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Mathematical Reasoning · Module 8

Mental Maths Shortcuts

The tricks that make hard sums easy — multiply, square and round in your head, with four tiers of practice.

Page 1 · Introduction

Mental maths shortcuts

Some multiplications look hard but have a hidden shortcut that makes them almost instant. This module is a collection of those tricks — the ones that let you skip the long working and just know the answer.

None of these are "cheating" — they're how strong mathematicians actually think. Learn them and you'll be faster and more accurate.

The big ideaTurn a hard sum into an easy one: round to a friendly number, or break it into pieces you can do in your head.
💡Each trick is a little tool. You don't need all of them at once — collect them one at a time and they'll start to feel natural.
On the real testWhere this helpsThe Mathematical Reasoning section is computer-based with no calculator (from 2025). Fast, accurate mental maths frees up time for the harder thinking questions.

Page 2 · The easy multipliers

Multiplying by 10 and 5

× 10 — just add a zero

34 × 10 = 340. Move every digit up one place.

× 5 — halve, then × 10

Since 5 is half of 10: for 16 × 5, halve 16 to get 8, then × 10 = 80. Much easier than adding 16 five times.

✅× 5 tip: if the number is odd, ×10 first then halve. 17 × 5 = 170 ÷ 2 = 85.

Page 3 · Doubling tricks

Multiplying by 4 and 8

× 4 — double, then double again

23 × 4: double 23 = 46, double again = 92.

× 8 — double three times

12 × 8: 12 → 24 → 48 → 96.

💡Doubling is one of the easiest things to do in your head, so turning ×4 and ×8 into doubling makes them simple.

Page 4 · The clever ones

Multiplying by 9 and 11

× 9 — ×10 then subtract

9 is one less than 10, so 12 × 9 = (12 × 10) − 12 = 120 − 12 = 108.

× 11 (two-digit) — split and add the middle

For 23 × 11: split the digits 2 _ 3, add them (2+3=5) and pop it in the middle: 253. So 23 × 11 = 253.

✅The ×11 trick needs a small carry if the middle sum is 10 or more — but for many test numbers it works instantly.

Page 5 · A party trick

Squaring numbers ending in 5

Any number ending in 5, squared, follows a beautiful pattern:

The rule

Take the digit(s) before the 5. Multiply by the next number up. Then stick 25 on the end.

25²
Before the 5 is "2". Next number up is 3. 2 × 3 = 6. Add 25: 625.
625
35²
3 × 4 = 12, add 25 → 1225.
1225
🌟This one always impresses people. 65²? 6×7 = 42, add 25 → 4225. Instantly.

Page 6 · The all-purpose trick

Round, then adjust

When a number is close to a round one, use the round number and fix it afterwards.

99 × 7
99 is nearly 100. 100 × 7 = 700, then take away one 7: 700 − 7 = 693.
693
48 × 5
50 × 5 = 250, then take away 2 × 5 = 10: 250 − 10 = 240.
240
The habitSee a number ending in 8 or 9? Round it up to the ten, multiply, then subtract the little bit you added. It works every time.

Page 7 · Practice

Level 1 · Easy

Warm up

Use the ×10, ×5 and doubling tricks. Tap to check.

1. 34 × 10 = ?
A 44
B 340
C 304
D 3400
×10 adds a zero: 340.
2. 16 × 5 = ?
A 60
B 75
C 80
D 90
Halve 16 = 8, then ×10 = 80.
3. 23 × 4 = ?
A 82
B 84
C 46
D 92
Double 23 = 46, double again = 92.
🎉Halving and doubling are doing the heavy lifting for you. Now the clever multipliers.

Page 8 · Practice

Level 2 · Medium

The 9, 11 and 25 tricks

1. 12 × 9 = ?
A 108
B 96
C 118
D 99
×10 then subtract: 120 − 12 = 108.
2. 23 × 11 = ?
A 233
B 243
C 253
D 263
Split 2_3, add the middle (2+3=5): 253.
3. 16 × 25 = ?
A 350
B 400
C 375
D 425
×25 = ×100 then ÷4. 1600 ÷ 4 = 400.
💪Each of these replaces a hard multiplication with something you can do in a couple of seconds. Worth memorising!

Page 9 · Practice

Level 3 · Hard

Squaring & rounding

1. 25² = ?
A 525
B 625
C 650
D 505
2 × 3 = 6, add 25 → 625.
2. 35² = ?
A 925
B 1025
C 1225
D 1250
3 × 4 = 12, add 25 → 1225.
3. 48 × 5 = ?
A 240
B 245
C 230
D 250
50 × 5 = 250, minus 2 × 5 = 10 → 240. (Or: half of 48 = 24, ×10 = 240.)
💡The squaring-5 trick feels like magic the first few times — then it becomes second nature.

Page 10 · Challenge

Level 4 · Challenge

Think smart

Pick the best trick for each. There's always a fast route if you spot it.

1. 99 × 7 = ?
A 707
B 700
C 693
D 686
Round up: 100 × 7 = 700, then subtract one 7 = 693.
2. 45² = ?
A 1625
B 1825
C 2000
D 2025
4 × 5 = 20, add 25 → 2025.
3. 8 × 125 = ?
A 1000
B 900
C 1025
D 950
Spot the friendly pair: 8 × 125 = 1000 (since 125 = 1000 ÷ 8). Recognising number pairs that make round numbers is a top-level shortcut.
🌟Choosing the right trick for each question is the real skill — and you're now doing it. That's how the fastest students work.

Complete

Fantastic!

You've completed the Mental Maths Shortcuts module.

You've collected a whole toolkit: ×5, ×9, ×11, doubling for ×4 and ×8, squaring numbers ending in 5, rounding-and-adjusting, and spotting friendly number pairs. Use them and you'll fly through the arithmetic.

Try a practice test More free modules
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