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Tricks · Multiplying

Multiply numbers near 100

Two numbers close to 100, such as 97 × 94 or 103 × 104.

97 × 94

The trick, step by step

  1. How far each is from 100: 97 is 3 below, 94 is 6 below.

  2. Cross: 97 − 6 = 91 (or 94 − 3, the same). These are the hundreds.

  3. Multiply the gaps: 3 × 6 = 18. These are the last two digits.

  4. So 97 × 94 = 9118. Above 100 it is the same with +: 103 × 104 = 107|12 = 10,712.

given working answer taken away

Why it works

(100 − x)(100 − y) = 100(100 − x − y) + xy. The cross step gives 100 − x − y, the hundreds, and xy fills the last two digits (carry if it is 100 or more). Above 100 both gaps are added; with one above and one below, xy is taken away.

Practise this trick