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30MSC 2023 #3: Subtraction Without Borrowing.

30MSC 2023 #3: Subtraction without Borrowing.

Next to addition, subtraction is the easiest arithmetic operation. What makes subtraction difficult is when regrouping or ‘borrowing” is needed.

There are several ways of avoiding “borrowing” in subtraction and one method is illustrated in our featured example which was one of the questions asked in the Juniors division of the 2nd MATH-Inic Vedic Mathematics National Challenge held last April 2022:

                   89,786 – 39,789 =?

If we place the subtrahend below the minuendend, just like in the method taught in schools,

               89,786

            – 39,789

we  can immediately see that we would need four regroupings to get the answer.

But we can also see that the 3 middle digits in both terms are identical so that by application of the Sutra, By the Completion or Non Completion, the problem can be easily solved mentally. Subtracting the first four digits of the subtrahend from the minuend would result into

               50,006

            – 00,009

And then if we deduct 6 from both terms, we would get

               50,000

            – 00,003

This is easily solved using By One Less than the One Before and All from 9 and the Last from 10 to get 49,997.

Another way of looking at this problem is to apply what I called Subtraction by Parts In my book 25 Math Short Cuts.

89,786 – 39,789

= 89,786 – (39,786 + 3)

= (89,786 – 39,786 ) – 3

= 50,000 – 3

= 49,997

Other ways to avoid “borrowing” in subtraction can be found in Chapter 3 of our rewritten e-book, 30 Master Strategies in Computing, Volume I, which will be available before the end of the year.                         

Follow us on our Facebook page, MATH-Inic Philippines at https://www.facebook.com/MATHInicPhils to see tomorrow’s 30MSC 2023 #4: Digit Sums.

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