05.08 वैदिक गणित (08) || भाग || 9 की संख्या से भाग करना
लेखक
ॐ जितेन्द्र सिंह तोमर
M.A., B.Ed., DNYS, MASSCOM
12/1/29/11/2021
05.08 वैदिक गणित (08) || भाग || 9 की संख्या से भाग करना
Dividing by 9
PART 01
Single digit No.÷ 9
0/9 = 0
1/9 = 0.111..... or Bar 1
2/9 = 0.222..... or Bar 2
3/9 = 0.333..... or Bar 3
4/9 = 0.444..... or Bar 4
5/9 = 0.555..... or Bar 5
6/9 = 0.666..... or Bar 6
7/9 = 0.777..... or Bar 7
8/9 = 0.888..... or Bar 8
9/9 = 1
Dividing by 9
PART 02
Double digit No.÷ 9
Consider some two digit numbers (dividends) and same divisor 9. Observe the following example.
15 ÷ 9
The quotient (Q) is 1, Remainder (R) is 6.
9) 15 (1
9
6
Each number to be divided has been separated into two parts by a slash mark (diagonal stroke). The left-hand part gives the first part of the answer and right-hand side gives the reminder. Steps
1) Separate off the last digit of the dividend with a diagonal
stroke.
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.
Q. 1: Find 13/9 , 34/9 and 80/9
Sol.
1 | 3
1 ,
1 | 4
13 ÷ 9 gives Q = 1, R = 4
Q. 2 : Find 13/9 , 34/9 and 80/9
Sol.
5 | 4
3
5 | 7
54 ÷ 9 gives Q = 5, R = 7
Q. 3 : Find 13/9
Sol.
7 | 0
7
7 | 7
70 ÷ 9 gives Q = 7, R = 7
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.
Logic Works
A B ÷ 9
A | B
A
A | (B+A)
PART 03
Three digit No.÷ 9
Consider for 3 digits
A B C ÷ 9
A B | C
A/(A+B)| (B+C)
Add the first digit A to second digit B getting A + B = AB.
Hence Quotient is AB. Now second digit of AB i.e.,, B is added to third digit C of dividend to get the remainder i.e.,, B + C = BC
Q. 4 : Find 124 /9
124 ÷ 9
1/(1+2)
1/3|(3+4)
13 | 7
Q = 13
R = 7
Add the first digit 1 to second digit 2 getting 1 + 2 = 3. Hence Quotient is 13. Now second digit of 13 i.e.,, 3 is
added to third digit 4 of dividend to get the remainder i.e.,, 3 + 4 = 7 now Q = 13, R = 7
CHECK
9 ) 1 2 4 ( 13
9 ↓
3 4
2 7
7
Q. 5 : Find 232 / 9
2 3 | 2
↓ 2 | ↓
2 5 | 4
Add the first digit 2 to second digit 1 getting 2 + 1 = 3. Hence Quotient is 23. Now second digit of 23 i.e.,, 3 is
added to third digit 2 of dividend to get the remainder i.e.,, 3 + 2 = 5 now Q = 23, R = 4
CHECK
9 ) 2 3 2 ( 25
1 8 ↓
5 2
4 5
7
2 3 | 2
↓ 2 | ↓
2 5 | 4
Q. 5 : Find 345 / 9
9 ) 345 ( 23 9 ) 3 4 / 5
18 ↓ 3 / 3
32 3 7 / 5
27
5
Add the first digit 3 to second digit 4 getting 3 + 4 = 7. Hence Quotient is 37. Now second digit of 37 i.e.,, 7 is
added to third digit 5 of dividend to get the remainder i.e.,, 7 + 5 = 12
Here Q = 23, R = 12
The remainder 12 is more than 9 , the divisor and so again divide 12 by 9 giving 1 and remainder 3. This 1 is carried over to the left to Quotient 23 and add 23+1=24.
Now Q = 24, R = 3
PART 04
Four and more digit No.÷ 9
Q. 5 : Find 34567 / 9
Sol.
9) 2 3 4 5 6 | 7
2 5 9 ¹4 ²0 | 27
2 6 0 6 3 | 0
The remainder 27 is larger than 9 , the divisor and so divide by 9 giving 3 and remainder 0. This 3 is carried over to the left giving answer are 26063/0
* Add the first digit 2 to second digit 3 getting 2 + 3 = 5. Hence Quotient is 25. Now second digit of 25 is 5.
* Add Second digit 5 to third digit 4 getting 5 + 4 = 9. Now third digit of 259 is 9.
* Add Third digit 9 to fourth digit 5 getting 9 + 5 = ¹4. Now third digit of 259 is 9.
and 9 added to fourth digit 5 of dividend to get the remainder i.e.,, 7 + 5 = 12
Here Q = 23, R = 12
The remainder 12 is more than 9 , the divisor and so again divide 12 by 9 giving 1 and remainder 3. This 1 is carried over to the left to Quotient 23 and add 23+1=24.
Now Q = 24, R = 3
Q3. 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
Exercise 01
(A) Divide The Following Numbers
A
9) 10 ( 9) 21 ( 9) 33 (
9) 44 ( 9) 54 ( 9) 65 (
9) 76 ( 9) 87 ( 9) 98 (
9) 12 ( 9) 57 ( 9) 36 (
9) 75 ( 9) 50 ( 9) 63 (
B
9) 12 ( 9) 21 ( 9) 21 (
9) 43 ( 9) 54 ( 9) 65 (
9) 76 ( 9) 87 ( 9) 87 (
8) 18 ( 9) 25 ( 9) 30 (
9) 47 ( 9) 60 ( 9) 73 (
C
9) 104 ( 9) 215 ( 9) 326 (
9) 437 ( 9) 548 ( 9) 659 (
9) 760 ( 9) 871 ( 9) 982 (
9) 123 ( 9) 254 ( 9) 365 (
9) 476 ( 9) 507 ( 9) 678 (
D
9) 109 ( 9) 210 ( 9) 321 (
9) 432 ( 9) 543 ( 9) 654 (
9) 765 ( 9) 876 ( 9) 987 (
9) 128 ( 9) 259 ( 9) 360 (
9) 471 ( 9) 502 ( 9) 673 (
E
9) 105 ( 9) 216 ( 9) 327 (
9) 438 ( 9) 549 ( 9) 650 (
9) 761 ( 9) 872 ( 9) 983 (
9) 124 ( 9) 255 ( 9) 366 (
9) 477 ( 9) 508 ( 9) 679 (
Exercise 02
(B) Divide The Following Numbers
A
9) 1600 ( 9) 2713 ( 9) 3824 (
9) 4935 ( 9) 5046 ( 9) 6157 (
9) 7269 ( 9) 8375 ( 9) 9483 (
9) 15235 (
9) 26579 (
9) 37684 (
9) 48792 (
9) 59036 (
9) 60756 (
B
9) 1305 ( 9) 2417 ( 9) 3525 (
9) 4633 ( 9) 5745 ( 9) 6853 (
9) 7965 ( 9) 8075 ( 9) 9185 (
9) 12218 (
9) 23526 (
9) 34634 (
9) 45743 (
9) 56062 (
9) 66773 (
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