## Thursday, February 2, 2012

### Multiplying by 9, 99 ,999 etc

Here is an interesting trick for multiplying numbers by 99, 999, 9999, and so on. This trick works with any number of 9's you have. To multiply numbers by 99  you subtract 1 from the number to be multiplied and you get the first digit in your answer. then you take the number you just got and subtract that from 99 and you get the second part of your answer. This method works for all numbers less than 99, 999 , 9999 depending on which one you are multiplying by. So if you were multiplying by 99 it would work for all numbers up to 98

Example:     99 X 3 = ?

1.)subtract 1 from 3:    3-1=2 First part of answer
2.)the subtract the result from 99:   99-2=97    second part of answer

and combine the two answer and you get 297

as you can see all you are doing is taking the answer you get form the first step and making it the first digit(s) in your answer, and the result from the second step is the rest of the digits.

Example 2:            99 X 12 = ?

1.)subtract 1 from 12,   12-1=11
2.)subtract 11 from 99,  99-11=88

and you combine the two and you have 1188

Example 3:    999 X 998 =?

1.) subtract 1 from 998,    998-1= 997
2.)subtract 997 from 999,  999-997=2

combine the two answers and you have 9972... but wait that's not right. So what happened? In this example, the second part of the answer only has 1 digit yet 999 has 3 which means that the second part of the answer must have 3 digits. so how do we show the number 2 as 3 digits. Its simple we just add 2 zeros at the beginning turning 2 into 002 so when we go over our example again:

1.) subtract 1 from 998,         998-1=997
2.) subtract 997 from 999,     999-997= 002

combining the two we get  997002

This is the same for the 2 digit examples the second half of our answer must have the same number of digits as the 9's we are multiplying by
Example: 99 X 98= ?

1.) subtract 1 from 98,     98-1= 97
2.) subtract 97 from 99,   99-97= 02 (here we added the 0 at the beginning to make the number of digits the same)

combining the two we get 9702

Summary:
To multiply numbers by 99  you subtract 1 from the number to be multiplied and you get the first digit in your answer. then you take the number you just got and subtract that from 99 and you get the second part of your answer. This method works for all numbers less than 99, 999 , 9999 depending on which one you are multiplying by. So if you were multiplying by 99 it would work for all numbers up to 98

The second half of our answer must have the same number of digits as the number of 9's you are multiplying by.