 # MSC #30 – “By Inspection”

We reserved this Sutra for the last of our 30 MATH-Inic Specials for Christmas because it depends largely on how much one has mastered the concepts presented in the previous specials. It also encourages adaptation and stimulates creativity because it shows how some problems can be easily solved By Inspection or By Mere Observation.

As an example, we used 385 x 999. The answer can be readily obtained by using two sutras, By one less than the one before and All from 9 and the last from 10.

The first part of the answer comes from 385 – 1 = 384, while the second part is the 10’s complement of 385: 1000 – 385 = 615. So 385 x 999 = 384,615.

Or after getting the first part 384, just get the 9’s complement of 384. In case there is a confusion in what rule to follow, it is best to use use “the last by the last” the last digits of the factors are 5 and 9 so the last digit of the product must be 5

Just by looking at the figures, we can announce the answer.

An interesting application of this is getting the recurring decimal equivalent of a fraction with a denominator of 13 like 5/13, for instance.

1. 5 x 7 = 35 (By Inspection)
2. 35 x 11 = 385 (By Inspection)
3. 385 x 999 = 384,615(By Inspection)
4. 5/13 = 0. 384615…

Note that:

1/1001 = 0.000999

5/ (7 x 11 x 13) = (5 x 999)/1,000,000)

5/13 = (5 x 7 x 11 x 999)/1,000,000

More examples of solving “by Inspection” are discussed in Chapter 30 of “30 Master Strategies in Computing”