Speed And Correct Division by 9 (Nine)

In Vedic Mathematics, there are several divisibility test for different numbers. I am going to explain one of the very simple and correct trick (method) of division by 9. You only require to have knowledge of addition and you will get your Remainder and Quotient. So, Lets start.

Example 1: So, start with easier two digit example. Divide 34 with 9

1. Write extreme Left side digit at bottom.

2. Put the first digit of the dividend as it is under the horizontal line. Put the same digit under the right hand part for the remainder, add the two and place the sum i.e.,, sum of the digits of the numbers as the remainder.

Let's consider some examples of two digits: Find 15/9 , 44/9 and 71/9

1 / 5       4 / 4           7 / 1
     1             4                7
1 / 6        4 / 8           7 / 8

15 / 9 gives Q = 1, R = 6
44 / 9 gives Q = 4, R = 8
71 / 9 gives Q = 7, R = 8

In the division of two digit numbers by 9, we can take the first digit down for the quotient-column and by adding the quotient to the second digit, we get the remainder.

Let's consider some examples of three digits: Find 124 /9, 215 / 9 and 403 / 9

12 / 4       21 / 5           40 / 3
  1 / 3        2 / 3             4 / 4
13 / 7      23 / 8           44 / 7

124 / 9 gives Q = 13, R = 7
215 / 9 gives Q = 23, R = 8
403 / 9 gives Q = 44, R = 7

Note : The remainder is the sum of the digits (digital sum) of the dividend. The first digit of the dividend from left is added to the second digit of the dividend to obtain the second digit of the quotient. This digit added to the third digit sets the remainder. The first digit of the dividend remains as the first digit of the quotient.

Division by 9 (nine) rules:

• The remainder is the sum of the digits (digital sum) of the dividend.
• The first digit of the dividend from left is added to the second digit of the dividend to obtain the second digit of the quotient.
• This digit is added to the third digit set the remainder.

Let's consider some more examples:

Example : Find 611 / 9

Add the first digit 6 to second digit 1 getting 6 + 1 = 7. Hence, Quotient is 67. Now second digit of 67 i.e.,, 7 is added to third digit 1 of dividend to get the remainder i.e.,, 1 + 7 = 8

9 ) 61 / 1
       6 / 7
    67 /  8
Q is 67, R is 8.

Example : Find 234571 / 9

The first digit 2 is set down as the first answer digit . Take this 2 and add the next digit 3. This (2+3) gives 5 as the next digit. Working this way 5+4 =9, 9+5 =14 , 14+7 =21 and the remainder is 21+1 =22

9 ) 234 5 7 / 1
259 14 21/ 22
26061 / 22

The remainder 22 is larger than 9 , the divisor and so divide by 9 giving 2 and remainder 4. This 2 is carried over to the left giving answer are 26063/4

Q= 26063, R = 4

Example : Find 13210 / 9

The first digit 1 is set down as the first answer digit . Take this 1 and add the next digit 3. This gives 4 as the next digit. Working this way 4+2 =6, 6+1 =7 and the remainder is 7+0 =7

9 ) 1321 / 0
     1467 / 7
Q = 1467, R = 7

Find 214091/9

9 ) 2140 9 / 1
2377 16/ 17
23786 / 17

The remainder 17 is larger than 9 , the divisor and so divide by 9 giving 1 and remainder 8. This 1 is carried over to the left giving answer are 23787/8

Q= 23787, R = 8

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