# MSC 2 – All from 9 and the Last from 10 Subtraction

As in Addition, we were taught to subtract from right to left. But when computing money, we struggle mentally with left to right computation.  If we paid for a P347.25 purchase with a P1,000 bill, for example, our mental process goes on like this:

1. 1000 minus 300 is 700 but my purchase is more than 300
so my change is less than 700, or 600+.
2. It is not 660, because we bought more than 340, so it must be 650+.
3. It is not 653, because we bought more than 347, so it must be 652+.
4. Aha!, we know that the change for .25 is .75, so we have our final change of P652.75

In Vedic Math, they have a nice Sutra or word formulafor this: “All from 9 and the Last from 10” , which means that when subtracting from a power of 10, we subtract, starting from the leftmost digit, all the digit from 9 except the last digit which we will subtract from 10.

Example 2.1 : How much change do I get if I pay for my P347.25 purchase with a P1,000 bill?

We are used to writing subtraction like this:

 ``` 1,000.00  -347.25 ``` ``` 1,000.00 -347.25 652.75 ```
1. Starting from the left, subtract every digit of the subtrahend, except the last,  from 9
2. Subtract the last digit from 10.

Some find it easier to add than to subtract. Using the same example above, we can readily announce the change:

1. “My change is” (what should I add to 3 hundred to make 9?)six hundred
2. (What should I add to 4 to make 9?) fifty
3. (What should I add to 7 to make 9?) two pesos and
4. (What should I add to 2 to make 9?) seventy
5. (What should I add to 5 to make 10?) five

When the subtrahend ends in zero(es), we make a slight modification in our procedure

Example 2.2 : How much change do I get if I pay for my P340.00 purchase with a P1,000 bill?

 ``` 1,000.00 -340.00 ``` ``` 1,000.00 -340.00 660.00 ```
1. Momentarily disregard the  three ending zeroes.
2. Apply the “All from 9 and the last from 10” only to 34 to get 66.

When the subtrahend contains less digits than the number of zeroes in the minuend

Example 2.3

 ```1,000.00 - 8.55 ``` ```1,000.00 - 008.55 99 ``` ```1,000.00 - 008.55 991.45 ```
1. Pad the given number with zeroes to the left so that it has as many digits as the power of 10 has zeroes.
2. Apply the “all from 9” procedure.

When the minuend is not a power of ten

Example 2.4:

 ``` 500.00 -68.95 ``` ``` 500.00 - 068.95 4 ``` ``` 500.00 - 68.95 431.05 ```
1. Subtract 1 from the leftmost digit.
2. Apply the “All from 9 and the last from10” to the rest of the digits.

When subtracting from a power of ten, the difference is called the ten’s complement of the subtrahend. When the minuend is not specified, it is assumed to be the next higher power of 10.

The 10’s complement of 8 is 2, of 286 is 714, and of 889 is 111. The ten’s complement of 2 with respect to 1000 is 998.

Exercise 2.1 : What change will you get when you pay P1,000 for the following purchases?

a)     P 347. 25
b)     P 489.80
c)     P 700.11
d)     P 826.35
e)     P 899.01

Exercise 2.2:

a)     P500.00 – 123.45 =
b)     P200.00 – 73.20 =
c)     P700.00 – 622.98 =
d)     P350.00 – 325.25 =
e)     P800.00 – 749.98 =

Exercise 2.3: Find the ten’s complement of the following numbers.
a)     76
b)     21
c)     97
d)     288
e)     898
f)       232
g)     1001
h)     6789
i)        9929
j)        9878