Welcome To DAY 4
Its time to look at the advanced method for Add/Subtract Method. I hope you are prepared and excited.
Add & Subtract Method
Rules: This method is based on selecting a proper base and then using the Vedic maths method to calculate. Selecting a proper base is one of the most important things in this method, which makes major calculations very simple. See the example of different bases and make sure you use your wits to choose a proper base while calculation. It works in the following manner.
Importance of choosing the RIGHT BASE.
25 x 98 [ We assume the base as 100 ]
25 – 75
98 – 2
24/50
Steps involved:-
We select the base as 100.
Then we check the difference for each number as compared to 100. In this case the difference is -2 & -75. So we write -2 & -75 on the right on side of these numbers respectively.
Then we multiply the right hand side. In this case -2 x -75. So we get 150 as the answer. But since the base is 100 we can only use 2 up to 2 digit and we will carry forward 1 to the left hand side
Then we do cross addition/subtraction. In this case we would subtract -2 from the number 25 or we subtract -75 from the number 98 and then we get the answer as 23 but due to carry forward we add 1 and the answer turns out to be 24. And the final answer as 2450.
So far we have looked at numbers where after addition/subtraction from the base, both the numbers were either positive or negative. Now lets consider the other way round.
12 x 8 [ We assume the base as 10 ]
12 + 2
8 – 2
10/-4 = 96
Steps involved:-
We select the base as 10.
Then we check the difference for each number as compared to 10. In this case the difference is +2 & -2. So we write +2 & -2 on the right on side of these numbers respectively.
Then we multiply the right hand side. In this case +2 x -2. So we get -4 as the answer.
Then we do cross addition/subtraction. In this case we would subtract -2 from the number 12 or we add +2 from the number 8 and then we get the answer as 10.
However since the we have – 4 on the right hand side we subtract it from the base and -1 from the left hand side.
And we get the answer 96
It is slightly confusing but you will get the hang of it pretty soon.
108 x 97 [ We assume the base as 100 ]
108 + 8
97 – 3
105/-24 = 104/76
Steps involved:-
We select the base as 100.
Then we check the difference for each number as compared to 100. In this case the difference is +8 & -3. So we write +8 & -3 on the right on side of these numbers respectively.
Then we multiply the right hand side. In this case +8 x -3. So we get -24 as the answer.
Then we do cross addition/subtraction. In this case we would subtract -3 from the number 108 or we add +8 from the number 97 and then we get the answer as 105.
However since we have – 24 on the right hand side we subtract it from the base and -1 from the left hand side.
And we get the answer as 10476
We have also been using the base such as 10, 100 & 1000. Now, lets try some different base. Play close attention to the difference as it will help you master this method.
49 x 49 [ We assume the base as 50 ]
49 – 1
49 – 1
48/01
24/01
Steps involved:-
We select the base as 50.
Then we check the difference for each number as compared to 50. In this case the difference is -1 & -1. So we write -1 & -1 on the right on side of these numbers respectively.
Then we multiply the right hand side. In this case -1 x -1. So we get 1 as the answer.
Then we do cross addition/subtraction. In this case we would subtract -1 from the number 49 or we subtract -1 from the number 49 (same thing in this case) and then we get the answer as 48.
But since the base is 50 which is nothing but 100/2. So we divide 48 by 2
And we get the answer 2401.
Similar Example:
46 x 46 [ We assume the base as 50 i.e 100/2 ]
46 – 4
46 – 4
42/16
21/16
23 x 23 (BASE AS 20 i.e. 10 x 2)
23 + 3
23 + 3
26/9
52/9
Steps involved:-
We select the base as 20.
Then we check the difference for each number as compared to 20. In this case the difference is +3 & +3. So we write +3 & +3 on the right on side of these numbers respectively.
Then we multiply the right hand side. In this case +3 x +3. So we get 9 as the answer. NOTE: We write 9 as the answer and not 09 as the answer because here the base is 10 x 2. That means the underlying base still remains 10. And that’s why we just write one number on the right hand side i.e. 9
Then we do cross addition/subtraction. In this case we would subtract +3 from the number 23 or we add +3 from the number 23 (same thing in this case) and then we get the answer as 26.
But since the base is 20 which is nothing but 10 x 2. So we multiply the base 26 x 2.
And we get the answer 529.
23 x 23 (BASE AS 20 i.e. 100/5) [ Notice the above sum has the same numbers]
23 + 3
23 + 3
26/09
5.20/09
5/29
Steps involved:-
We select the base as 20.
Then we check the difference for each number as compared to 20. In this case the difference is +3 & +3. So we write +3 & +3 on the right on side of these numbers respectively.
Then we multiply the right hand side. In this case +3 x +3. So we get 9 as the answer. NOTE: We write the base as 09 as our basic base or main base is 100/5. The whole idea is if the basic base or main base is a multiple or division of 100 then we will have 2 digits on the left hand side. And when the basic base of main base is a multiple of 10 then we take only one digit on the left hand side, rest we carry forward to the left hand side after doing the division.
Then we do cross addition/subtraction. In this case we would subtract +3 from the number 23 or we add +3 from the number 23 (same thing in this case) and then we get the answer as 26.
But since the base is 20 which is nothing but 100/5. So we divide 26 by 5 and get the answer 5.20
Now whenever we get answer in decimal form after division we transfer it to the right hand side by adding it. Therefore we add 20 to right hand side and get the answer as 29
And we get the final answer as 529.
GOLDEN RULES FOR ADD SUBTRACT METHOD.
Choose the base according to your common sense so that the calculation becomes easy.
If the base is 100 there will be 2 digits on the right hand side, if the base is 10 there will be 1 digit on the right hand side, if the base is 1000 there will be 3 digits on the right hand side and so on. And the extra digit you carry over to the left hand side.
Remember to always divide the left hand side or multiply it first, if required. And then minus right hand side (if negative) or carry forward from left hand side (if positive).
If your answer is something like 24/-26 (with your base being 10). You carry forward -2 to the left hand side. Then your answer will be 22/-6. And then you subtract. This will give you the answer 21/4. However, you can do it directly too, since you know by subtraction of 24 by 3 will give you 21 and you will be able to carry 30 to the left hand side and then you will be able to get your answer easily. i.e. 30 – 26 = 4.
It been a long a lesson and I hope you understand each method clearly. It might take some time to understand this method but in the end you will get the hang of it easily. Try to use your mind to calculate the above steps rather then depending on a piece of paper. I would again suggest you to practice this step and make sure you are ready for tomorrows test.
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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