Vedic Math Short Trick – How to multiply the numbers near to 100
In this topic we will see how to multiply the numbers which are near to 100 . When we are considering the number that two numbers should be below 100 or both above 100.
So, let us see what is the trick here.
N1*N2 = (N1 + d2), (d1*d2)
Where, N1 is the first number near to 100
N2 is the second number near to 100
And d1 = N1 – Base And d2 = N2 – Base
See here we are taking multiplication of numbers which are near to 100 only. That’s why here the base considered is 100.
Base = 100 = 102
As the power of 10 is 2 here and hence the product (d1*d2) should be always two digit number only. Otherwise we have adjust it as given in the following examples.
So, here d1= N1 – Base = N1 – 100
And d2 = N2 – Base = N2 – 100
Let us understand this trick by solving examples for numbers which are below 100:
1.) 93*91
Both these numbers 93 and 91 are near to 100 and also below 100.
Here d1 = 93-100 = -7
And d2 = 91-100 = -9
Let us put all these values in formula given,
93*91= 93+(-9), (-9)*(-7)
= 84, 63
Here 63 is the product which is already 2 digit, no need to adjust it again.
Hence our final answer is 93*91= 8463
2.) 98*99
Here, d1 = 98-100= -2
And d2 = 99-100 = -1
This, by using given formula we can write
98*99 = 98+(-1), (-2)*(-1)
= 97, 2
Here the product came is 2 which is 1 digit number but here base is 100= 102 that’s why the product d1*d2 should be 2 digit number only.
So we can write, 2 = 02
Then, 98*99 =97, 02
Thus, 98*99= 9792
3.) 91*88
Here, d1= 91-100= -9
And d2 = 88-100= -12
Then, 91*88= 91+(-12), (-9)*(-12)
= 79, 108
Here, the product of d1*d2 obtained is 108 which is three digit number but we want two digit number only that’s why we will take last number from left side that is 1 carry and we add to the term 79.
We will get, 91*88= 80, 08
Finally, 91*88= 8008
Now we will consider examples of numbers which are above 100:
1) 102*104
Here, d1 = 102 – 100= 2
And d2 = 104 -100 = 4
This, by using given formula we can write
102*104= 102+4, 2*4
= 106,8
Here the product came is 8 which is 1 digit number but here base is 100= 102 that’s why the product d1*d2 should be 2 digit number only.
So we can write, 8= 08
Then, 102*104= 106, 08
Thus, 102*104= 10608
Or 10.2*1.04= 10.608
2) 115*110
Here, d1= 115-100 = 15
And d2 = 110-100 = 10
Then, 115*110= 115+10, 15*10
= 125, 150
Here, the product of d1*d2 obtained is 150 which is three digit number but we want two digit number only that’s why we will take last number from left side that is 1 carry and we add to the term 125.
We will get, 115*110= 126, 50
Finally, 115*110= 12650
Also, 0.115*110= 12.650