How to Do Math in Your Head

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

To add quickly in your head, work from the left: 47 + 38 is 70 + 15 = 85, the tens first and the units after. When one number is close to a round number, round it and adjust: 47 + 95 is 47 + 100 − 5 = 142.

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

Round, then adjust

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

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

Make ten first

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

$7+38+3\to$7 + 38 + 3 → the 7 and 3 make $10\to 48$10 → 48.

How to do multiplication fast in your head

To multiply fast in your head, swap the awkward number for a friendly one nearby and correct, or break it into parts: 16 × 25 is 16 × 20 + 16 × 5 = 320 + 80 = 400. When one factor is even, double and halve: 16 × 25 = 8 × 50 = 400.

Multiply by 11

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

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

Practice ×11 in the game →

Multiply by 5

Halve the number, then multiply by 10.

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

Practice ×5 in the game →

Doubling and halving

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

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

Square any number ending in 5

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

$65^2\to 6\times 7=42\to 4225$65² → 6 × 7 = 42 → 4225. $85^2\to 8\times 9=72\to 7225$85² → 8 × 9 = 72 → 7225.

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

How to subtract and divide in your head

To subtract in your head, add the same amount to both numbers until the second is round: 83 − 47 is 86 − 50 = 36, because the gap does not change. To divide, use the multiplier of the divisor: dividing by 25 is multiplying by 4 and dividing by 100.

Count up instead of taking away

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

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

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\to$83 − 47 → slide both up $3\to 86-50=36$3 → 86 − 50 = 36.

Divide by halving repeatedly

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

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

How to work out percentages in your head

To work out a percentage in your head, start from 10%, the number with its decimal point moved one place left, and build the rest from it: 35% of 80 is 3 × 8 + 4 = 28. When that is awkward, flip it: 4% of 25 equals 25% of 4 = 1.

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\to 50$50 → 50% of 18 = 9.

Build everything from 10%

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

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 do you actually get faster at mental math?

Getting faster at mental math comes from three habits, not talent. Make times tables automatic, since every trick assumes instant recall. Practice five minutes daily rather than an hour once a week, so recall keeps strengthening. Estimate before you calculate, rounding to catch large errors.

• 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. Related guides: Estimation and Rounding, Fractions and 36 Math Tricks and Number Shortcuts, and Why Each One Works.

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