Multiplying by 9 Tricks and Shortcuts

If we multiply numbers by 9, we can actually find some pattern. Let us look at the pattern as shown below.

1 × 9 = 9

2 × 9 = 18

3 × 9 = 27

4 × 9 = 36

5 × 9 = 45

6 × 9 = 54

7 × 9 = 63

8 × 9 = 72

9 × 9 = 81 

Notice that the sum of the digits of the product is always 9. The sum of 1 and 8 in 18 is 9, the sum of 2 and 7 in 27 is 9 and so on. We can also see starting from 2 that the tens digit of the product is always 1 less than the multiplier (2, 3, … , 8, 9).  For example, 6 × 9 = 54. Thus, we can use this technique to memorize the multiplication table.

Example:

What is  8 × 9?

The tens digit of the product is less than 8, so it is 7.

The digits add up to 9, so the ones digit must be 2.

Therefore, 8 × 9 = 72.

Note:

This trick is probably convenient for some, but there are only 9 numbers, so I would still recommend memorizing the multiplication table in multiplying by 9.

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