## Base method of multiplication

1 st of all question is, why it is called base method. In Vedic mathematics there is a saying in Sanskrit,

**“Nikhilam Navatascaramam Dasatah”.** It means “all form 9 and last form 10”

In this method we have to determine the base of the number first. Detailed steps of this method is given

below,

- 1 st of all find the base and the difference with the base.
- Number of digits in the RHS is equal to number zeros in the base.
- Multiply the differences on the RHS.
- Put the cross answer in LHS.

### Type 1: Multiply the two numbers with same base.

*Example 1: 997×995*

Answer: 1 st of all the base of the given two number is same which is 1000.

What we see in the above multiplication is in the RHS we put 015 because (5×3=15). But since zero in

the base number is 3, so we have to put a “0” before 15 in the RHS such that total digit in the RHS is

equal to the zeros in the base number.

For LHS we have to subtract either (3 from 995) or (5 from 997). That‟s why we put 992(995-3 or 997-5) in the LHS.

So,** 997×995=992015.**

#### Example 2: *Find 103×105.*

Answer: Here Base is 100.

In the above illustration we see that since the base is 100 so we have to put only two digit in the RHS of

the slash(/), so we put just 15(3×5). And in the LHS we put **108(103+5 or 105+3).**

So **103×105=10815.**

### Type 2: Multiply a number below the base with a number above the base

Earlier we multiply two numbers either above the base or below the base. But in Type 2 we multiply one number below the base with other above the base.

*Example 1: Find 91×106*

Answer: Here actual base for 91 is 100 and 106 is 1000. But we will take 100 as working base since 100 is closer to both 91 and 106.

Here final answer =** (97×Base)-54= (97×100)-54=9646.**

Here also we put RHS and LHS as we put in Type 1. But since there is a minus sign before 9 we put (-54) in RHS. In the final answer we have to multiply the LHS with the base number then subtract RHS to get the final answer. So final answer is **9646.**

*Example 2: 855×1004*

Answer: Here actual working base is 1000.

Here we put -580(-145×4) in RHS. Put 859(855+4 or 1004-145) LHS. Final answer will be like below,

(859×Base)-580= (859×1000)-580=858420.

**Example 3: 82×105**

Answer: Working base is 100.

Final answer = **(87×Base)-90= (87×100)-90=8610.**

### Type 3: When number of digits in RHS exceeds number of zeros in the base

You can understand Type 3 with some example given below,

*Example 1: Find 961×951*

Answer: Here working base is 1000. Number zeros in the base are 3.

Here we get 1911 by multiplying 39 by 49, but we need only 3 digits in the RHS since the base has only 3zeros. So what to do next?

Now we must add „1‟ in the extreme left of the number „1911‟of the RHS to the number „912‟of the LHS.And put only „911‟ in the RHS. Numerically final answer is,

913911, since **(912+1=913).**

*Example 2: Find 1223×1227*

Answer: Here working base is 1000. Number of zeros in the base is 3.

Here we get 50621(223×227) in the RHS. But we need only 3 digits in the RHS since zeros in the base is3. So we add „50‟ in the extreme left of the number „50621‟ of the RHS to the number „1450‟ in the LHSto get the final answer.

**1450+50=1500** in the LHS and 621 in the RHS.

So, final answer is **1500621.**