All From 9 and the Last from 10

If I pay the shirt which I purchased for P768.45 with a P1,000 bill, how much change will I get?

This is a problem which we always encounter whenever we go to the market or go shopping. This is simple exercise in subtraction, but we can not use the method taught to us in school, that is, starting from the right (0 – 5) with a lot of “borrowings”. We would need paper and pencil to list down the results by columns and only after completing the calculation, can we determine the answer by reading from left to right.

But we can begin to announce the answer as we compute if we will start from left to right. This can be done easily by using the Vedic Sutra, All from 9 and the last from 10. This is discussed in Chapter 2 of our book, 25 Math Short Cuts.

To do this, we just deduct every digit of the purchase price from 9 except the last digit which we will subtract from 10. But before that, we can just look at the subtrahend to know that it starts with “seven hundred” and that must be the place value of the first answer digit.

7 from 9 is two hundred,

6 from 9 is thirty

8 from 9 is one pesos, and

4 from 9 is fifty

5 from 10 is five centavos.

Some people find it easier to add than subtract:

What should I add to 7 to make 9: Two hundred

What should I add to 6 to make 9: thirty–  

What should I add to 8 to make 9: one pesos and

What should I add to 4 to make 9: fifty

What should I add to 5 to make 10: five centavos

We will discuss other cases in the next issue of this newsletter. Meanwhile try to answer these questions mentally:

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

1. P123.45
2. P241.75
3. P364.12
4. P468.44
5. P589.89
6. P648.16
7. P747.26
8. P888.88
9. P989.89
10. P747.47

See the answers in the next issue of the MATH-Inic Newsletter

Answers to last week’s exercises:

1. 3 + 9  + 4 + 7 + 6 = 29
2. 7 + 7 + 8 + 3 + 6 + 5 = 36
3. 98 + 67 = 165
4. 48 + 76 + 52 = 176
5. 74 + 68 + 46 = 188
6. 636 + 583 + 364 = 1583
7. 597 + 388 = 985
8.  989 + 789 = 1778
9. 2995 + 2345 = 5340
10. 599967 + 333333 = 933300