# Simplifying Division by Doubling

While I was preparing for the review webinars intended for those who are participating in the national and international Vedic Math Olympiads and for those who are taking the IAVM assessments later this month, I came across this question which was given in the beginner’s category of the 1^{st} MATH-Inic Vedic Mathematics National Challenge.

This can be easily solved using the traditional method: moving the decimal point of both the dividend and the divisor one place to the right to make the divisor a whole number. But Vedic Math competitions require speed. Thus, mental solutions are very helpful.

At school, we are taught the “blanket method” of moving the decimal point of the divisor to the right to eliminate the decimal part. The decimal point of the dividend is similarly adjusted. In our example, the decimal points will be moved one place to the right making the division 315 ÷ 35.

Depending on one’s ability, it may take two or more “guess and check” attempts before the correct answer is obtained given that the divisor has two digits.

However, moving the decimal point which means multiplying by a power of ten is not the only way to make the divisor a whole number. If the divisor ends in 5, doubling it results in and ending zero and will reduce the decimal place by one.

In our featured question, doubling both the dividend and the divisor will give use 63 ÷ 7 which easily gives us a quotient of 9.

Similarly, we can also use doubling in the following:

10.5 ÷ 1.5 = 21 ÷ 3 = 7

3.6 ÷ 0.45 = 7.2 ÷ 0.9 = 72 ÷ 9 = 8

45 ÷ 7.5 = 90 ÷ 15 =180 ÷ 30 = 6

Practice simplifying division by doubling.

- 12 ÷ 1.5 =
- 21 ÷ 1.5 =
- 28 ÷ 3.5 =
- 45.5 ÷ 3.5 =
- 27 ÷ 4.5 =
- 44 ÷ 5.5 =
- 12 ÷ 0.75 =
- 27 ÷ 0.5 =
- 23 ÷ 0.25 =
- 21 ÷ 0.125 =

Here are the answers to last week’s practice exercises:

- 39 = 78
- 68 = 136
- 348 = 696
- 459 = 918
- 2, 436 = 4, 872
- 4, 829 = 9, 658
- 26, 467 = 52, 934
- 63, 476 = 126, 952
- 385, 498 = 770, 996
- 754, 849 = 1. 509, 698

See the complete list of Vedic Math activities here: https://www.math-inic.com/blog/revised-schedule-of-vedic-math-activities-in-the-philippines/

The registration link for the Vedic MATH Review webinars is: https://bit.ly/MATH-Inic2022