30MSC 2023 #7: The Last Digits Adding up to 10.

There are many multiplication techniques available when the last digits of the multiplicands add up to 10 and most of them are applications of the Sutra,  By One More than the One Before. Squaring numbers ending in 5 and multiplying complementary numbers are some examples. But they are also applicable to multiplicand pairs with ending parts which add up to any unity – 1 , 100 or any whole.

This problem given in the seniors group of the 1st Math2Shine International  Vedic Mathematics Competition last July 2023, illustrates how this sub-Sutra can be applied to multiplication of mixed numbers:  7  2/13 x  7  11/13 = ?

The conventional solution is to 1) convert the mixed numbers into improper fractions; 2) perform the multiplication of these fractions; and 3) convert the resulting fraction into its mixed form.

7  2/13 x  7  11/13 = 93/13 x 102/13

= 9486/169

= 56  22/169

This would be difficult given the large sizes of the multiplicands. We can mentally convert the mixed numbers into 93/13 and 102/13, respectively, and by using base multiplication, we can determine their product also mentally as 9486/169. But converting this result back to a mixed form would need paper and pencil.

We can notice, however, that their whole number parts are the same and their fractional parts 2/13 and 11/13 add up to 13/13 or one whole. Therefore, we can use By One More than the One Before and quickly get the answer as

7  2/13 x  7  11/13 = 7 x 8 | (2 x 11)/ (13 x 13) = 56  22/169

Many other applications of  technique are discussed in Chapter 7 of our e-book, 30 Master Strategies in Computing, Volume I.  The rewritten version 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 #8: Proportionately (Doubling and Halving).