Numbers just under 100, like 97 and 96, can be multiplied without a calculator.

🪄 The trick: Find how far each number is below 100. Take one number minus the other number’s gap for the front two digits. Multiply the gaps for the last two digits.

Example 1: 97 × 96

Gaps: 97 is 3 below, 96 is 4 below

Front: 97 − 4 = 93

Back: 3 × 4 = 12

97 × 96 = 9312

Example 2: 98 × 95

Gaps: 2 and 5

Front: 98 − 5 = 93

Back: 2 × 5 = 10

98 × 95 = 9310

Challenge: 88 × 89 (the back is more than two digits)

Gaps: 12 and 11

Front: 88 − 11 = 77, so 7700

Back: 12 × 11 = 132

7700 + 132 = 7832

Why it works

(100 − a)(100 − b) = 100(100 − a − b) + ab. The front part is 100 − a − b hundreds, and the back part is the gaps multiplied.

Your turn

  1. 96 × 94
    Show answer

    96 − 6 = 90, 4 × 6 = 24, so 9024

  2. 99 × 97
    Show answer

    99 − 3 = 96, 1 × 3 = 03, so 9603

  3. 93 × 98
    Show answer

    93 − 2 = 91, 7 × 2 = 14, so 9114

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