# MSC #6 – Completing the Whole – Addition

Our illustrated example involves adding time periods expressed in hours and minutes. This type of computation is avoided by young learners, but it provides a good illustration of our technique of “completing the whole” which is based on the Vedic Math Sutra “By Completion or Non-Completion”. Computations involving whole quantities are easy, but they are not common. The best strategy to simplify calculations, therefore, is to make some quantities whole. The addition of 1 hour, 56 minutes and 4 hours, 37 minutes, which ordinarily requires two regroupings, is quickly solved using the “completing the whole” technique. Adding 4 minutes to 1 hour, 56 minutes will make it an even 2 hours. Simultaneously deducting 4 minutes from the uphill climb time of 4 hours, 37 minutes will transform the addition to a simpler 4 hours, 33 minutes plus 2 hours. In order for students and teachers to easily remember this method, we named it “dagdag-bawas” Other examples of completing the whole to solve 67 + 98 are:

1) Add a whole then subtract

67 + 98 = 67 + (100 – 2) = 167 – 2 = 165

2) Split and complete:

67 + 98 = (65 + 2) + 98  = 65 + (2 + 98) = 65 + 100 = 165

3) Use Bar Numbers:

67 + 10(2) = 167 – 2 = 165

Variations of “completing the whole” in addition is discussed in the first chapter, “Creating Zeroes” of 25 Math Short Cuts and in Chapter 14 of “Inspirational Maths from India – A Teachers Handbook”. Both books are available at MATH-Inic Philippines (