# Subtraction by Parts

This is the term we apply to the 3rd method of avoiding “borrowing” in subtraction as discussed in our book, 25 Math Short Cuts, which is very helpful when the last few digits of the subtrahend is a little larger than the corresponding digits than the corresponding digits in the minuend

In the first technique, Subtraction by Steps, we “over-subtract” while here, we “under-subtract”.

The procedure here is to partition the subtrahend so that subtracting the first part from the minuend will create zeroes in the initial result. Let us apply this to a question in the Juniors category of the 1st Math2shine International Vedic Mathematics Competition:

What is  74365 – 24369?

Here we notice that the last four digits of the subtrahend is only 4 more than the last four digits of the minuend.  We can write the subtrahend as 24365 + 4. The subtraction now becomes 74365 – (24365 + 4) =  50000 – 4.

Applying All from 9 and the Last from 10(Nikhilam), we have 50000 – 4 = 49996.

We will try another way of using subtraction by parts by solving a question given in the 2nd International Vedic Mathematics Olympiad (IVMO 2022):

11.1 – 1.11 = ?

Since we have two decimal places in the subtrahend we will suffix a zero in the minuend to express it with two decimal places also.

11.10  →     11.10 → 10.00

– 1. 11 →    – 1.11 –  0.01

9.99

Since 1.1 is common in both terms, we can cross them out leaving a simple 10.00 minus 0.01 which can be easily solved using Nikhilam.

Try these examples:

1. 2.22 – 0.222 =
2. 9.99 – 0.999 =
3. 13.33 – 3.333 =
4. 5432 – 2435 =
5. 7884 – 5889 =
6. 6777 – 4888 =
7. 87878 – 77879 =
8. 78756 – 59768 =
9. 345678 – 135579 =
10. 578987 – 278999 =