vedic math trick to divide any number easily with 8 .
This is similar to previous post with few changes.
divisor will be 8 here and the number which is to be divided by is dividend.
Take another example
423115/ 8
1) 4 2 3 1 1 / 5
2) 4 2 3 1 1 / 5
+
0
3) 4 2 3 1 1 / 5
+
0
4
4) 4 2 3 1 1 / 5
+ + + + +
8 20 46 94 190
This is similar to previous post with few changes.
divisor will be 8 here and the number which is to be divided by is dividend.
Method
- Differentiate last digit of dividend with slash (/) for remaining digits .
- write compliment under divisor or just remember it. (compliment = 10 -8 =2)
- write 0 under first digit of dividend then add first digit with 0.
- The result obtained in second step by adding 0 and first digit is multiplied with compliment , result is written under second digit and than they undergo addition. Repeat this step up-to last digit of dividend. If any of the result are of more than one digit than last digit of resultant is written and others are carries to previous digit.Note that the result obtained is added to next digit even if it is more than 1 digit number.
- Now if the remainder obtained is number greater than 8 than that remainder is again divided by 8.
- Now repeat step 4 until you get remainder less than 8.
Lets understand with example
13 / 9
|
| 1) 8 is divisor , 13 is dividend.
13 / 9
|
| 1) 8 is divisor , 13 is dividend.
| 2) 2 is compliment
| 3) 1 / 3 is given as divisor is only 1 digit
| number and last digit is for remainder and
| remaining for quotient.
| 4) 1 + 0 = 1
| 5)2*1=2 , 2 is written under 3 and added to get
| 5 . 3+2= 5
| 6) 1 is quotient and 5 is remainder.
275/8
| number and last digit is for remainder and
| remaining for quotient.
| 4) 1 + 0 = 1
| 5)2*1=2 , 2 is written under 3 and added to get
| 5 . 3+2= 5
| 6) 1 is quotient and 5 is remainder.
275/8
1) separate last digit of dividend with slash for remainder and place 0 under first digit :
2) add 2 and 0 and it gives 2 , multiply that 2 with the compliment 2 (2*2=4) and write it under 7 => 4+7 =11 now multiply compliment that is 2 with 11 (2*11=22) and write it under 5 and add them it gives 5+22 =27 . Here 1 from 11 is carried forwarded to 2 so we get quotient as 31
3) Now quotient : 31 , Remainder: 27 , here 27 is bigger than 8 so again it is divided by 8.now again divide 27 in two parts 2 / 7 and adding first digit with 0 we get 2 . Now 2 is multiplied with compliment of 8 that is 2 and added with 7 which gives 11 . Thus it gives 2 = quotient and 11 as remainder as 11 is greater than 8 , so again repeat same process , split 1 / 1 and add first digit with 0 we get 1 . Now 1 is multiplied with compliment of 8 that is 2 and added with 1(2*1+1) which gives
3 . Thus it gives 1 = quotient and 3 as remainder as 3 is less than 8 thus its final remainder .
3 . Thus it gives 1 = quotient and 3 as remainder as 3 is less than 8 thus its final remainder .
4) quotient 29 and sub-quotient from above step are added to get final quotient ,
Quotient 1= 31 , Quotient 2= 2 , quotient 3 =1 => final Quotient = 34
Quotient 1= 31 , Quotient 2= 2 , quotient 3 =1 => final Quotient = 34
Final quotient is 34 , Remainder : 3
Take another example
423115/ 8
1) 4 2 3 1 1 / 5
2) 4 2 3 1 1 / 5
+
0
3) 4 2 3 1 1 / 5
+
0
4
4) 4 2 3 1 1 / 5
+ + + + +
8 20 46 94 190
4 10 23 47 95 195
5) 4 2 3 1 1 / 5
5) 4 2 3 1 1 / 5
+ + + + +
8 20 46 94 190
8 20 46 94 190
4 1 0 2 3 4 7 9 5 / 195
+ + + +
6) 4 2 3 1 1 / 5
9) AS 11 is greater than 8 it cannot be remainder , so it is again divided by 8 repeating same steps as above . Split 11 into two parts
4 2 3 1 1 / 5
0 2 22
21 // 2 / 7
+
0 4
2 // 1 / 1
+
0 2
1 / 3
8) Now as 3 is less than 8 it is final remainder. 52865, 21,2,1 are quotients and are added to get final quotient
5 2 8 6 5 / 3
+ 2 1
+ 2
+ 1
Final Answer : 52889 / 3
Quotient : 52889 Remainder : 3
NOTE : If remainder is single digit number is greater than or equal to 8 than divide it with regular division method.
similarly practice some examples and get expertise over it for mental calculation
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6) 4 2 3 1 1 / 5
+ + + + +
8 20 46 94 190
8 20 46 94 190
5 2 7 1 6 5 / 195
7) AS 195 is greater than 8 it cannot be remainder , so it is again divided by 8 repeating same steps as above . Split 195 into two parts .
4 2 3 1 1 / 5
8) AS 27 is greater than 8 it cannot be remainder , so it is again divided by 8 repeating same steps as above . Split 27 into two parts .
4 2 3 1 1 / 5
0 2 22
1 11 // 2 / 7
+
7) AS 195 is greater than 8 it cannot be remainder , so it is again divided by 8 repeating same steps as above . Split 195 into two parts .
4 2 3 1 1 / 5
+ + + + +
8 20 46 94 190
8 20 46 94 190
5 2 8 6 5 // 19 / 5
8) AS 27 is greater than 8 it cannot be remainder , so it is again divided by 8 repeating same steps as above . Split 27 into two parts .
4 2 3 1 1 / 5
+ + + + +
8 20 46 94 190
8 20 46 94 190
5 2 8 6 5 // 1 9 / 5
+ 0 2 22
1 11 // 2 / 7
+
9) AS 11 is greater than 8 it cannot be remainder , so it is again divided by 8 repeating same steps as above . Split 11 into two parts
4 2 3 1 1 / 5
+ + + + +
8 20 46 94 190
8 20 46 94 190
5 2865 // 1 9 / 5
+0 2 22
21 // 2 / 7
+
0 4
2 // 1 / 1
+
0 2
1 / 3
8) Now as 3 is less than 8 it is final remainder. 52865, 21,2,1 are quotients and are added to get final quotient
5 2 8 6 5 / 3
+ 2 1
+ 2
+ 1
Final Answer : 52889 / 3
Quotient : 52889 Remainder : 3
NOTE : If remainder is single digit number is greater than or equal to 8 than divide it with regular division method.
similarly practice some examples and get expertise over it for mental calculation
Do Like, Comment , Share my blogs if you like them.
Follow for more updates.