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Tricks · Multiplying

Same start, ends add to 10

Two numbers that start the same and whose last digits add to 10, such as 43 × 47 or 62 × 68.

43 × 47

The trick, step by step

  1. Check: both start with 4, and 3 + 7 = 10.

  2. Multiply the start by the next number up: 4 × 5 = 20.

  3. Multiply the last digits: 3 × 7 = 21 (always write two digits: 1 × 9 = 09).

  4. Put them side by side: 43 × 47 = 2021.

given working answer taken away

Why it works

(10t + u)(10t + v) = 100t² + 10t(u + v) + uv. When u + v = 10 the middle part is 100t, so the whole is 100t(t + 1) + uv: t(t + 1) hundreds, and uv in the last two digits.

Practise this trick