Multiply Numbers Near the Same 10s Value

Use this trick when both numbers are close to the same multiple of 10 (like 10, 20, ..., 100).

  1. Pick a base which is the multiple of 10 that both numbers are close to.
  2. Figure out how far each number is from the base (positive or negative).
  3. Add one number to the other’s difference from the base.
  4. Multiply that result by the base.
  5. Then multiply the two differences.
  6. If both numbers are on the same side of the base, add the result from Step 5. If they’re on opposite sides, subtract it.
14 × 12
Base = 10 → Differences: +4 and +2
14 + 2 = 16 → 16 × 10 = 160
(Or: 12 + 4 = 16 — same result)
4 × 2 = 8 → 160 + 8 = 168
48 × 52
Base = 50 → Differences: −2 and +2
48 + 2 = 50 → 50 × 50 = 2500
(Or: 52 − 2 = 50 — same result)
(−2) × 2 = −4 → 2500 − 4 = 2496
104 × 107
Base = 100 → Differences: +4 and +7
104 + 7 = 111 → 111 × 100 = 11100
(Or: 107 + 4 = 111 — same result)
4 × 7 = 28 → 11100 + 28 = 11128

This only works if both numbers are close to the same base