VEDIC MATHS
By OMKAR TENDOLKAR
Hello friends,
This is post number 47 from the series of "Vedic maths" blogs. Here in this blog we will learn about "Example of (Division part-B)"
In the previous blog we saw how the Base Method can be used in the process of division. One of the drawbacks of the Base Method of division is that we can only use higher numbers like 7, 8 and 9 in the divisor. The obvious question that arises is how to solve a problem of division where the divisor includes numbers like 1, 2, 3, etc. The answer is given by the Paravartya Sutra of Vedic Mathematics, which we shall study in this chapter. The Vedic sutra ‘Paravartya Yojayet’ means transpose and apply. The format and working of this system is the same as explained in the previous blog.
However, in this case we will have a negative difference
Reference:
We had already learn about "Base Method of Division part-1" our previous blog. If you have missed my last blog then please visit "VEDIC MATHS-44".
We had already learn about "Base Method of Division part-2" our previous blog. If you have missed my last blog then please visit "VEDIC MATHS-45".
We had already learn about "Base Method of Division part-3" our previous blog. If you have missed my last blog then please visit "VEDIC MATHS-46". Examples:
1.Divide 1296 by 113
100
113 1 2 | 9 6
-13 -1 | -3
| -1 -3
|
------------------
1 1 | 5 3
Here in this example, divisor is related to the base 100 and therefore we split the dividend in such a way that the RHS has two digits.
- The base is 100 and the difference is -13 (negative).
- We write down the first digit 1 of the dividend as it is.
- We multiply 1 with the difference -13 and write the answer as -1 and -3 below the second and third digits of the dividend.
- Next, we go to the second column of the dividend. We bring down 2 minus 1 is 1.
- We multiply 1 with -13 and write the answer as -1 and -3 below the last two digits of the dividend.
- Thus, the quotient is 11 and the remainder is 53.
(Note: In this case we have represented the difference as -13. Alternatively, it can be shown as -1-3. From the second example onwards we will use the latter way.)
Answer:
1296 divided by 113
quotient is 11
remainder is 53
2. Divide 2688 by 120
100
120 2 6 | 8 8
-20 -4 | 0
| -4 0
|
--------------------
2 2 | 4 8
Here in this example, The divisor is 120. Therefore, the base is 100 and the difference is -2 and -0.
We bring down 2 from the dividend.
We multiply 2 with -2 & -0 and write the answer as -4 & -0.
Next, we go to the second digit of the dividend.
We bring down 6 - 4 = 2.
We multiply 2 with -2 & -0 and get the answer as -4 & -0.
The quotient is 22 and the remainder is 48.
Answer:
2688 divided by 120
quotient is 22
remainder is 48.
3. Divide 1693 by 131
100
131 1 6 | 9 3
-31 -3 | -1
| -9 -3
|
------------------------
1 3 | -1 0
= (13-1) | (-10+131)
= 12 | 121
In example (g) the quotient is 13 and the remainder is -10. Therefore, we reduce the quotient by 1 and subtract the remainder from the divisor. Hence, the quotient is 13 -1 = 12 and the remainder is 131 - 10 = 121.
Answer:
1693 divided by 131
quotient is 12
remainder is 121.
Let us understand the logic of this calculation used in above example,.
Suppose we have to divide 710 by 100. Now, the quotient we have is 8 and the remainder is -90
(because 100 multiplied by 8 plus -90 is 710).
Q = 8 ; R = -90
Another way of representing the number 890 is quotient = 7 and remainder = 10.
Q = 7 R = 10
In this case we have reduced the quotient by 1 and reduced the remainder from the divisor. This same concept has been used in above example..
4. Divide 1999 by 180
100
180 1 9 | 9 9
-80 -8 | 0
| -8 0
|
---------------------
1 1 | 1 9
Answer:
2211 divided by 88
quotient is 11
remainder is 19.
Find Division of following:
- Divide 113968 by 1023, then quotient is 111 and remainder is 415.
- Divide 110999 by 1321, then quotient is 84 and remainder is 35.
- Divide 14189 by 102, then quotient is 139 and remainder is 11.
The simplicity of this method can be vouched from examples given above.
You may try following example:
Find Division of followings
1. Divide 1389 by 113
2. Divide 145516 by 1321
3. Divide 136789 by 12131
You may answer this in comment box. You may ask your any query or doubt in comment box. I will try to resolve as early as possible.
In next blog we will discuss about "Division by substitution method".
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Then, please wait for it.
I will post my new blog in next week.
We will meet very soon through our next blog. Till that stay connected, stay healthy and stay safe.
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Good day😊.
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