The Nines Multiplier!

Tired of long multiplication? What if you could multiply ANY number by 9, 99, or 999 almost instantly, even in your head?

Subject: mental-calculation • Classes: 6–12 • Difficulty: basic (6-8)

The Trick

The Nines Multiplier! To multiply any number $X$ by $9$, think of $9$ as $(10-1)$. So, $X \times 9 = X \times (10-1) = (X \times 10) - X$. This means, just add a zero to $X$ and then subtract $X$ itself! For multiplying by $99$, think of it as $(100-1)$, so $X \times 99 = (X \times 100) - X$. Generalizing, for numbers like $9, 99, 999, \ldots$ (which are $10^k-1$), you simply multiply $X$ by $10^k$ (add $k$ zeros) and then subtract the original number $X$. It works because you are adding $X$ too many times when multiplying by $10^k$ instead of $10^k-1$, so you subtract $X$ once to correct it.

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