How to Multiply by 9, 99, 999, 9999 Faster

Before I explain the previous post about multiplication, I would like to discuss first multiplication by 9, 99, 999, 9999 or any number whose digits are all 9. For example, how do we multiply 87 × 99? To multiply by numbers whose digits are all 9, we just add 1 to 9, 99, 999, 9999 and so on and then subtract the number that we are multiplying with it.

Example 1: 7 × 9

1. 7 × 9 = 7 × 10 – 7

= 70 – 7 = 63

The reason that we subtract 7 is that because 9 = 10 – 1 and that 7 × 9 = 7 (10 – 1) = 70 – 7 = 63.

Example 2: 4 × 99

4 × 99 = 4(100 – 1) = 400 – 4 = 396

Example 3: 18 × 999

18 × 999 = 18(1000 – 1) = 18000 – 18 = 17982 

This one looks difficult, but you don’t really need to think of 18,000 but only think of 100 – 18. Subtracting 100 by 18000 equals 17900. Then, subtracting 18 from 100 is 82, and 18900 + 82 is equal to 17982. We will discuss strategies such as this in the next posts.

Example 4: 256   × 9999  = 2,560,000 – 256 = 2559744

Notice that even if you calculate by paper and not mentally, the steps are still a lot shorter.

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