In easy methods for multiplication by 9 we used the fact that the sum of the digits of any multiple of 9 will always be 9. There is another simple and easy method to multiply any number by 9. Let us look at that method today.

We know that 9 is 1 less than 10. When we need to multiply a number by 9, multiply it by 10 and then subtract the given number from the answer once to get the correct answer. This is so simple that we can do it mentally and it does not involve multiplication at all.

Example: 42 x 9

Multiply 42 x 10 = 420 (very simple to do mentally)

Now subtract 42 from the answer. 420 – 42 = 378.

That is the answer.

This is not only for two-digit numbers, this method can be used for any number to be multiplied by 9.

Example: 148 x 9

Multiply 148 x 10 = 1480

Subtract 148 from the answer. 1480 – 148= 1332.

That is the answer.

At this point we can also check the sum of the digits of the answer to see whether it comes to a total of 9. 1 + 3 +3 + 2 = 9. So the digit sum check tells us the answer is correct.

Using this method can we think of multiplying any number by 99? Yes, of course! 99 is one less than 100. So to multiply a number by 99 we need to multiply the number by 100 and then subtract the number from the answer. The steps are the same.

Example: 112 x 99

112 x 100 = 11200

Subtract 112 from the answer.

11200 – 112 = 11088.

That is the answer.

Multiplication by 9, 99, 999, 9999 etc can be done in the same manner. We need to be careful to add the right number of zeroes in the first step. To multiply a number by 999, we multiply by 1000 and subtract the number. So the number of 9s will decide the number of zeroes to be added in the first step of multiplication.

For multiplication by 9, one zero is added as we multiply by10.

For multiplication by 99, two zeroes are added as we multiply by 100.

For multiplication by 999, three zeroes are added and so on.

So let us do some problems:

a) 321 x 99

321 x 100 = 32100

32100 – 321 = 31779

So the answer is 321 x 99 = 31779

b) 503 x 999

503 x 1000 = 503000

503000 – 503 = 502497

So 503 x 999 = 502497