Long multiplication is reliable on paper, but in your head it asks you to remember too many partial answers at once. Mental multiplication works differently: you reshape the problem into one or two easy steps. This guide shows the reshaping tricks that cover most everyday products, explains when each one helps, and finishes with ways to check your answer and a practice set.
All of these methods rest on your times tables. If those still need work, start with how to learn times tables fast and come back.
This is the method behind all the others. Break a number into tens and ones, multiply each part, and add the results.
For 23 × 45, split both numbers and multiply every pair:
Then add: 800 + 100 + 120 + 15 = 1035. So 23 × 45 = 1035.
In your head, splitting only one number is usually easier. For 32 × 26: 30 × 26 = 780 and 2 × 26 = 52, then 780 + 52 = 832. Two partial answers are easier to hold than four.
If you halve one number and double the other, the product doesn't change. Keep going until the problem is easy.
It works best when one number is even and the other ends in 5, because doubling a 5 makes a round number. Our full guide to the doubling and halving trick has more examples and practice.
These are disguised divisions, because 5 is 10 ÷ 2, 25 is 100 ÷ 4 and 50 is 100 ÷ 2.
When a number sits just below a round number, multiply by the round number and take off the extra.
Take 97 × 43. Round 97 up to 100, which is 3 more. Multiply the round number: 100 × 43 = 4300. That counts 3 extra lots of 43, so take them away: 3 × 43 = 129, and 4300 − 129 = 4171. So 97 × 43 = 4171.
Smaller numbers work the same way: 49 × 8 is 50 × 8 = 400, take away one 8, which gives 392. And 99 × 24 is 2400 − 24 = 2376.
Times 9 is a special case: times 10, then take away the number once. 36 × 10 = 360, and 360 − 36 = 324, so 36 × 9 = 324.
Write the two digits apart and put their sum in the middle.
If the sum is 10 or more, carry the 1 to the first digit. For 86 × 11, the sum is 8 + 6 = 14. Write the 4 in the middle and add the 1 to the 8, which gives 946.
For numbers in the 90s, look at how far each one is below 100. For 96 × 97, the gaps are 4 and 3.
So 96 × 97 = 9312. This is the Vedic Nikhilam method; our Nikhilam guide explains why it works and how to use it above 100. For any two-digit pair, the Urdhva Tiryagbhyam method gives the answer in one line.
Answers:
Speed comes from using these tricks often. Play the multiplication game to practise against the clock, and keep the underlying facts fresh with the times tables chart.
Split one number into tens and ones, multiply each part by the other number, and add the two answers. If a shortcut fits, such as a number ending in 5 or one just below 100, use that instead.
Halving one number and doubling the other is the same as multiplying by 2 and dividing by 2, which cancel out. The product stays the same, but the numbers become easier.
Yes. Every trick here ends in a times-table fact or a multiplication by 10 or 100. The tricks save steps, but the facts underneath still have to be quick.