VEDIC MATHS-48

VEDIC MATHS

                           By OMKAR TENDOLKAR

Hello friends,

                      This is  post number 48 from the series of "Vedic maths" blogs. Here in this blog we will learn about "Division by substitution method"

Sometimes the divisors are such that it is difficult to calculate the answer by itself. In these cases, we substitute the divisor using another number and then calculate the answer.

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".

We had already learn about "Example of (Division part-B)" our previous blog. If you have missed my last blog then please visit "VEDIC MATHS-47".

Examples:

1.Divide 10030 by 827

1. In this case the dividend is 10030 and the divisor is 827. 
2. We will solve the question using the normal method and the substitution method. 
3. In the normal method we will take the divisor as 827 and the difference as 173. 
4. In the substitution method, we will take the divisor as 827 and the difference 173 will be represented as 200 – 30 + 3 = 2 – 3 + 3

1000

    NORMAL METHOD        SUBSTITUTION METHOD

827        1 0 | 0 3 0             827         1 0 |  0  3  0

173           1 | 7 3                2 -3 3         2 | -3  3             

                    | 1 7 3                                  |  4 -6  6

                    |                                           |

           -----------------                       ---------------------

              1 1 | 9 3 3                            1 2 |  1  0  6

         =    12 | 106

The answer is the same in either case.

Answer:

10030 divided by 827

quotient is 12

remainder is 106.

2. Divide 10000 by 819

1. In the normal method we will take the divisor as 819 and the difference as 181. 
2. In the substitution method we will write the divisor as 819 and the difference 181 as 200 - 20 + 1 = 2 -2 +1.

1000

    NORMAL METHOD        SUBSTITUTION METHOD

819        1 0 | 0 0 0             827         1 0 |  0  0  0

181           1 | 8 1               2 -2 1          2 | -2  1             

                    | 1 8 1                                  |  4 -4  2

                    |                                           |

           -----------------                       ---------------------

              1 1 | 9 9 1                            1 2 |  2 -3  2

         =    12 | 172                         =    12 | 172 

                                                      (Reminder = 200 - 30 +2 = 172)          

The answer is the same in either case.

Answer:

10000 divided by 819

quotient is 12

remainder is 172.

In the two examples given above we substituted the difference with some other number. Another way of substitution is by dividing/multiplying the divisor with a suitable number so that it becomes closer to a base and then we can multiply it quickly.

3. Divide 1459 by 242

We divide 242 by 2 and make it 121. We will now perform the division with the new dividend 121. 

100

121        1  4 |  5   9   

-2 -1         -2 | -1                    

                     | -4  -2   

                     |

         ------------------------

              1  2 |  0   7

         2 ) 1  2 |  0   7

            =  06 | 07

1. The quotient is 12 and the remainder is 07. 
2. But this answer is with respect to the divisor 121. 
3. We want to find the answer with respect to the divisor 242. 
4. Since 242 is divided by 2 to obtain 121, we divide the quotient by 2 and get the answer 6. 
5. The remainder always remains the same.

Answer:

1459 divided by 242

quotient is 06

remainder is 07.

4. Divide 1112 by 33

In this case we multiply the divisor 33 by 3 and make it 99. Note that the difference in this case is 01 and not 1.

100

 99                1 1 | 1 2

01                    0 | 1                     

                           | 0 1

                           | 

                ---------------------

                     1 1 | 2 3

                   *   3 

                  -------

                    3 3

The quotient is 11 and the difference is 23. Since, 33 is multiplied by 3 to obtain 99, we multiply 11 by 3 and make it 33. The remainder remains the same. The final quotient is 33 and the final remainder is 23.

Answer:

1122 divided by 33 

quotient is 33

remainder is 23.

Find Division of following:

1. Divide 12657 by 791, then quotient is 16 and remainder is 01.
2. Divide 110999 by 1321, then quotient is 84 and remainder is 35.
3. 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 101156 by 808 (Hint: Take difference 192 as 2 – 1 + 2)

2. Divide 4949 by 601 (Hint: Use 601 × 2 = 1202 as divisor)

3. Divide 14799 by 492 (Hint: Use 492/4 = 123 as divisor)

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 "Method of Cubing Number".     

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