# MSC #12 – Base Division

Just as the complements of numbers below powers of ten are used in **Nikhilam** or base multiplication, we will now show how we can use those complements to make division easier.

In cases where the divisor is a little more than the base, the Sutra **Transpose and Apply** is used instead.

Mastering Base division is very helpful for young learners because the same method can be extended to Algebraic Division even with trinomial and even longer divisors.

Base division will be discussed by Prof Emmanuel Nadela of the Cebu Institute of Technology-University on Dec 5 while Algebraic Division and the Power Series will be explained bhy James Glover, chair on the Institute for the Advancement of Vedic Mathematics on Dec 11, 2021 in the Inspirational Maths from India webinars.

It would be difficult to solve this division problem given in the junior level of the 1^{st} International Vedic Mathematics Olympiad, 12,032 ÷ 879, using long division because of the large digits in the divisor. But with base division, finding the quotient is easy.

Here is the step by step solution:

- In the space for the divisor, place 879 and its complement, 121, underneath it. This complement is easily determined using the Sutra
or*Nikhilam navatascaramam dasatah*We will use this complement as our multiplier.*All from 9 and the Last from 10”.*

- Separate the last three digits of the dividend by a remainder bar. The number of digits separated should be equal to the number of zeroes in the base. In this case the base is 1000.

- Bring down the first digit of the dividend, 1, as the first digit of the quotient. This is because we have the same number of 879s as there are thousands in the dividend. As in long division, we will consider the first four digits 1203 as our first dividend.

- We then multiply this first quotient figure by 121 which is the remainder when 879 is taken from every thousand and place the product under the second to the fourth digits of the dividend.

- The sum obtained in the second column (2 +1 = 3) will be the second figure in the answer.

- Write the product of this latest answer 3 and 121 which is 363 under the 3
^{rd}to the 5^{th}columns of the dividend as shown.

- The sum of the figures in the 3
^{rd}to the 5^{th}columns which all lie after the remainder bar, will be the remainder.

More examples of base division can be found on Chapter 4 of the ** Inspirational Maths from India: A Teacher’s Handbook**, an e-copy of which will, be given to the 1

^{st}100 registrants of IMI 4.