.
Now we shall discuss another Simple and Useful method for
Multiplication. In this method we take a base (according to the given
numbers) and do the multiplication according to that base. Assume that
you have to multiply 97 with 92. The power of 10 to which these two
numbers are close is 100. We call this 100 as the base. Now write these two numbers with the difference from the base.
97 ------> -3 (because 97 is obtained as 100 - 3)
92 ------> -8 (because 92 is obtained as 100 -8)
Then take the sum of the two numbers (including their signs) along
either one of the two diagonals (see, it will be same for both cases).
Have a look at the above example,
The diagonal sum is 97 - 8 = 92 - 3 = 89
This will form the first part of the Answer.
The second part of the answer is the product (taken along with the sign)
of the difference from the power of 10 written for the two numbers. In
the above example it is the product of -3 and -8 which is 24.
So, putting these two parts (89 and 24) together one next to the other, the answer is 8924, i.e., the product of 97 and 92 is 8924.
Note : Here keep in mind that the product of the two deviations
should have as many digits as the number of zeros in the base. For
Example, in this case the product of -8 and -3 has 2 digits which is the
same as the number of zeroes in 100.
Lets have a look at another example so that you can understand the above method completely.
Find the product of 113 and 118
Here, both the numbers are greater than 100 and the base here is 100.
Taking the difference of the two numbers 113 and 118 from the base, we
get +13 and +18 and write them as below.
113 ----- > + 13
118 ----- > +18
_____ _______
131 234 Ans : 13334
The first part of the answer is the cross-total of 113 and +18 which is
131. The second part of the answer, i.e., the product of the deviations
(+13 and +18) is equal to 234. But we said there should be as many
digits in this product as the number of zeroes in the base (which is 100
here). Since the base has two zeroes, the second part of the answer
should also have two digits. Since 234 has three digits, we should
retain two digits 4 and 3 and carry forward the third digit 2 to the
first part of the answer. hence, the first part of the answer now
becomes 133 and the second part is 34. The product of 113 and 118 is
thus equal to 13334.
