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

In the two past issues of our MATH-Inic Newletter, we discussed how the sutra “all from 9 and the Last from 10 can be applied in computing the change not only from P1,000 and P100 bills but also from other multiples of P100.

But there are other cases when we can not immediately apply the Nikhilam Sutra.

The first of these cases is when the number of digits in the subtrahend is less than the number of zeroes in the minuend. Here we can add zeroes at the front of the digits of the subtrahend to make them equal to the number of zeroes of the minuend or simply apply “By One less than the One Before” to the digits in excess of the digits of subtrahend before applying Nikhilam.

For example, P 1,000.00 less 78.15. Here we have a total of 5 zeroes in the minuend and only 4 digits in the subtrahend. So, we need to add 1 zero in front of 78.15 to make the subtraction P1,000.00 – 078.15.

The change will be:

0 from 9 is nine hundred

7 from 9 is twenty

8 from 9 is one pesos and

1 from 9 is eighty

5 from 10 is five centavos

Other examples:

P 1,000.00 – 5.74 = P1,000.00 – 005.74 = P994.26

1,000,000 – 2,468 = 1,000,000 – 002,468 = 997,532

In our first example, P1,000.00 – 78.15, there are only 4 digits in the subtrahend while there are 6 digits in the minuend. We therefore deduct 1 from 10 to get 9, then apply “All from 9 and the Last from 10” to 78.15 to get P921.85.

More examples:

P500.00 – 5.74 → 50 – 1 = 49 and then 4.26 to get a final P494.26

7,000,000 – 2,468 → 700 – 1 = 699 and 7532 to get 6,997,532

Try these:

1. P100.00 – 3.45 =
2. P100.00 – 7. 82 =
3. P1000.00 – 32.54 =
4. P1000.00 – 75.68 =
5. 100,000 – 376 =
6. 1,000,000 – 7634 =
7. P500.00 – 97.65 =
8. 300,000 – 234 =
9. 7,000,000 – 4,567 =
10. 23,000,000 – 17,257 =

Here are the answers to last week’s questions:

How much change will you get from the following?

1. P 200.00 – 123.45 = P 76.55
2. P 200.00 – 74.34 = P 124.66
3. P 500.00 – 234.65 = P 265.35
4. P500.00 – 375. 15 = P 124.85
5. P500.00 – 445.45 = P 54.55
6. P600.00 – 485.67 = P 114.33
7. P600.00  – 512.85 = P 87.15
8. P1500.00 – 1283.95 =.P 216.05
9. P2000.00 – 1367.57 = P 632.43
10. P2500.00 – 2133. 89 = P 366.11