flip trick, building from 10%, and working backwards. These make you genuinely fast.
Complete
Brilliant!
You've completed the Percentages module.
You've learned to build any percentage from 10%, use halves and quarters, flip awkward percentages around, handle discounts by finding "what's left", and even work backwards. That's a serious speed advantage on test day.