Base Method Of Multiplication (PART-1)

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Let us have a look at the procedure involved in this technique of multiplication. I have outlined below the four steps required in this technique.

STEPS:

(a) Find the Base and the Difference

(b) Number of digits on the RHS = Number of zeros in the base

(c) Multiply the differences on the RHS

(d) Put the Cross Answer on the LHS

To understand how the method will work we solve following questions.

Step1: 

The first part of the step is to find the base. Have a look at example A. In this example the numbers are 97 and 99. We know that we can take only powers of 10 as bases. The powers of 10 are numbers like 10, 100, 1000, 10000, etc. In this case since both the numbers are closer to 100 we will take 100 as the base.

Similarly, in example B both the numbers are closer to 10,000 and so we will take 10,000 as the base.

So we Have Found the bases.

We are still on step A. Next, we have to find the differences.

In Example A the difference between 100 and 97 is 3 and the difference between 100 and 99 is 1.

In Example B the difference between 10,000 and 9989 is 11 and the difference between 10,000 and 9995 is 5.

Step2: 

In example A the base 100 has two zeros. Hence, the RHS will be filled in by a two-digit number.

In example B, the base 10,000 has four zeros and hence the RHS will be filled by a four-digit number.

Step3: 

The third step (step C) says to multiply the differences and write the answer in the right-hand side.

In example A we multiply the differences, viz. -3 by -1 and get the answer as 3. However, the RHS has to be filled by a two-digit number.

Hence, we convert the answer 3 into 03 and put it on the RHS.

In example B we multiply -11 by -5 and get the answer as 55.

Next, we convert 55 into a four-digit number 0055 and put it on the RHS.

Step4: 

Step D says to put the cross answer in the left hand side. Let us observe how Step D will be applied

in each of the alternatives.

In example A, the cross answer can be obtained by doing (97 – 1) or (99 – 3). 

In either case the answer will be 96. This 96 we will put on the LHS. But we already had 03 on the RHS. Hence, the

complete answer is 9603.

In example B, we subtract (9989 – 5) and get the answer as 9984. We can even subtract (9995 –11). 

In either case, the answer is the same. We put 9984 on the LHS. We already had 0055 in the RHS.

The complete answer is 99840055.

Let us solve a few examples:

Q.9750×9998?

A.

Since both the numbers are closer to 10000, we take it as the base. The difference between 10000and 9750 is 250 and the difference between 10000 and 9998 is 2. Next, the base 10000 has four zeros and hence the RHS will be filled by a four-digit answer. Next, we multiply -250 by -2 and write the answer as 0500 (converting it into a four-digit number) and putting it on the RHS. 

Finally, we subtract2 from 9750 and put it on the LHS. The final answer is 97480500.

Q.1007×1010?

A.

You can solve it by the above 4 steps.

In the next part we will see the cases of base method of Multiplication.