We will discuss here how to use short cut method of division without remainder and with remainder. We know that when we share equally or we make equal groups we use division.
Suppose, Maya has 20 pencils, 4 pencils are put in 1 holder. How many holders are needed to put 20 pencils?
We observe that 5 holders are required for 20 pencils.
i.e.,
20 ÷ 4 = 5
Number of pencils pencil in each holder Number of holders
This can also be shown by Repeated Subtraction.
Total pencil 20
Pencils in 1 holder 4
Pencils left 16
Pencils left 26
Again pencils in another holder 4
Pencils left 12
Pencils still left 12
Again pencils in another holder 4
Pencils left 8
Pencils still left 8
Pencils in another holder 4
Pencils left 4
Pencils still left 4
Pencils in another holder 4
Pencils left 0
So, we observe that we used 5 holders to keep 20 pencils.
This can be expressed.
20  4 16 First time 
16  4 12 Second time 
12  4 8 Third time 
8  4 4 Fourth time 
4  4 0 Fifth time 
We also know that division is an inverse process of multiplication.
i.e.,
2 × 4 = 8 means 8 ÷ 2 = 4 and 8 ÷ 4 = 2
(Multiplication fact) (Division fact) (Division fact)
Note:
Remainder is always less than the divisor.
Quotient is either less or equal to the dividend.
In 29 ÷ 6 = 4 and 5 left ones.
Dividend Divisor Quotient Remainder
Here remainder 5 is less than the divisor 6.
Quotient 4 is less than the dividend 29.
Short division method without remainder:
We recite table till we come to the conclusion i.e.,
(i) Divide 28 by 7
728
4
7 × 4 = 28
28 ÷ 4 = 7
(ii) Divide 200 by 25
25200
8
25 × 8 = 200
200 ÷ 8 = 25
Short division method with remainder:
In short division, we subtract mentally rest of the process remains the same as in the case of without remainder.
(i) Divide 35 by 8
835
4 with remainder 3
(ii) Divide 113 by 15
15113
7 with remainder 8
Verification of result whether short division or long division can be ne by using division algorithm, that is, Dividend= Divisor × Quotient + Remainder.
For example,
27 ÷ 4 = = 6 with remainder 3
Here dividend = 27
Divisor = 4, Quotient = 6, Remainder = 3 Since, D = d × Q +R
= 4 × 6 + 3 = 24 + 3 D = 27 
D → Dividend d → Divisor
Q → Quotient R → Remainder 
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