How to multiply by 9 and 99
9 and 99 look like awkward numbers to multiply by — but they're each one step away from a round number, and that's all this shortcut needs.
The rule
Multiply by the round number just above instead — 10 in place of 9, or 100 in place of 99 — then subtract the original number once.
n × 99 = n × 100 − n
Why it works
9 is exactly 10 − 1, and 99 is exactly 100 − 1. Distributing the multiplication: n × (10 − 1) = 10n − n. Multiplying by a power of ten is instant (just shift digits), so the only real operation left is one subtraction.
Worked examples — ×9
47 × 9 — 470 − 47 = 423.
82 × 9 — 820 − 82 = 738.
136 × 9 — 1360 − 136 = 1224.
Worked examples — ×99
23 × 99 — 2300 − 23 = 2277.
150 × 99 — 15000 − 150 = 14850.
It generalizes further
The same logic applies to any "one less than round" multiplier — 999, 9999, and so on — and to numbers close to round values on the other side too (×11 is, in a sense, the mirror-image case: one more than 10, using addition instead of subtraction).
Practice it
Practice arithmetic → · See the rest of the shortcuts guide →