Completing the Whole

Vedic Math is based on how the mind naturally works. While we were trained to add from left to right or from top to bottom, our brain tells us that it is oftentimes easier to to get the total of several addends if we combine certain terms first, not necessarily in the order they were presented.

A natural technique is to complete the whole. A whole can be a single unit like a foot, a pound or a peso or it can be a defined group or base like a dozen, or a score. Since we are using the decimal system, our wholes are usually tens, hundreds or other multiples of ten.

If we are given three piles of coins with amounts of P85, P97 and P49 and we were asked to find the total amount, we will not get a calculator or paper-and-pencil. Instead we usually take P15 from the smallest pile and add it to P85 to complete P100. Then we will get another P3 from the P49 pile and add it to P97 to make another hundred. Now we just count what remains from P49 after deducting P25 and P3. Finding it to be P21, we can announce the total as two hundred twenty-one.

Workers in egg farms do not bother counting the number of eggs produced in a day. They just place them in trays of 30 pieces. This is similar to the practice of placing empty soda bottles in their cases instead of counting them directly.

A thought process flow which can describe and easier way of solving our example is as follows:

1. The first addend ends in 7 so we must combine it with a term which ends in 3 if there is any.
2. The last addend is 423. We can mentally transfer to it the 7 of 37 to make it 430 so that the addition of the two will be transformed into 430 + 30 = 460.
3. Next, if we transfer the 40 of 140 to 460, we will easily get 600 from 100 + 500.
4. Finally 600 + 88 equals 688.

Exercises: Find the sum using completing the whole:

1. 8 + 9 + 2 =
2. 6 + 7 + 4 + 9 + 3 =
3. 11 + 32 + 89 =
4. 24 + 38 + 50 + 226 =
5. 17 + 38 + 79 + 45 =
6. 3/5 + 3/4 + 2/5 =
7. 58 min + 57 min + 56 Min =
8. 3 ft 5 in + 4 ft 6 in + 5 ft 7 in =
9. 9999 + 999 + 99 + 9 + 5 =
10. 1 3/4 + 2 4/5 + 3 2/8 =