I hope you enjoyed the last lesson and understand how learning vedic math's can make calculations fun and easy. Today we will start learning to have fun calculation with number 9. I still remember the trick taught to me by my school professor. While doing the tables for 9, the ten's digit or left part increased by 1 and units digit or right part decreased by 1.

For example,
9 x 2 = 18
9 x 3 = 27
9 x 4 = 36
...

See there is a simple pattern. But in fact it is much easier. So lets begin..

Fun with number 9

Part A (Original number and the number of 9 is same, for example 234 x 999 but we cannot use this method for 234 x 9999 or 234 x 99)
Rules: As usual there is a left hand part of the answer and the right hand part of the answer. When multiplying by 9 we subtract one from the original number and write it down on the left hand side. Then we subtract each number on the left hand side from 9 and write it down on the right hand site (this will become clearer with the examples that follow).

234 x 999 = 233 | 766
Explanation: We subtract one from 234 and write it down on the left hand side i.e 234 - 1 = 233. Then we take each individual number and subtract that number from 9 in the order - left to right. So we subtract 9 - 2 = 7, then we subtract 9 - 3 = 6 and again 9 - 3 = 6. Hence, we get the right part of our answer i.e 766

Common Mistake: As you see from the above example we subtract 9 from each individual number, but we did so from the left hand side of our answer and not the original number. In simple words, we should subtract individually from 233 and not from 234. This is a common mistake I have found and would advice you to remember this crucial point.

948224243 x 999999999 = 948224242 | 051775757
Explanation: Wow! I can beat the calculator. Most of the calculator cannot perform calculation more than 12 digits and I doubt even your mobile phones can do that. Here is how its done, we subtract 1 from 948224243 and get 948224242 . Then we subtract 9 - 9 get 0, then 9 - 4 = 5, then 9 - 8 and so on. I am sure by now you get the idea.

But now here is the question what if the number of 9's are more than the number which we going to multiply, for example,
273 x 99999 ( we cannot do this as of now)

Part B (Original number is less then the number of 9's, for example 234 x 99999)
Rules: Similar to above method, but just imagine 0's in front of the original number. But make sure the number of 9's are more and not less or equal.)

383 x 9999 will become 0383 x 9999 = 0382 | 9617
Explanation:It is simple, we imagine the number to be 0383. Subtract one from it and get 0382. Then as usual we calculate 9 - 0 = 9, then 9 - 3 = 6 and so one.

383 x 999999 will become 000383 x 999999 = 000382 | 999617
Explanation: In this case we had 3 extra 9's. So we imagine 3 extra 0's in front of 383. Therefore our first case will be 000383 - 1 = 000382, which becomes the left part of the answer. And like before we subtract 9 - 0 and get 9, then again 9 - 0 = 9 and again 9 - 0 = 9, then 9 - 3 = 6 and so on.

Part C (Original number is more then the number of 9's, for example 234 x 9, this method is tough to undestand so pay close attention to this one)
Rules:I will directly goto the example in this case, as the rules will confuse you at this level.

14 x 9 = 12 | 6
Explanation: From the number 14 we choose 1(the number in the ten's digit), increase it by 1 i.e. 2 or we add + 1. Subtract that from 14 and we get 12. Next we subtract 4 from 10 and and get 6 i.e. 10 – 4 = 6. The method is confusing but once a person gets a hang of it, it’s pretty easy.

24 x 9 = 21/6

Explanation: From the number 24 we choose 2(ten's digit); increase it by 1 i.e. 3 or we add + 1 (2 + 1). Subtract that from 24 and we get 21 (24 -3). Next we subtract 4 from 10 and get 6 i.e. 10 – 4 = 6.

47 x 9 = 42/3

Steps involved: From the number 47 we choose 4(ten's digit); increase it by 1 i.e. 5. Subtract that from 47 and we get 42 (47 - 5). Next we subtract 7 from 10 and get 3 i.e. 10 – 7 = 3.

112 x 99 = 110/88

Steps involved: From the number 112 we choose 1; increase it by 1 i.e. 2 or we can say we add + 1 (1 + 1). Subtract that from 112 and we get 110 (112 - 2). Next we subtract 99 from 12 and then add 1 i.e. 99 – 12 + 1 = 88.

112 x 9 = 100/8

Steps involved: From the number 112 we choose 11; increase it by 1 i.e. 12 or we can say we add + 1 (11 + 1). Subtract that from 112 and we get 100 (112 - 12). Next we subtract 9 from 2 and then add 1 i.e. 9 – 2 + 1 = 8

I hope this lesson was fun and you enjoyed it as much as I enjoyed writing it down for you!

See you tomorrow.

Rahul Makhija

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Day 1

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