Completing the Whole

VMO Tip #5

COMPLETING THE WHOLE  is what our mind naturally does. We often see a “whole” even if it is not there. We can identify an object even if parts of it are missing. We can see a “full moon” even when a section of it is covered by clouds. We “get the idea” even if the explanation is incomplete.

In Vedic Mathematics, we have the Sutra, “By the Completion or non-Completion” which leads us to many techniques in solving Arithmetic, Algebraic and Geometric problems.

We can quickly determine the sum of numbers with large digits by adding a “whole’ and later subtracting the number’s deficiency from the whole.

Let us take the first question to illustrate: 89,999 + 99,988. Both addends are near a “whole” 100,000.  We can see that 99,988 is just 12 less than 100,000. So the easy mental process for this addition is to add 100,000 to 89,999 before subtracting 12. So we can immediately announce the answer beginning with “one hundred eighty-nine thousand” while mentally deducting 12 from 999 then continuing with “nine hundred eighty-seven”

In the second question, the addends are just 1, 2, 3 and 4 less than 50,000, 5,000, 500 and 50 respectively so the sum 50,000 + 5,000 + 500 + 50  less 1 + 2 + 3 + 4 which is equal to 55,550 minus 10 or 55,540.4

In the third question  we need to add two mixed numbers 4 4/5 and 5 6/7. We can add the whole number parts and the fractional parts separately and then combine the results. But a quick look at the fractional part will show that it will sum up to an “improper” fraction so that an additional step of conversion to a mixed number is needed.

This operation is easier by “completing the whole” in this case completing 5 6/7 into 6 and later deducting 1/7. The answer can be announced as “ten (6 + 4) and” while mentally deducting 1/7 from 4/5 which is easily “twenty-three (4 x 7 – 1 x 5) over thirty-five (5 x 7).

In the fourth question, 8 2/3 – 4 9/10,  subtraction is easier if we will subtract a whole 5 and adding back 1/10. So we can say that the answer is “three (8 -5) and twenty- three (2 x 10 + 1 x 3) over thirty( 3 x 10)”

In the last question, we notice the last four digits of the minuend 9867 is only 2 less than the last four digits of the subtrahend, 9869. We can apply here the “by Non-Completion” part of the Sutra. We will first deduct 49, 867 from 79, 867 to get 30,000, then subtract 2 from the result to get a final 29,998 answer.

Detailed explanation to these techniques plus how to quickly determine the ten’s complements of numbers will be discussed in session 1 of our Vedic Math Webinars Series #2 on July 22, 2021 at 3:30 to 5:00 pm.