Shortcut for Multiplication (Base Number Method Part 2)

We've already discussed about the Shortcut Method (Base Number Method) for doing multiplications. In the earlier post we've discussed doing the multiplication by taking the base as 100 (Click Here to read that). I mean, you can do the multiplication for the numbers nearer to the 100. Then what about the remaining numbers? Well, being the Guide 4 Bank Exams we have solutions for all Banking Problems... So, lets have a look at some more approaches of the Base Number Method so that it will be easier for you to multiply any number with any number :)

Find the product of 117 and 88

117   --->   +17

  88   --->   -12

____         _____

105             -204           Ans : 10296

Here, note that to take care of -204 of the second part, borrowing a 1 from the first part is not sufficient (because the 100 it becomes when it comes to the second part is not numerically greater than -204). So, we should borrow 3 from 105 (leaving 102 as the first part) which becomes 300 in the second part to which -204 should be added giving us 96. Hence, the product of 117 and 88 is 10296.

Find the product of 997 and 983.

Here, both the numbers are close to 1000. So take 1000 as the base number.

997   --->   -3

983   --->   -17

_____         _____

980             +51              Ans : 980051

The Second part 51 has only two digits whereas the base 1000 has three zeroes. So, 51 will be written as 051. hence the Product is 980051.

Find the product of 297 and 292.

Here, the numbers are not close to any power of 10 but are close to 300 which is a multiple of 100 which itself is a power of 10. So we adopt 300 as a "temporary base". This temporary base is a multiple (or a sub-multiple) of the main base 100. Here, the temporary base 300 = 3 X 100. Then, the procedure of finding out the deviation from the base, getting the cross-totals and the product of the deviations should be done in a manner similar to the previous cases except that the deviations will be taken from the temporary base.

297   --->      -3

292   --->      -8

____           ____

289              +24            Ans : 86724

We've got the first part of the answer as 289 and the second part of the answer as 24. But before we put these two parts together to get the final result, one more step is involved. The first part of the answer is not the final figure. This is an intermediate stage of the first part. This first part should be multiplied by the same figure with which the power of 10 is multiplied to get the temporary base. In this case, we multiplied 100 (which is the power of 10) by 3 to get the temporary base 300. So, the intermediate stage figure of the first part (289) will also have to be multiplied by 3 to get the final figure for the first part. Hence the first part wil be 867 ( = 3 x 289). Now putting the first and the second parts together , the product of 297 and 292 is 86724 (here remember that the product of the deviations should still have as many digits as the number of zeroes in the base, in the above case it is TWO. because 100 has TWO zeroes).

Thats all for now friends. Tomorrow we shall discuss another Shortcut Method. Happy Reading :)

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