How to Multiply by Doubling One Number and Halving the Other

Updated 4 October 2026

Halve one side, double the other — the product stays the same.

14 × 45 = 630

How do you multiply by halving one number and doubling the other?

Halving one number while doubling the other leaves the product unchanged, so turn the pair into one you can do in your head. For 14 × 45, halve the 14 and double the 45: 7 × 90 = 630. It works because you have only moved a factor of 2 from one number to the other, and multiplication does not care how its factors are grouped: 14 × 45 is 7 × 2 × 45, which is 7 × 90. Double the number that becomes round, such as 5, 15, 35 or 45, and halve the one that is even. When the halved number is still even, go again: 16 × 35 becomes 8 × 70 = 560, and 28 × 25 becomes 14 × 50, then 7 × 100 = 700. If both numbers are odd, there is no factor of 2 to move, and splitting one number is the better route: 13 × 15 is 130 + 65, which is 195.

1. Halving 14 while doubling 45 just moves a ×2 across. The product never changes.

2. Now it is easy: 7 × 90 = 630.

3. Aim the doubling at the number ending in 5 — it becomes a friendly ten.

Can you double and halve more than once?

Keep going while one number is even. For 24 × 125: halve and double once to 12 × 250, again to 6 × 500, and again to 3 × 1000 = 3000. For 36 × 15: 18 × 30 = 540. Each step moves one factor of 2 across, so the product never changes.

Which number should you double?

Double the one that becomes a round number: 5 becomes 10, 15 becomes 30, 25 becomes 50, 45 becomes 90, 125 becomes 250. Halve the other, which has to be even. If both are odd, this trick does not apply, and splitting one of them is the move instead.

All 36 shortcuts: the Magic Tricks library.