Subtraction Without Borrowing: Subtraction by Parts.

The third method of avoiding borrowing in subtraction is what I called “Subtraction by Parts” in my book  “25 Math Short Cuts”.  When the value of last few digits of the minuend is slightly smaller than the corresponding figures in the subtrahend, this technique can be used to get a very quick answer not only in Math contests but in every day life.

In our example 45,753 – 15,764, we will need 5 regroupings or borrowings if we will use the traditional right to left method of subtraction. However, we can see that the last four digits of the minuend 5, 753 is only 11 less than the last 4 digits of the subtrahend 5,764.

See also the revised schedule of Vedic Math events this year here: https://www.math-inic.com/blog/revised-schedule-of-vedic-math-activities-in-the-philippines/

In our first technique of avoiding borrowing, “subtraction by steps”,  we “over-subtract”, here we “under-subtract”

Here is the step-by-step solution;

1. Split the subtrahend such that the ending digits of the first part will be the same  as the ending digits of the minuend. 15, 764 = 15, 753 + 11  
2. Deduct, 15, 753 from 45,753 to get an even 30, 000.
3. Get the difference 30, 000 – 11 using Nikhilam or “All from 9 and the Last from 10”: 29,989.

More examples of this type of subtraction will be discussed in a webinar series on “25 Math Short Cuts” which we will schedule this coming May 2022.

Try this method using the following figures:

1. 457 – 359 =
2. 784 – 589 =
3. 872 – 584 =
4. 657 – 478 =
5. 2, 345 = 1, 354 =
6. 5, 734 – 4, 845 =
7. 8, 547 – 5, 668 =
8. 12, 345 – 11, 477 =
9. 45, 784 – 34, 885 =
10. 364, 257 – 176,378 =

Here are the answers to last week’s practice exercises:

1. 342 – 289 = 53
2. 734 – 497 = 237
3. 4, 125 – 3, 879 = 246
4. 5, 245 – 4, 868 = 377
5. 8, 124 – 3, 766 = 4, 358
6. 9, 232 – 5, 768 = 3, 464
7. 73, 514 – 27, 647 = 45, 867
8. 92, 465 – 38, 878 = 53, 587
9. 86, 485 – 23, 776 – 43, 554 = 19,155
10. 88, 543 – 65, 374 + 43, 923 – 48, 778 = 18, 314