General Subtraction using Nikhilam

In the past 4 issues of our MATH-Inic Newsletter, we discussed various money applications of the Vedic Math Sutra, All from 9 and the Last from 10 or Nikhilam Navatascaraman Dasatah in Sanskrit which are discussed in our book 25 Math Short Cuts.

Now we will apply this sutra in a general subtraction technique which will eliminate “borrowing”.

Consider this: any number can be expressed as a difference between its base and its ten’s complement. For instance, using the Nikhilam sutra we can easily get the ten’s complement of  676 as 324 , and it can also be expressed as (1000 – 324).

Now, if we want to  deduct 676 from say,  865,

We have 865 – 676 = 865 – (1000 – 324)

= (865 + 324) – 1000

= 1189 – 1000 = 189.

We can see that instead of direct subtraction which may lead to “borrowings”, we can add the ten’s complement of the subtrahend to the minuend and disregard the leading “1” in the sum to get the difference.

Let’s take some more examples: 5386 – 2897= 2489

            5 3 8 6           →     5 3 8 6 

2 8 9 7           → + 7 1 0 3  – 1 0, 0 0 0

                                       1 2 4 8 9

7 4 3, 2 5 7 – 2 5 6, 4 8 9 = 4 8 6, 7 6 8

            7 4 3, 2 5 7   →     7 4 3, 2 5 7 

2 5 6 4 8  9   → + 7 4 3, 5 1 1 – 1, 0 0 0, 0 0 0  

                                      1 4 8 6, 7 6 8

Try these:

1. 632 – 345 =
2. 745 – 268 =
3. 813 – 444 =
4. 5232 – 3475 =
5. 7524 – 3667 =
6. 8413 – 5578 =
7. 43,264 – 24,789 =
8.  75, 243 – 36, 564 =
9. 405, 432 – 236, 567 =
10. 823, 526 – 545, 687 =

Here are the answers to last week’s questions:

1. 100 – 30 = 70
2. 1000 – 400 = 600
3. 1000 – 540 = 460
4. 10,000 – 3,450 = 6,550
5. 10,000 – 7,200 = 2,800
6. 100, 000 – 27,000 = 73,000
7. 100,000 – 53, 230 = 46,770
8. 1,000,000 – 325, 000 = 675,000
9. 1,000,000 – 645, 200 = 354,800
10. 1,000,000 – 165,430 = 834,570