Multiplying in Your Head

Last updated September 18, 2026

Multiplication is where mental arithmetic gets a reputation for being hard, and it is the place where the school method serves you worst. Long multiplication is designed for paper, where you can park partial products and come back to them. In your head there is nowhere to park anything.

Everything below is a way of turning one hard multiplication into two or three easy ones.

Split the number you are multiplying by

This is the workhorse. Break one number into parts you can handle, multiply each part, and add.

7 × 46 → 7 × 40 = 280, and 7 × 6 = 42 → 322.

The order matters. Doing the big part first means your running total is already close to the answer, so the second step is a small adjustment rather than a leap.

Two-digit by two-digit

Same idea, one more step. Split the second number into tens and units, multiply the whole first number by each, and add.

23 × 47:

• 23 × 40 = 920
• 23 × 7 = 161
• 920 + 161 = 1081

Three easy steps and one addition. Compare that with trying to hold four partial products from the paper method.

Round and correct

When a number is close to something round, go past it and come back.

• 19 × 24 → 20 × 24 = 480, minus 24 → 456
• 98 × 15 → 100 × 15 = 1500, minus 2 × 15 = 30 → 1470
• 34 × 9 → 34 × 10 = 340, minus 34 → 306

The trap is forgetting how many lots you took off. In 98 × 15 you rounded 98 up by two, so you owe back two fifteens, not one.

Halve one side, double the other

Especially good when 25 or 50 is involved, because they turn into 50 and 100.

• 16 × 25 → 8 × 50 = 400
• 24 × 25 → 12 × 50 = 6 × 100 = 600 (twice, if it helps)
• 14 × 50 → 7 × 100 = 700

Squares you should simply know

Squares from 11 to 20 come up constantly, and knowing them outright removes a whole step from other problems.

Using a square you already know

Neighbours of a known square are one step away. To go up one, add the number you squared and the next one.

16² from 15²: 225 + 15 + 16 = 256.

To go down one, subtract the number you squared and the one below.

14² from 15²: 225 − 15 − 14 = 196.

Numbers straddling a round number

When both numbers sit the same distance from a round one, square the round number and subtract the gap squared.

• 48 × 52 → 50² − 2² = 2500 − 4 = 2496
• 17 × 23 → 20² − 3² = 400 − 9 = 391
• 95 × 105 → 100² − 5² = 10000 − 25 = 9975

Dividing is multiplying asked backwards

For awkward divisions, factor the divisor and divide in stages.

• 456 ÷ 8 → ÷2 = 228, ÷2 = 114, ÷2 = 57
• 270 ÷ 15 → ÷5 = 54, ÷3 = 18

Three easy halvings beat one hard division every time.

Practising it

Reading these is the easy part; the gap between knowing a method and reaching for it under time pressure is where the actual work is. Short daily rounds do more than long occasional ones. Carry the One‘s Difficult mode is where most of this becomes second nature — the numbers are big enough to need a method and small enough to finish before the clock does.

More like this: all the mental arithmetic guides.