# Division of Whole Numbers

In this post we will learn division of large whole numbers.

First we will understand the concept of division.

Then move on to calculate division of any number using Long Division Method.

After the concept we will solve worksheets related to this concept

## Concept of Division

In Division we basically separate the number into small parts.

The symbol for division is ÷
If we write 16 ÷ 4, it means that we are dividing number 16 with 4.

Let us understand division with the help of examples.

Example
Divide the 20 balls into 4 parts

The question can be expressed as: 20 ÷ 4

There are 20 balls in the below box.

Now you have to find 20 ÷ 4
It means for given 20 balls, you have to form group of 4

When we form group of 4, we get total of 5 boxes (see the image below)

This means that 20 ÷ 4 = 5

Hence for number 20, if we try to form groups of 4, we will get total of 5 groups

### Concept of Remainder

Remainder is the numbers left when the given division is not fully possible

Example
Divide 17 by 4

It means that from given number 17, we have to form group of 4

You can see from above that the number 17 is not completely divisible by 4.

When number 17 is formed into group of 4, we get 4 box of the group and 1 is left as a remainder.

So the above result can be expressed as:
17 ÷ 4 = 4 groups & 1 remainder

### How to do Division

Division of big numbers is done by Long Division Method

We will understand the concept with the help of examples

#### 3 by 1 digit Division

Divide 736 by 8

Solution
The above question can be written as 736 ÷ 8

Representing the above expression in long division as:

The dividend is always kept inside the symbol
The divisor is always outside the sumbol

Try to divide number 7 with 8
Since 7 is smaller than 8, the division is not possible

On including next digit we get 73

Try dividing 73 with 8 (i.e. 73 ÷ 8 )

we know that:
9 x 8 = 72
9 x 9 = 81

we will take 72 as it is smaller than selected number 73
Subtract 72 from 73

In the above figure you can see
⟹ 9 is part of quotient (Since we are taking 9 x 8 = 72)
⟹ 01 is remainder (as 73 – 72 = 01)

Include next digit of dividend (number 6)

we know that:
8 x 2 = 16

Include 2 as part of Quotient
and subtract 16 with 16

You can see here remainder is 0, so the division is complete

From the above calculation we now know that
736 ÷ 8 = 92

It means that if we divide 736 number into group of 8, we will get total of 92 groups

#### 4 by 2 digit Division

Divide 1035 by 23

Solution
The problem can be expressed as 1035 ÷ 23

Representing the expression in the form of long division

Divide First number of divided (which is 1)

Since 1 is smaller than 23 (1 < 23), division is not possible

Include the next number 0 to make number 10
Again 10 is less than 23 (10 < 23), division is not possible

Include next number 3 to make 103

Try dividing 103 by 23

We know that:
23 x 4 = 92
23 x 5 = 115

Here 115 is larger than 103
So we select 92 (23 x 4)

⟹ 4 is written in quotient
⟹ when we subtract 103 – 92 = 11 i

Now 11 is left which is not divisible by 23

Include next digit ( number 5) of the dividend

Now we have to divide 115 with 23

We know that
23 x 5 = 115

Include 5 as a part of quotient
And Subtract 115 with 115

You can see that remainder is 0, so division is complete
And we get 45 as final quotient

So 1035 ÷ 23 = 45

It means if we divide 1035 into group of 23, we will get total of 45 groups

Example 02
Divide 1030 by 32

Solution
The above problem can be expressed as (1030 ÷ 32)

Representing the expression in the form of long division

Let’s divide the first number of dividend (i.e. 1)

Since 1 is smaller than 32 (1 < 32), division is not possible

Now include next number (number 0) to form 10

Again 10 is smaller than 32 (10 < 32), division is not possible

Include next number (digit 3) to form number 103

103 is greater than 32, hence division is possible

we know that
32 x 3 = 96
32 x 4 = 128

Since 128 is larger than 103, we will select 96

⟹ Number 3 is written in quotient
⟹ we subtract 103 – 96 to get 07 as remainder

Now include next number (digit 0) of the dividend to get 70

Again 70 is greater than 32, so division is possible

we know that
32 x 2 = 64
32 x 3 = 96

we will select number 64 (32 x 2)

Here we get
⟹ 32 as quotient
⟹ 06 as remainder

Since there is no number left in dividend, the division process is complete

Here the division 1030 ÷ 32 is leaving remainder 6 at the end. Hence the number 1030 is not fully divisible by 32.

Example 03
Divide 4275 by 45

Solution
The problem can be expressed as 4275 ÷ 45

Divide the first number of dividend ( i.e. 4)

Since 4 is smaller than 45 (4 < 45), division is not possible

Taking the second number of dividend, the number will be 42

Again 42 is less than 45 (42 < 45), the division is not possible

Taking the third number of dividend, the number becomes 427

427 is greater than 45, the division is possible

45 x 9 = 405
45 x 10 = 450

we will take 405 because it is smaller than 427

⟹ we get 9 as quotient
⟹ 22 as remainder

Now we include next number (digit 5) to get 225

we know that
45 x 5 = 225
45 x 6 = 270

we will ignore 270 and take 225

Here we get
⟹ 0 remainder, which means division is complete
⟹ 95 as the final quotient

Hence 4275 ÷ 45 = 95

## Grade 5 Long Division Worksheet

Here we will solve some questions related to Long Division Method.

All the questions are solved with explanation.

Take out pencil and paper and try solving the questions

### Simple Division Questions

Solve the division and select the right answer

(01) 192 ÷ 8

(a) 24
(b) 25
(c) 26
(d) 27

Option (a) is the right answer

(02) 512 ÷ 16

(a) 26
(b) 30
(c) 32
(d) 36

Option (c) is the right answer

(03) 1035 ÷ 23

(a) 47
(b) 45
(c) 50
(d) 55

Option (b) is the right answer

(04) 4355 ÷ 67

(a) 56
(b) 65
(c) 70
(d) 75

Option (b) is the right answer

(05) 3469 ÷ 34

(a) 102
(b) 102 & 2 remainder
(c) 102 & 1 remainder
(d) 102 & 4 remainder

Option (c) is the right answer

(06) 80257 ÷ 97

(a) 827 & 38 remainder
(b) 827 & 28 remainder
(c) 827 & 26 remainder
(d) 827 & 36 remainder

Option (a) is the right answer

(07) 21474 ÷ 42

(a) 511
(b) 512 & 11 remainder
(c) 512
(d) 511 & 12 remainder

Option (d) is the right answer

(08) 2079 ÷ 63

(a) 43
(b) 23
(c) 33
(d) 53

Option (c) is the right answer

(09) 28812 ÷ 12

(a) 2401
(b) 3001
(c) 2503
(d) 3112

Option (a) is the right answer

(10) 14683 ÷ 33

(a) 445 & 30 remainder
(b) 444 & 29 remainder
(c) 450 & 31 remainder
(d) 444 & 31 remainder

Option (d) is the right answer

(11) 86762 ÷ 79

(a) 1099
(b) 1099 & 20 remainder
(c) 1098
(d) 1098 & 20 remainder

Option (d) is the right answer

(12) 1625 ÷ 25

(a) 66
(b) 65
(c) 64
(d) 63

Option (b) is the right answer

(13) 29550 ÷ 80

(a) 369 & 50 remainder
(b) 369 & 10 remainder
(c) 369 & 30 remainder
(d) 369 & 20 remainder

Option (c) is the right answer

(14) 29887 ÷ 64

(a) 366 & 63 remainder
(b) 466 & 63 remainder
(c) 366 & 36 remainder
(d) 466 & 36 remainder

Option (b) is the right answer

(15) 1656 ÷ 18

(a) 91
(b) 92
(c) 93
(d) 94

Option (b) is the right answer

### Missing Digits of Division Worksheet

Here complete division structure is provided with empty boxes.

Do the division and fill up the boxes with right numbers

(01) Fill the missing numbers in division of 9978 ÷ 6

(02) Below is the division of 35481 ÷ 25
Fill up the empty boxes with correct number

(03) Incomplete division of 80552 ÷ 17 is given
Fill up the empty boxes

(04) Fill up the missing numbers in below division

(05) Division of 10640 ÷ 80 is shown below.
Fill up the empty boxes with right numbers

(06) For the below division, fill up the empty boxes

(07) For the below long division, fill up the empty boxes

(08) Find the right numbers for the below division

(09) Division of 61765 ÷ 55 is given
Fill up the boxes with correct number

(10) For the below division, find the correct number for boxes