Last updated on July 14th, 2024 at 05:56 pm
The division is a method of distributing or splitting a large group of things into equal smaller parts. It is a major arithmetic operation apart from addition, subtraction and multiplication, in which large numbers are divided in such a way that it forms a new number.
In order to perform division, we use two symbols. They are ÷ and /.
For example, 8 ÷ 2 = 4, and 8/2 = 4
The formula of division is:
Dividend = (Divisor × Quotient) + Remainder
Example: 265 is divided by 4
Term | Description | Value |
---|---|---|
Divisor | Total number of equal groups | 4 |
Dividend | Total number that are split | 265 |
Quotient | The number of parts | 65 |
Remainder | The remaining part | 5 |
You can easily verify whether your answer is correct or not by putting the values in definition.
Dividend = (Divisor × Quotient) + Remainder
265 = (4 × 65) + 5 = 260 + 5 = 265
265 = 265
Divisor Dividend
⬇️ ⬇️
4 | 2 6 5 | 65 ⬅️ Quotient
2 4
______
2 5
2 0
_______
5 ⬅️ Remainder
In vedic maths depending on divisor and dividend, we can divide any number by using certain sutras/techniques such as
Nikhilam Sutra, Paravartya Sutra, Anurupyena Sutra, Ekadhikena Purvena, and Vestanas.
Division With Single Digit
With 5
Example 1: 4314 ÷ 5
Traditional method so long and boring
5 ) 3 1 2 4 ( 6 2 4. 8
3 0
‐——
1 2
1 0
______
2 4
2 0
________
4 0
4 0
Vedic maths method
Step 1: Just double the number by multiplying with 2
Step 2: After doubling, put a point just before the unit digit, you get the result.
3 1 2 4 ÷ 5
⬇️- just double the number
6 2 4 8
6 2 4 . 8 is the Answer
Example 2: 34323 ÷ 5
3 4 3 2 3
6 8 6 4 6 (Double by multiplying with 2)
6864.6 – (put one point before unit digit)
Example 3: 6848 ÷ 5
6 8 4 8
×2 ×2 ×2 ×2 – do it only in mind
_________________
12 | 1 6 | 0 8 | 1 6 – Apply Balancing Rule
|➕| |➕| |➕|
_______________
1 3 6 9 6
》Answer is 1369.6
With 9
Step 1: Drop the first number from the left as it is.
Step 2: Add that number with next, again add with next and continue till end.
Step 3: Put a point before unit digit
Example 1: 2213 ÷ 9
2 2 1 3
2 4 5 8
》Answer is 245.8
Example 2: 23578 ÷ 9
2 3 5 7 8
2 | 5 | 10 |17 | 25 + 2 — { 9 ) 25 ( 2 }
2 | 5 | 1 0 |1 7 | 2 7 18
____________________
2 6 1 9 7
》Answer is 2619.7
Example 3: 467389 ÷ 9
4 6 7 3 8 9
4 | 10 | 17 | 20 | 28 | 37+4 —-9 ) 37 (4
4 | 10 | 17 | 20 | 28 | 41 36
______________________
5 1 9 3 2 1
》 Answer is 51932.1
Division With Two Digit Number
With 25
Example : 34343423 ÷ 25
Step 1: In case of 25 you multiply every digits with 4 not two as you were doing in case of 5. But do this multiplication in your mind so don’t write ×4.
Step 2: Put one point before tens place
3 4 3 4 3 4 2 3
×4 ×4 ×4 ×4 ×4 ×4 ×4 ×4-only in mind
12 |1 6 |12 | 16 | 12 | 16 | 08 | 12
1 3 7 3 7 3 6 9 2
》 Answer is 1373736.92
With 99
Step 1: As 99 is a double number, divide the number in pairs.
Step 2: Same as 9, add to next number
Step 3: Put one point before tens place
Example: 12231 ÷ 99
Pairs
⬇️ ⬇️ ⬇️
01 22 31
⬇️↗️ ⬇️↗️ ⬇️
1 23 54 (23+31)
⬆️
(22+1)
》 Answer is 123.54
With 50
Step 1: Same as 5
Step 2: Put one point before tens digit
Example: 22345 ÷ 50
2 2 3 4 5
×2 ×2 ×2 ×2 ×2 –do it in mind
_________________
4 | 4 | 6 | 8 | 10
4 4 6 9 0
》 Answer is 446.9
With 11
Step 1: As we have doubled the numbers in case of 5, 50, here we have to subtract
Step 2: Put one point before unit digit
Example 1: 2467 ÷ 11
2 4 6 7
(From left drop 2 then deduct 2 from 4 and from 6 etc.)
2 4 6 7
2 2 4 3
⬆️ ⬆️ ⬆️
(4-2) (6-2) (7-4)
》 Answer is 224. 3
⬇️ ⬇️
Quotient Remainder
Example 2: 8367 ÷ 11
8 3 6 7
8 here 8 is bigger than 3 so we have to make this bigger than 8. 3 borrow 1 from 8 and become 13, and 8 become 7.
8 3 6 7
7 6 0 7
⬆️ ⬆️ ⬆️ ⬆️
⬆️ (13-7) (6-6) (7-0)
(Write 7 not 8)
》 Answer is 760. 7
⬇️ ⬇️
Quotient Remainder
Final Words
From the above article you must have learned very effective techniques of vedic maths division. These techniques needs a lot of practice, so as to do any division fast, within 2 to 5 seconds.