How to Multiply Two Numbers Either Side of 100

Updated 4 October 2026

Two numbers the same distance from a friendly number (e.g. 98 × 102 from 100).

98 × 102 = 9996

How do you multiply two numbers the same distance either side of 100?

When two numbers sit the same distance either side of a round number, square the round number and subtract the square of the distance. For 98 × 102, the round number is 100 and the distance is 2, so 98 × 102 = 100² − 2² = 10000 − 4 = 9996. It works because (m − d)(m + d) = m² − d²: multiplying out gives two middle terms, −md and +md, which cancel exactly. For 57 × 63, the middle is 60 and the distance is 3, so 60² − 3² = 3600 − 9 = 3591. For 36 × 44, the middle is 40 and the distance is 4, so 1600 − 16 = 1584. To find the middle, add the two numbers and halve: 57 + 63 = 120, and half of 120 is 60. If the halfway point is not a whole number, as in 57 × 64, the trick does not apply directly.

1. 98 and 102 sit 2 either side of 100, so this is (100 − 2)(100 + 2).

2. Multiplied out, the middle terms are +200 and −200 — they cancel exactly.

3. What survives is one square minus another: 10000 − 4 = 9996.

Does it work away from 100?

Any round number in the middle will do. 47 × 53 sits 3 either side of 50: $50^2-3^2=2500-9=2491$50² − 3² = 2500 − 9 = 2491. 28 × 32 sits 2 either side of 30: 900 − 4 = 896. 195 × 205 sits 5 either side of 200: 40000 − 25 = 39975.

How do you spot when to use it?

Two numbers whose sum is a round number sit the same distance either side of half that sum: 47 + 53 = 100, so the middle is 50 and the distance is 3. When the sum is not round the identity still holds, but the middle number is not friendly, and the long way is faster.

All 36 shortcuts: the Magic Tricks library.