Skip to main content

Division (Vedic Mathematics)

Image
By

1. Division by 9

Division by 9 is derived from the second sutra of Vedic Mathematics, known as the ‘Nikhilam sutra’.
Watch the following video to understand the method.
Solved Example
Example 1:
Divide 1241 by 9
Solution:

Q = 137, R = 8
In this case, the remainder is less than 9. But what will happen if the remainder is greater than 9?
To understand this case, watch the following video.
Solved Examples
Example 1:
Divide 28491 by 9
Solution:

Q = 3163
R = 24 = 6 + 2 × 9
∴Qnew = 3163 + 2 = 3165
Rnew = 6
Example 2:
Divide 92864 by 9
Solution:

Q = 10315
R = 29 = 2 + 3 × 9
∴Qnew = 10315 + 3 = 10318
Rnew = 2

2. Division Method - I

The contemporary method of division is a very long process, in which, there are chances of making errors and is also very time consuming. However, the Vedic method of division is very useful in dividing numbers.
Look at the following video to understand the method:
Solved Examples
Example 1:
Divide 10042 by 89
Solution:
Base = 100
Deficit = 100 − 89 = 11

Q = 112
R = 74
Example 2:
Divide 101010 by 8998
Solution:
Base = 10000
Deficit = 10000 − 8998 = 1002

Q = 11
R = 2032
Example 3:
Divide 10102 by 899
Solution:
Base = 1000
Deficit = 1000 − 899 = 101

Q = 11
R = 213
In all the above cases, the remainder was always less than the divisor. How to solve a problem, where the remainder turns out to be more than the divisor?
Look at the following video to understand the method:
Solved Examples
Example 1:
Divide 11007 by 88
Solution:
Base = 100
Deficit = 100 − 88 = 12

Q = 124
R = 95 = 7 + 1 × 88
∴Rnew = 7
Qnew = 124 + 1 = 125
Example 2:
Divide 15004 by 89
Solution:
Base = 100
Deficit = 100 − 89 = 11

Q = 167
R = 141 = 52 + 1 × 89
∴Rnew = 52
Qnew = 167 + 1 = 168
Note:
This method is very useful when the divisor is close to the base, that is, close to 10n.

3. Division Method - II

This method of division is derived from the 5th sutra of Vedic Mathematics, known as the “Parvartya sutra”, which means “transpose and apply”.
Transpose generally refers to the transpose of operators, i.e., “+” becomes “−”, “−” becomes “+”, “÷” becomes “×” and “×” becomes “÷”, and can be used in cases where the first digit of the divisor is 1. This Vedic method of division uses the rule of transpose of operators.
To learn this method, watch the following video.
Solved Examples
Example 1:
Divide 1232 by 110
Solution:

Q = 11
R = 22
Example 2:
Divide 1386 by 113
Solution:

Q = 12
R = 30
In the above examples, the remainder obtained after calculation came out to be less than the divisor. But what will happen if the remainder comes out to be greater than the divisor?
Let us understand this case with the help of following video.
Solved Examples
Example 1:
Divide 18428 by 161
Solution:

Q = = 11(10 − 9) = 111
R = 557 = 74 + 3 × 161
∴Qnew = 111 + 3 = 114
Rnew = 74
Example 2:
Divide 1221 by 192
Solution:

Q = = 0(10 − 7) = 3
R = 645 = 69 + 3 × 192
∴Qnew = 3 + 3 = 6
Rnew = 69
Let us now take another case. To get an insight into it, try dividing 13456 by 1123.

In this case, the quotient comes out to be 12, while the remainder comes out to be −20. However, can a remainder be negative? No. In fact, in such a case, one has to perform an additional step in.
Watch the following video to learn this case.
Solved Examples
Example 1:
Divide 13905 by 115
Solution:

Q = 122
R = = −125
Qnew = 122 − 1 = 121
Rnew = 115 − 125 = −10
Since Rnew is negative, the process is repeated once.
∴Qnew = 121 − 1 = 120
Rnew = 115 − 10 = 105
Example 2:
Divide 13456 by 1122
Solution:

Q = 12
R = = −10 + 2 = −8
∴ Qnew = 12 − 1 = 11
Rnew = 1122 − 8 = 1114
Till now, the concept involved division of a number where the first digit of the divisor was equal to 1. However, what will happen if the first digit of the divisor is not 1?
Look at the following video to understand the method.
Solved Examples
Example 1:
Divide 15224 by 224
Solution:

Q = = 13(10 − 4) = 136
R = 12 = −20 + 12 = −8
∴Qnew = 136 − 1 = 135
Rnew = 112 − 8 = 104
Since the leftmost digit of the divisor is 2, the quotient also needs to be divided by 2.
∴Qnew = 135 ÷ 2 = 67.5 and Rnew = 104
⇒ Qnew = 67.5 − 0.5 = 67 and Rnew = 104 + 0.5 × 224 = 104 + 112 = 216
Example 2:
Divide 19212 by 484
Solution:

Q =
R = 215 > 121
∴Rnew = 215 − 121 = 94
Qnew = 157 + 1 = 158
Since the leftmost digit of the divisor is 4, the quotient also needs to be divided by 4.
∴Qnew = 158 ÷ 4 = 39.5 and Rnew = 94
⇒ Qnew = 39.5 − 0.5 = 39 and Rnew = 94 + 0.5 × 484 = 94 + 242 = 336
Note:
This division method is very useful when the first digit of the divisor is 1.

4. Straight Division

Straight division is the most general method of division provided by Vedic Mathematics. It is based on the “Urdhva-tiryak” sutra, which translates into English as “vertical and cross-wise”.
This method can be applied to all cases of division, which are difficult to solve by any other method.
This method can be better understood by dividing a number by a 2-digit divisor.
Look at the following video to understand the method of straight division:
Solved Examples
Example 1:
Divide 1942 by 42
Solution:

Step I:
1 ÷ 4 gives Q = 0, R = 1
Step II:
Gross dividend = 19
Actual dividend = 19 − 2 × 0 = 19 − 0 = 19
19 ÷ 4 gives Q = 4, R = 3
Step III:
Gross dividend = 34
Actual dividend = 34 − 2 × 4 = 34 − 8 = 26
26 ÷ 4 gives Q = 6, R = 2
Step IV:
Gross dividend = 22
Actual dividend = 22 − 2 × 6 = 22 − 12 = 10
This actual dividend is the remainder.
⇒ R = 10
Q = 46
The above method can be applied for dividing any number by a 2-digit divisor. Often, we need to calculate division up to the required decimal places. This is a major application of division under Vedic Mathematics, and hence, calculating division up to the required decimal place becomes as easy as calculating division normally.
Watch the following video to learn the method.
Solved Example
Example 1:
Divide 7453 by 79 up to two decimal places.
Solution:

Step I:
7 ÷ 7 gives Q = 1, R = 0
However, if R = 0, then in the next step, the actual dividend comes out to be negative.
Hence, Q = 0, R = 7 is taken.
Step II:
Gross dividend = 74
Actual dividend = 74 − 9 × 0 = 74 − 0 = 74
74 ÷ 9 gives Q = 10, R = 4
However, if R = 4, then in the next step, the actual dividend comes out to be negative.
Hence, Q = 9, R = 11 is taken.
Step III:
Gross dividend = 115
Actual dividend = 115 − 9 × 9 = 115 − 81 = 34
34 ÷ 7 gives Q = 4, R = 6
Step IV:
Gross dividend = 63
Actual dividend = 63 − 9 × 4 = 63 − 36 = 27
27 ÷ 7 gives Q = 3, R = 6
Step V:
Gross dividend = 60
Actual dividend = 60 − 9 × 3 = 60 − 27 = 33
33 ÷ 7 gives Q = 4, R = 5
∴7453 ÷ 79 = 94.34
The division method for divisors with more than two digits can now be generalized. This involves the application of the “Urdhva-tiryak” sutra, which means “vertical and cross-wise”.
Go through this video to understand this concept.
Solved Example
Example 1:
Divide 15824 by 331
Solution:

Step I:
Gross dividend = Actual dividend = 15
15 ÷ 3 gives Q = 5 and R = 0
However, if R = 0, then in the next step, the actual dividend comes out to be negative.
Hence, Q = 4, R = 3 is taken.
Step II:
Gross dividend = 38
Cross-product of 04 and 31 = 0 × 1 + 3 × 4 = 0 + 12 = 12
Actual dividend = 38 − 12 = 26
26 ÷ 3 gives Q = 8 and R = 2
However, if R = 2, then in the next step, the actual dividend comes out to be negative.
Hence, Q = 7, R = 5 is taken.
Step III:
Gross dividend = 52
Cross-product of 47 and 31 = 4 × 1 + 3 × 7 = 4 + 21 = 25
Actual dividend = 52 − 25 = 27
27 ÷ 3 gives Q = 9 and R = 0
However, if R = 0, then in the next step, the actual dividend comes out to be negative.
Hence, Q = 8, R = 3 is taken.
Step IV:
Gross dividend = 34
Cross-product of 031 and 478 = 0 × 8 + 4 × 1 + 7 × 3 = 0 + 4 + 21 = 25
Actual dividend = 34 − 25 = 9
9 ÷ 3 gives Q = 3 and R = 0
Steps to find remainder:
The last two digits of the quotient and the flag are 47 and 31 respectively.
Cross-product of 47 and 31 = 4 × 1 + 3 × 7 = 4 + 21 = 25
Product of cross-product and 10 = 25 × 10 = 250 … (1)
The last digits of the quotient and the flag are 7 and 1 respectively.
Product of these last digits = 7 × 1 = 7 … (2)
(1) + (2) = 250 + 7 = 257 … (3)

⇒ R = 524 − 257 = 267
∴Q = 47, R = 267
Labels:

Comments

Post a Comment

Most Viewed Posts

Summary of The Enemy - Pearl S. Buck

By
THE ENEMY                                  - Pearl S. Buck Dr. Sadao – a surgeon and scientist Dr Sadao Hoki, a Japanese surgeon and scientist, lived with his wife Hana and two children on the Japanese sea-coast. His house was located on the sea-coast where he had spent his childhood. He was greatly influenced by his father whose chief concern was Sadao’s education. At the age of twenty-two, he was sent to America to study surgery and medicine. Sadao too, as an obedient son, fulfilled his father’s wishes and came back a famous surgeon and scientist to serve his nation and people. Although there was a war going on, he was not sent abroad with the troops for two reasons – he was perfecting a discovery on wounds and the old General might need him for an operation. Hana – a dedicated wife With his father’s consent, ...
28 comments
Read more

Summary of Evans Tries an O-level - Colin Dexter

By
EVANS TRIES AN O-LEVEL                                                 - Colin Dexter An unusual request from a prisoner In early March, the Secretary of the Examinations Board gets a call from the Governor of HM Prison in Oxford. The call is regarding a prisoner at Oxford Prison. The prisoner, James Roderick Evans, has been taking night classes in O-level German since last September and now aspires to write the exam to add to his education qualification. The Governor informs the Secretary that Evans is a congenital kleptomaniac but has a pleasant personality and no record of violence. As Evans is in a cell of his own, he can sit for his exam there itself. The call ends with the decision to get a parson from St. Mary Mags to invigilate and to kee...
7 comments
Read more

Summary of Memories of Childhood - The Cutting of My Long Hair - Zitkala-Sa and We Too are Human Beings - Bama

By
MEMORIES OF CHILDHOOD This lesson presents the idea of marginalization from the perspective of two women, Zitkala-Sa and Bama, as they walk down the memory lane to the episodes that had significant influence on their lives. I. The Cutting of My Long Hair (Zitkala-Sa) The raucous cage The author narrates the incidents of the agonizing first day of her new boarding school life as a Native American. The day was bitterly cold and she was aghast to find herself amidst the chaos of the annoying loud noises of the ringing bell, clattering shoes and ceaseless murmuring in English, the language which was still “unknown” to her. In that new place, she fell prey to the European missionaries who were prejudiced and biased against the Native American clan. Caught in this strange new world, she yearned for her “lost freedom”. Discipline of the dining hall The ringing bell was an indication for breakfast. As Zitkala-Sa entered the room in a line with her Indian counterparts, who...
7 comments
Read more

Summary of Indigo - Louis Fischer

By
INDIGO                              – Louis Fischer The author visits Sevagram Fischer visited Sevagram, the ashram of Gandhi, in 1942. There, Gandhi revealed the reason behind the decision to urge the departure of the British, in 1917. A Champaran peasant and his request In 1916, Gandhi attended the annual convention of the Indian National Congress in Lucknow. During the proceedings, an illiterate peasant, Rajkumar Shukla, approached Gandhi and requested him to visit his district. He was one of the sharecroppers of Champaran, who had come to appeal against the injustice of the landlord system in Bihar. The peasant accompanied Gandhi everywhere he went and unrelentingly begged him to ‘fix a date’ for his visit to Champaran. In due course, Gandhi, impressed by the determination and the woeful tale of the peasant, consented to his request and asked him to meet in Calcutta. Gandhi’s visit to Ra...
6 comments
Read more

Summary of On the Face of It - Susan Hill

By
ON THE FACE OF IT                                   - Susan Hill Scene one Lonely Derry avoids people Fourteen-year-old Derry, in an attempt to hide from the hustle-bustle and yet unfriendly world, jumps over the wall to Mr. Lamb’s garden. Unaware of Mr. Lamb’s presence, Derry stumbles upon him and is dumbfounded as he expected the house as well the garden to be unoccupied. Derry has a distorted face, a side of which was burnt by acid, and this crushed his self-confidence. Unconcerned about the way he looked, Mr. Lamb easily starts a conversation with the boy. The friendly Mr. Lamb Mr. Lamb, even without knowing him or his name, considers Derry as a friend.  The play highlights how he kept the gate of the garden always open, welcoming everyone. His house did not have any curtains as he did not like “shutting things out, shutting things in”. While talking to Derry, he said, ...
17 comments
Read more