# All from 9 and the Last from 10 (Part II)

In last week’s issue of the MATH-Inic Newsletter, we discussed the application of the Vedic Math sutra All from 9 and the Last from 10 which is Nikhilam Navatashcaramam Dashatah in Sanskrit,  in getting the changefrom a P1,000 bill. This technique can, of course, be appliednot only ingetting our change from also from P10 or P100 payments, but also in all cases of subtraction where the minuend is a power of 10.

But how do we apply it when the minuend is not a power of 10?

For example, if instead of a P1,000 bill, I gave the cashier P900 – one P500 and 2 P200 bills – for the P768.45 shirt which I purchased. How much will be my change?

Before applying the Nikhilam, we must first use another Vedic Math Sutra, By one less than the one before, which simply means to deduct 1 from the initial non- zero digits  before performing the subtraction.

In the given case above, first we deduct 1 from 9 to get 8 and then subtract 7 to get 1.

P 9 0 0. 0 0 – 7 6 8. 4 5 = P 1 _ _ . _ _

Then we can apply all from 9 and the last from 10 to 68.45.

So our change is one hundred,

6 from 9 is thirty

8 from 9is one pesos and

4 from 9 is fifty

5 from 10 is five centavos.

P 9 0 0. 0 0 – 7 6 8. 4 5 = P 1 3 1 . 5 5

How about if we paid P1,500 for our purchase of P1, 126.75?

By applying by one less than the one before from 15, we get 14. Then we subtract 11 from 14 to get 3, which is three hundred.

P 1 5 0 0. 0 0 – 1 1 2 6. 7 5 = P 3 _ _ . _ _

We can now use Nikhilam on P26.75 to get

2 from 9 is seventy

6 from 9 is three pesos and

7 from 9 is twenty

5 from 10 is five centavos

P 1 5 0 0. 0 0 – 1 1 2 6. 7 5 = P 3 7 4 . 2 5

How much change will you get from the following?

1. P 200.00 – 123.45 =
2. P 200.00 – 74.34 =
3. P 500.00 – 234.65 =
4. P500.00 – 375. 15 =
5. P500.00 – 445.45 =
6. P600.00 – 485.67 =
7. P600.00  – 512.85 =
8. P1500.00 – 1283.95 =.
9. P2000.00 – 1367.57 =
10. P2500.00 – 2133. 89 =

The answers will be posted in the next issue of this newsletter.

Answers to our previous issue’s practice exercises:

What change will I receive from my P1,000 payment if my total purchase is:

1. P123.45 → P876.55
2. P241.75 → P758.25
3. P364.12 → P635.88
4. P468.44 → P531.56
5. P589.89 → P410.11
6. P648.16 → P351.84
7. P747.26 → P252.74
8. P888.88 → P111.12
9. P989.89 → P10.11
10. P747.47 → P252.53