MSC #8 – Proportionately – Direct Proportion.

Elementary school students are trained to always reduce fractions to lowest terms by dividing both the numerator and denominator by their lowest common factor.

In division having a divisor with decimal parts, the learners are taught to convert the divisor to a whole number by moving the decimal point to the right. The decimal point in the dividend is also shifted by the same number of decimal places. Effectively, both the dividend and divisors are multiplied by the same power of ten thus maintaining their proportionality before the division is performed.

When the last non zero digit of the divisor is 5, as shown in our illustration, a simpler solution can be obtained by multiplying the divisor and the dividend by 2. This “doubling“ can be done several times as needed.

Doubling and Halving will be discussed by IAVM co-founder Swati Dave and Proportionately by Rolito Asombra, LET board topnotcher and VM coach of the San Jose National High school, San Pablo City in the Inspirational Math from India webinars on Dec 5, 2021.

The short cut for dividing by 5 – doubling the dividend then dividing by 10 can be explained by using this technique: 234 ÷ 5 = 468 ÷ 10 = 46.8

Similarly, the short cut for dividing by 25 is to double the dividend twice then dividing by 100: 234 ÷ 25 = 468 ÷ 50 = 936 ÷ 100 = 9.36

Other examples of this method are:

82.5 ÷ 0.75 = 165 ÷ 1.5 = 330 ÷ 3 = 110.

67.5 ÷ 0.125 = 135 ÷ 0.25 = 270 ÷ 0.5 = 540 ÷ 1.0 = 540