# Shortcut Method of Division

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

7|28

4

7 × 4 = 28

28 ÷ 4 = 7

(ii) Divide 200 by 25

25|200

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

8|35

4         with remainder 3

(ii) Divide 113 by 15

15|113

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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