When the final digits add up to 10

Last week we discussed squaring numbers ending in 5. The technique used the Vedic Mathematics Sutra, By One More the One Before. This is possible because it uses another VM Sub-Sutra, When the Final Digits Add Up to 10, since 5 + 5 = 10.

We can also apply it in multiplying number pairs like 44 x 46, 113 x 117 and 9992 x 9998 where the sum of the last digit is 10 and initial digits are the same.

We will apply By One More Than the One Before to the initial digits and regular multiplication to the final digits:

44 x 46 = 4 x 5 | 4 x 6 = 2024

113 x 117 = 11 x 12 | 3 x 7 = 13,221

9992 x 9998 = 999 x 1000| 2 x 8 = 99,900,016

For our featured example, 3333333 x 3333337, we have no problem getting the second part of the answer which is 3 x 7 = 21.

Multiplying 333333 by 333334 will be a little harder. However, if we consider this pattern:

3 x 4 = 12

33 x 34 = 1122

333 x 334 = 111222

We can see that 333333 x 333334 would give 111111222222 thus the answer is c) 11111122222221.

Practice exercises:

1. 22 x 28 =
2. 49 x 41 =
3. 53 x 57 =
4. 82 x 88 =
5. 91 x 99 =
6. 102 x 108
7. 194 x 196 =
8. 206 x 204 =
9. 292 x 298 =
10. 404 x 406 =

 Answers to last week’s exercises:

1. 25^2 = 625
2. 75^2 = 5625
3. 115^2 = 13225
4. 125^2 = 15625
5. 305^5 = 93025
6. 505^2 = 255025
7. 1005^2 = 1010025
8. 3335^2 = 11122225
9. 66665^2 = 4444222225
10. 0.000055^2 = 0.000000003025