Dividing numbers is time-consuming. If we perform divisions quickly then we can even calculate faster than calculators.
The trick to divide any number with number nearing base is divided into two parts
1) number which is near to the base but less than the base (for example dividing by 89 or 91 or any such number less than and near to 100 )
2) number which is near to the base but greater than the base ( for example 103 is greater than 100 but near to it).
In this blog I will explain first part: Number nearing base but less than the base.
Starting with simplicity I shall recall division with 9 which was covered in the last blog.
Dividing 160 with 9 :
1) Find out complement of 9 (10-9=1 =>complement of 9)
2) As complement is of 1 digit put a slash after 1 digit from right, the digit after the slash indicates the remainder.
3)Now 1 of 160 is brought down as it is.
4)1 * 1 = 1 (1 which is the complement of 9 * 1 which was brought down in the last step).
5)1+6=7 ( Add 1 of above step with 6 of 160 ).
6)1*7(1 which is the complement of 9 * 7 from above step).
7) 7+0( 7 from above step added with 0 of 160).
8) final quotient Q= 17 Remainder R= 7
Similarly, we have to perform division when the base is 100 or 1000 or further added zeros.
1) Dividing 2401 with 99.
2) write complement of 99 (100-99=01). Here as the complement is of 2 digits we put a slash before two digits from the right of number 2401.
3) Now bring 2 of 2401 as it is.
4) 0* 2 =0 and 1* 2 = 2 write 0 under 4 and 2 under 0
5) now adding 0 and 4 from above step we get 0 +4 =4 , multiplying 4 with 0 and 1 4*0=0, 4*1=4
write 0 under 2 from above step and write 4 under 1 (next digit).
Now we have quotient as 24 and remainder as 25.
if you don't understand check out this video.
Similarly for base 1000
6) 4 2 / 3 1 5
7) 4 2 / 3 1 5
8) Now as 1421 is greater than 889 it is further divided again by 889
4 2 / 3 1 5
1 // 4 2 1
+1 + 1 +1 (1*111)
1 // 5 3 2
9) 4 6 from step 7 and 1 from step 8 are added to get the final quotient
46 //1 /532
+
47 // 532
10) 47 is quotient and 532 is remainder.
similarly, other divisions such as dividing by 88, 999 or any number nearing this base number can be done easily.
Try this questions by yourself and after practice, you might divide numbers quickly and easily without the need to write any calculations on paper.
1) 2532/89 ---> quotient -28 and remainder is 40
2)13224/888---->14 as quotient and 792 as remainder.
Keep on practicing and you will master it.
Please do share ,like and comment.
The trick to divide any number with number nearing base is divided into two parts
1) number which is near to the base but less than the base (for example dividing by 89 or 91 or any such number less than and near to 100 )
2) number which is near to the base but greater than the base ( for example 103 is greater than 100 but near to it).
In this blog I will explain first part: Number nearing base but less than the base.
Starting with simplicity I shall recall division with 9 which was covered in the last blog.
Dividing 160 with 9 :
1) Find out complement of 9 (10-9=1 =>complement of 9)2) As complement is of 1 digit put a slash after 1 digit from right, the digit after the slash indicates the remainder.
3)Now 1 of 160 is brought down as it is.
4)1 * 1 = 1 (1 which is the complement of 9 * 1 which was brought down in the last step).
5)1+6=7 ( Add 1 of above step with 6 of 160 ).
6)1*7(1 which is the complement of 9 * 7 from above step).
7) 7+0( 7 from above step added with 0 of 160).
8) final quotient Q= 17 Remainder R= 7
Similarly, we have to perform division when the base is 100 or 1000 or further added zeros.
1) Dividing 2401 with 99.
2) write complement of 99 (100-99=01). Here as the complement is of 2 digits we put a slash before two digits from the right of number 2401.
3) Now bring 2 of 2401 as it is.
4) 0* 2 =0 and 1* 2 = 2 write 0 under 4 and 2 under 0
5) now adding 0 and 4 from above step we get 0 +4 =4 , multiplying 4 with 0 and 1 4*0=0, 4*1=4
write 0 under 2 from above step and write 4 under 1 (next digit).
Now we have quotient as 24 and remainder as 25.
if you don't understand check out this video.
Similarly for base 1000
42315 / 889
1) 4 2/ 3 15
2) 4 2 / 3 1 5
+
0
3) 4 2 / 3 1 5
+
0
4
4) 4 2 / 3 1 5
+ + +
4 4 4 (111*4 from last step)
1) 4 2/ 3 15
2) 4 2 / 3 1 5
+
0
3) 4 2 / 3 1 5
+
0
4
4) 4 2 / 3 1 5
+ + +
4 4 4 (111*4 from last step)
4 6 /
5) 4 2 / 3 1 5
5) 4 2 / 3 1 5
+ + +
4 4 4
+ + +
6 6 6 (6 from last step * 111 -> the complement of 889)
4 4 4
+ + +
6 6 6 (6 from last step * 111 -> the complement of 889)
4 6 / 13 11 11
6) 4 2 / 3 1 5
+ + +
4 4 4
+ + +
6 6 6 (6 from last step * 111 -> the complement of 889)
4 4 4
+ + +
6 6 6 (6 from last step * 111 -> the complement of 889)
4 6 / 13 1 1 1 1
+ +7) 4 2 / 3 1 5
+ + +
4 4 4
+ + +
6 6 6 (6 from last step * 111 -> the complement of 889)
4 4 4
+ + +
6 6 6 (6 from last step * 111 -> the complement of 889)
4 6 / 1421
8) Now as 1421 is greater than 889 it is further divided again by 889
4 2 / 3 1 5
+ + +
4 4 4
+ + +
6 6 6 (6 from last step * 111 -> the complement of 889)
4 6 / 1421 4 4 4
+ + +
6 6 6 (6 from last step * 111 -> the complement of 889)
1 // 4 2 1
+1 + 1 +1 (1*111)
1 // 5 3 2
9) 4 6 from step 7 and 1 from step 8 are added to get the final quotient
46 //1 /532
+
47 // 532
10) 47 is quotient and 532 is remainder.
similarly, other divisions such as dividing by 88, 999 or any number nearing this base number can be done easily.
Try this questions by yourself and after practice, you might divide numbers quickly and easily without the need to write any calculations on paper.
1) 2532/89 ---> quotient -28 and remainder is 40
2)13224/888---->14 as quotient and 792 as remainder.
Keep on practicing and you will master it.
Please do share ,like and comment.