# By One More than the One Before

Only about 10% of the participants correctly answered this question in the Beginners Category of the 1st MATH-Inic Vedic Mathematics National Challenge held last June 26, 2021.

By One More than the One Before, the first Vedic Math sutra, has varied applications. Aside from its natural use in counting – the next number is one more than the previous one, it is also used in many multiplication techniques, and in division and divisibility tests and in converting fractions into recurring decimals.

Each pair of multiplicands in the given question can be considered “complementary” numbers: They have the same initial digit(s) while their ending digits or parts complete a “whole”

For 35 x 35,  5 + 5 = 10; the number before 5 is 3 and one more than 3 is 4. To find the square of 35, we multiply 3 by 4 to get 12, the first part of the answer and square 5 to get 25, the second part. So 35 x 35 = 1225.

In the next pair, 7 + 3 = 10. Thus 47 and 43 are complimentary numbers and their product can be easily computed using By one more than the One Before. So we have 4 times the next number 5 is 20 and 7 x 3 = 21. Therefore, 47 x 43 is 2021.

Proofs of these techniques can be found in pages 53 and 59 of our book 25 Math Short Cuts.

For 5 1/4  x 5 3/4, we have 1/4 + 3/4 = 1, so the multiplicands are complimentary. Their product is simply  5 x 6 | 1/4 x 3/4 = 30 3/16.

For the last pair, 6’ 5” and 6’ 7”, 5” + 7” = 1 foot. The product is (6 x 7)| (5 x 7) or 42 square feet and 35 square inches.

This multiplication method can also be used to quickly get the product of the following:

52 x 52

47 x 47

76 x 36

68 x 28

1192 x 1108

46 x 88

Join us in Session 5 of the Vedic Math Webinars, Series #2 on Sunday August 1 at 3:30 PM.

Send message to Math-Inic Philippines for details.