For multiplying two numbers together which are both close to a base of 10, 100, 1000, etc., the quick method of All from nine and the last from ten can be used. In Sanskrit the sutra is
Nikhilam Navatascaraman Dasatah - (Nikhilam for short).
When applied to any number the All from 9 and the last from 10 rule gives the complement of that number. For example, for 876, the complement is 124, that is, 8 from 9 = 1,
7 from 9 = 2 and 6 from 10 = 4. 124 is the complement of 876 because when added together these two numbers make 1000. Note that when the number ends with a zero then the rule is applied to the last number. For example, with 790, the last number is 9, since 0 is not a number. The All from nine rule should be taken as, All from nine and the last number from ten. Any final zeros are placed at the end. The complement of 790 is then 210.
7 from 9 = 2 and 6 from 10 = 4. 124 is the complement of 876 because when added together these two numbers make 1000. Note that when the number ends with a zero then the rule is applied to the last number. For example, with 790, the last number is 9, since 0 is not a number. The All from nine rule should be taken as, All from nine and the last number from ten. Any final zeros are placed at the end. The complement of 790 is then 210.
Multiplying numbers using complements requires only one line of easy working. Look at the example below.
Example 86 x 97
Example 63 x 92
Now work through this exercise...
You can download a pdf of this by clicking on this link Exercise 1.1 pdf download
