Quick 9s Multiplication!

Ever get stuck multiplying by 9, 99, or even 999? What if there was a lightning-fast secret to conquer these calculations in seconds?

Subject: mental-calculation • Classes: 6–12 • Difficulty: basic

The Trick

The trick is to think of 9 as $(10-1)$, 99 as $(100-1)$, and so on. Instead of multiplying by 9, multiply by 10 (just add a zero!), then subtract the original number. For $N \times 9$, calculate $(N \times 10) - N$. For $N \times 99$, calculate $(N \times 100) - N$. This works because of the distributive property: $N \times (10-1) = (N \times 10) - (N \times 1)$.

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