# 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 :)

1. Product of 177 and 88 equal to 15576. Your answer is wrong 10296.

1. Please check the number once Unknown...

Its 117 not 177 ;)

2. it is not clear to me

3. this technique is too good, but clarify this problem also
398x431
plz
plz
tell me the technic
i tried as
398 -2
431 +31
---------------
429 -62
428 38
428*4
=171238
it should come like
171538
am missing some where
i could not find it
help me in that

1. subtract as 400-62 = 338
and add 3 carry with the unite digit of 1712 i.e. 2+3 = 5
now ans is 171538

2. First multiply 429 by 4 which is equal to 1716. Then borrow 1 form this number which make it 1715. Then substract 62 form 100 which is 38. Combining both we get 171538. That's the ans.

4. 5. i gt the answer sir thank you it was very helpful for me

6. the answer for my question is the sum of 1st part and the first three digis in 2nd part i.e.,843 and combine last 2 digits of 2nd part wth the answer so finally we get 84318

7. It is not useful ...Calculate 975*951
and show me correct explanation of the following problem.

1. Consider base as 950, as it is near to both the numbers
975 +25
951 +1
First number : 975+1=951+25=976
AS our base number is 950. Multiply first number with 9.5 = 976*9.5=9272.
Second number = 1*25=25.

8. I'm unable to understand the product of 117*88

9. Its easy 117*88
Take first the base as 100 so the calculations would be
117 17
88 -12
------- ---------
105 -204
Now, we got a number -204 that is lesser than 100, so in order to calculate, we will use temporary base as 300 and subtract 204 from 300 to get 96.. So, as we used base 300, we are also need to subtract 3 from 105 which will be 102
So, the final answer would be 10296.
Lets take another example
138*79
138 38
79 -21
----- --------
117 -798
Here we can see that the product is -798 which is again less than 100, so in order to get a positive number we will just check for the nearest temporary number, which is 800 here... so, it shold be 800-798=2. And also, we need to subtract 8 from 117 which will be 109.
So, the answer would be 10902.

Hope this helps :)

10. Hello there, its an easy calculation...
117*88
Take the base as 100
117 17
88 -12
----- --------
105 -204
Here the product is -204, which is lesser than 100 and we need to get a positive number. So, lets take the base number as 300 temporarily and the answer will be 300-204 = 96.
And as we are using the base number now as 300, we will be subtracting three from 105, which gives us 102
Lets check another example
138*79
138 38
79 -21
----- -------
117 -798
Here the product is -798, and now in order to make it a positive number we will take the nearest base number which is 800, so it will be 800-798 = 2
Now, the temporary base is 800, we need to take 8 from 117 and it will be 117-8=109

Hope this helps :)

1. thanks.doubts cleared

11. 118*78=?
pls give me description

1. 118 18
78 -22
---- -----
96 -396

Here the product of 18 and -22 is -396 but its a negative answer, so to round of to a positive number, we will take the nearest temporary base which is 400. So, 400-396 is 04
And we will also subtract 4 (as the base number is 400) from 96 which will be 92.
So, the final answer will be 9204

12. 118*78=?
pls give me description.

13. my coments never get posted... or i dont know how to post..please tell me how to post. Thanks in advance

14. 1. BAse 500
487. -13
546. +46
-------------
First part = 487-13 or 546+46 multiplied by 500
=533 * 5=2665
Now second part = -(13 * 46)= -598
Borrow 6 from 2665 to make 600 then calculate second part as 600-598=02
And after borrowing 6 from 15 , 9 left so first part becomes 2659 so the final result= 265902

15. pls explain the multiplication method for 245 x 376
in this suituations how we take tha base number