How can I add numbers quickly in my head?

Work left to right instead of right to left, and round to a friendly number before correcting. For 67 + 28, add 30 to get 97, then take back the 2 you over-added to reach 95. Adding the big part first means you always have a rough answer in mind, which is what stops you losing track.

What is the fastest way to multiply in your head?

Reshape the problem into an easier one before you calculate. Doubling and halving turns 14 x 5 into 7 x 10. Multiplying by 5 is halving then multiplying by 10. Multiplying by 11 is adding the digits and dropping the sum in the middle. Each works because it rewrites the sum, rather than because you calculated faster.

How do I work out a percentage in my head?

Use the percentage flip: x% of y always equals y% of x, and one side is usually far easier. 4% of 25 looks awkward, but 25% of 4 is 1. Build the rest from 10%, which is just moving the decimal point one place.

Do mental math tricks work if you are bad at math?

Yes, because they are not really about arithmetic speed. Every trick here replaces a hard calculation with an easier one, so the work you do in your head is smaller. What matters is knowing why each shortcut is true, so you can tell when it applies.

Mental Math Tricks

Fast mental arithmetic isn't about being "a math person". It is a handful of shortcuts that turn a hard-looking sum into an easy one before you calculate anything. That is the whole idea: you are not calculating faster, you are calculating less.

Every trick below comes with a worked example and the reason it is true. Learn the reason and you will remember the trick — and, more importantly, you will know when it applies and when it doesn't.

How to add numbers quickly in your head

Work left to right, not right to left

On paper you add the ones column first. In your head, do the opposite — start with the biggest part.

386 + 245 → 300 + 200 = 500 → 80 + 40 = 120, so 620 → 6 + 5 = 11 → 631.

Column addition works right to left so carries have somewhere to go. But in your head you have no paper to lose track on, and starting big means you always hold a rough answer — 600-ish — from the first second. If you get interrupted, you still have most of the answer.

Round, then adjust

Push one number to a friendly round number, then take back what you added.

67 + 28 → 67 + 30 = 97, then −2 → 95. 154 + 99 → 154 + 100 = 254, then −1 → 253.

Adding 30 is genuinely easier than adding 28, and the correction is a single small step. Anything ending in 8 or 9 is worth rounding up; anything ending in 1 or 2 is worth rounding down.

Make ten first

When numbers are small, find a pair that makes ten and add it as a block.

7 + 38 + 3 → the 7 and 3 make 10 → 48.

Addition gives the same answer in any order, so you are allowed to choose a friendly order. This is the first real strategy children meet, and it is still the one adults use most.

How to do multiplication fast in your head

Multiply by 11

For a two-digit number, add its digits and drop the sum in the middle.

36 × 11 → 3 (3+6) 6 → 396. 72 × 11 → 7 (7+2) 2 → 792. If the middle sum is 10 or more, carry the 1: 85 × 11 → 8 (13) 5 → 935.

×11 is ×10 plus ×1. Writing 36 × 10 = 360 above 36 and adding them lines the digits up so the tens column becomes 3 + 6. The "drop it in the middle" rule is that addition, done in advance.

Practice ×11 in the game →

Multiply by 5

Halve the number, then multiply by 10.

5 × 48 → half of 48 is 24 → 240. For odd numbers, ×10 first then halve: 5 × 37 → 370 → 185.

5 is half of 10, and 10 is the easiest number to multiply by in a base-10 system. You are trading a hard multiplication for a halving and a digit shift.

Practice ×5 in the game →

Doubling and halving

Double one number and halve the other to reach an easier product.

14 × 5 → 7 × 10 = 70. 16 × 25 → 8 × 50 = 4 × 100 = 400.

Doubling one factor and halving the other leaves the product unchanged, because you multiplied by 2 and divided by 2. You can repeat it until one side is a number you like.

Square any number ending in 5

Take the tens digit, multiply it by the next number up, and put 25 on the end.

65² → 6 × 7 = 42 → 4225. 85² → 8 × 9 = 72 → 7225.

A number ending in 5 is (10n + 5). Squaring gives 100n² + 100n + 25, which is 100 × n(n+1) + 25 — the "n times the next number up, then 25" rule exactly.

Practice squaring numbers ending in 5 →

Multiply by 9 on your fingers

Hold up ten fingers and fold down the one you are multiplying by. The fingers to the left are the tens, the fingers to the right are the ones.

9 × 7 → fold the 7th finger → 6 to the left, 3 to the right → 63.

×9 is ×10 minus one lot, so every answer's digits add to 9 and the tens digit is always one less than the number you multiplied. The fingers are just a way of reading that off.

How to subtract and divide in your head

Count up instead of taking away

For a subtraction with a big gap, count up from the smaller number.

1000 − 674 → 674 up to 700 is 26, up to 1000 is 300 → 326.

Subtraction is the distance between two numbers, and distance can be measured from either end. Counting up avoids borrowing across zeros entirely, which is where most mistakes happen.

Practice subtracting from 1000 in the game → — the lesson there gets to the same answers by a different route (take each digit from 9, the last from 10), which is worth having as a second method.

Slide both numbers

Adding the same amount to both numbers leaves the gap unchanged — so slide them somewhere friendlier.

83 − 47 → slide both up 3 → 86 − 50 = 36.

The gap between two numbers doesn't move when both move together. Sliding until the smaller one is a round number turns almost any subtraction into an easy one.

Divide by halving repeatedly

To divide by 4, halve twice. To divide by 8, halve three times.

232 ÷ 4 → 116 → 58. 96 ÷ 8 → 48 → 24 → 12.

How to work out percentages in your head

The percentage flip

x% of y always equals y% of x — and one side is usually far easier.

4% of 25 is awkward; flip it to 25% of 4 = 1. 18% of 50 → 50% of 18 = 9.

Both sides are the same multiplication, x × y / 100, just read in a different order. The flip is free, and it costs nothing to check whether the other side is nicer.

Build everything from 10%

10% is one decimal place. Every other percentage is built from it.

Want	Do this	Example (of 60)
10%	move the point one place	6
5%	half of 10%	3
20%	double 10%	12
15%	10% + 5%	9
1%	move the point two places	0.6

A 15% tip on a £43 bill: 10% is £4.30, half of that is £2.15, so about £6.45.

Those two cover most everyday percentages. Percentage change, discounts and working backwards from a sale price have their own guide: how to work out percentages.

How to actually get faster

Three things separate people who are quick from people who aren't, and none of them is talent.

The times tables have to be automatic. Every trick above assumes you are not spending working memory on 7 × 8. If that isn't instant yet, start with times tables practice — it is the single highest-value thing to fix.
Short and daily beats long and occasional. Five minutes a day will outrun an hour on Sunday, because recall strengthens each time you retrieve a fact, not each minute you look at it.
Estimate before you calculate. Round each number to one significant figure and get the size of the answer first. It takes a second and it catches the errors that matter — the ones that are wrong by a factor of ten.

Practice these in the game

Math Challenge has 36 illustrated Magic Tricks lessons. Each one explains the idea behind a shortcut — the same "why" boxes you have been reading — and then drops you straight into practice on it, with the difficulty adapting as you go.

There are also 35 arithmetic topics and a free Daily Challenge that needs no account.

Your turn

Three to try — tap what you get.

45 × 11, in your head

35²

98 × 102

Play Math Challenge free →