# 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:

- 22 x 28 =
- 49 x 41 =
- 53 x 57 =
- 82 x 88 =
- 91 x 99 =
- 102 x 108
- 194 x 196 =
- 206 x 204 =
- 292 x 298 =
- 404 x 406 =

Answers to last week’s exercises:

- 25^2 = 625
- 75^2 = 5625
- 115^2 = 13225
- 125^2 = 15625
- 305^5 = 93025
- 505^2 = 255025
- 1005^2 = 1010025
- 3335^2 = 11122225
- 66665^2 = 4444222225
- 0.000055^2 = 0.000000003025