# 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:

- 632 – 345 =
- 745 – 268 =
- 813 – 444 =
- 5232 – 3475 =
- 7524 – 3667 =
- 8413 – 5578 =
- 43,264 – 24,789 =
- 75, 243 – 36, 564 =
- 405, 432 – 236, 567 =
- 823, 526 – 545, 687 =

Here are the answers to last week’s questions:

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