# Guest Post: Vedic Mathematics 3 – Multiplication with a series of 9’s

*Sanjay Guilati (author) has been teaching computer and mathematics in Bhilai , state Chattisgarh in India for 15 years. Currently he is a teacher in a senior secondary school and he is also involved in teacher training. His online work can be found in Mathematics Academy.*

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Students often fear multiplication of numbers, which involve lot of 9’s in them. However the truth is exactly the opposite. The higher the number of 9’s in the question, the easier it is to calculate the correct answer.** **

There can be three cases with multiplication with series of 9’s

- Multiplying a number with an equal number of 9’s
- Multiplying a number with more number of 9’s
- Multiplying a number with less number of 9’s

Here we are discussing Case 1 only and leaving the rest two cases for the readers to explore.

**Question: Multiply 764 by 999**

- We subtract 1 from 764 and write half the answer as 763.
- Now we will be dealing with 763. Subtract each of the digits seven , six and three from nine and write down them in answer followed by 763 one by one.

- Nine minus seven is two, nine minus six is three and nine minus 3 is six.
- The half answer already obtained was 763 and now we suffix the digits obtained in previous step. The final answer is 763236

**Question: Multiply 2345123 by 9999999**

Subtract 1 from 2345123 to get 2345122 as left part of answer. Now subtract individual digits of 2345122 from 9 and write answer as 7654877. This becomes right part of answer. The final answer is 23451227654877

**Use of Yavadunam Sutra for Finding square of a number near 100**

Sutra Yavadunam function over a base value. The bases may be 10 , multiples of 10 or 100 , multiples of 100 or 1000 , multiples of 1000 etc. Here we limit ourselves to base 100 only.

The sutra says whatever be the difference of the number from the base add (if the number is more than the base) or subtract (if the number is less than the base) that much to the number and on the right hand side set the square of the difference. This gives us the final answer. Remember that the number of digits on right hand side is equal to the number of zeros in base.

Since 108 is 8 more than 100 therefore we have added 8 here as per the sutra and on the right hand side we set square of 8.

Since 98 is 2 less than 100 therefore we have subtracted 2 here as per the sutra and on the right hand side we set square of 2. See that we set 4 as 04 as the right hand side of the answer should have number of digits equal to the number of zeroes in the base.