# 30MSC 2023 #17: Straight Division: the Crowning Gem of Vedic Mathematics

Straight division is the general division method in Vedic Mathematics. Using this method, numbers of any size can be divided in one line. Sri Bharati Tirthaji, the father of Vedic Mathematics called this “the crowning gem of Vedic Mathematics.

We will illustrate how this straight division is done using a question given in the Junior International Vedic Mathematics Olympiad in 2021:

A bottling factory produces 19,866 bottles in 42 hours. In using straight division to find how many bottles are produced each hour, what is the second to last step?

The divisor 42 is written with the 2 On The Flag  or raised up to the level of the dividend. We will separate the last digit of the dividend by a remainder bar. Note that in using this technique, we separate a number of ending digits of the dividend equal to the number of digits On The Flag.

2   | 1   9   8   6  |  6

4          |

|_____________

1. The first step is to divide the first two digits of the dividend by 4, the first digit of the divisor, to get the first digit of the quotient,4, and a remainder of 3 which is placed as shown. 38 becomes the next figure in the dividend.

2   | 1   9   8   6  |  6

4          |         3

|_____________

4

• The second step is to subtract the product of the Flag digit, 2, and the first quotient figure, 4, from 38 and divide the difference by (26 – 14) ÷ 4: (38 – 8) ÷ 4 = 7 r 2 . Place 7 and 2 as shown below to make 7 the next answer figure and 26 the new dividend figure.

2   | 1   9   8   6  |  6

4          |         3   2

|_____________

4    7

• Repeat the cycle described in step 2: deduct from the dividend figure, 26 the product of the flag digit,2,  and the last answer digit, 7, and divide the difference by 4: (26 – 14) ÷ 4 = 3 r. 0

2   | 1   9   8   6  |  6

4          |         3   2     0

|_____________

4    7   3  |

• The last step is to subtract 2 x 3 from 6 getting no remainder. The second to the last step is, therefore, (26 – 14) ÷ 4.

More examples of straight division are discussed on Chapter 7 of our forthcoming book, 30 Master Strategies in Computing Vol II.

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