How to Multiply Two Numbers Just Below 100

Multiply two numbers just below 100, using their "distance from 100".

97 × 94 = 9118

How do you multiply two numbers just below 100?

To multiply two numbers just below 100, take the distance of one from 100 off the other number, then attach the product of the two distances as two digits. For 97 × 94, the distances are 3 and 6. Take 94 − 3 = 91 for the first two digits and 3 × 6 = 18 for the last two, giving 9118. It works because (100 − a)(100 − b) is 100 × (100 − a − b) + ab, so the first part counts hundreds and the product of the distances fills the last two places. A product under 10 still takes two digits: 92 × 99 has distances 8 and 1, which gives 91 and 08, so 9108. A product of 100 or more carries into the hundreds: 88 × 85 has distances 12 and 15, so 88 − 15 = 73 and 12 × 15 = 180, giving 7300 + 180 = 7480.

  1. 97 × 94each one's distance from 100(100 − 3)(100 − 6)

    97 is 3 below 100 and 94 is 6 below, so this is (100 − 3)(100 − 6).

  2. 10000 − 300 − 600100 − 3 − 6100 × 91

    Both distances come off the hundreds: 100 − 3 − 6 = 91, the same as 97 − 6.

  3. 3 × 6 = 18the corner both distances left

    The corner where the two distances overlap is 3 × 6 = 18, and it goes last.

  4. A corner under 10 still fills two places: 8 × 1 = 8 is written 08, so 92 × 99 = 9108.

Your turn

Three to try in your head — tap what you get.

96 × 95

98 × 97

94 × 91

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