Subtraction by Parts

This is the term we apply to the 3^rd 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 1^st 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 2^nd 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 =

Answers to last week’s exercises:

1. 163 – 128 =35
2. 134 – 89 = 45
3. 216 – 77 =139
4. 544 – 268 = 276
5. 1452 – 967 = 485
6. 3241 – 1789 = 1452
7. 54,123 – 27,886 = 26,237
8. 83,623 – 64,765 = 18,858
9. 444,555 – 255,666 = 188,889
10. 724,313 – 535,997 = 188,316