# Division

Division is the process of sharing a collection of items into equal parts and is one of the basic arithmetic operations in maths. We may face different situations every day where we use the division technique. For example

Let’s consider the example given in the above figure. This method is actually about how children divide when they distribute some objects repeatedly. In this case, they might first pack 4 sweets each in 10 or 15 boxes and then next pack the remaining sweets in the second round to simplify the procedure. They could as well pack by taking a few more boxes. Children can, thus, use any way to complete the process of division. This is the beauty of this method.

## Division Rule

Division rule involves four steps; they are:

Step 1: Identify the dividend and divisor and then write in the respective places.

Step 2: Multiply the divisor with a suitable number such that we get a result close to the dividend.

Step 3: Subtract the values in the dividend column.

Step 4: Now, bring down the result and repeat the preceding two steps until the remainder is less than the divisor.

This can be understood clearly with the help of the below figure:

## Division Symbol

We can represent the division with ÷, slash (/) or a horizontal line ( _ ). We can use these symbols as per our convenience when dealing with different types of computations or division questions. Here, x/y or $\frac{x}{y}$ can be read as “x by y” or “x over y”.

For example, the division of 48 by 6 can be expressed in either of the following ways.

48 ÷ 6 = 8

48/6 = 8

Or

$\frac{48}{6}=8$

However, the result is the same in all three representations.

In some situations, colon (:) is also taken as division. For example, 24 : 9 can be written as 24/9 or $\frac{24}{9}$ or 24 ÷ 9.

We can obtain the simplified form of 24 : 9 from all these representations. That means,

24 : 9 = 8 : 3

24/9 = 8/3

$\frac{24}{9}=\frac{8}{3}$

24 ÷ 9 = 8 ÷ 3

### Division Sums

The process of division can be better understood with the help of the below sums. Here, different cases have been covered in the division of numbers.

1) What is the remainder from the division of 906 by 6?

Here, remainder = 0

Quotient = 151

2) Complete the division: 8503 ÷ 18 = ______ + 7

Therefore, 8503 ÷ 18 = 18 × 472 + 7

3) Write the quotient when 2037 is divided by 12.

Therefore, the quotient is 169.

### Division of Fractions

The division of fractions is quite different from the division of natural numbers. While dividing fractions, we have to convert the division operator to multiplication. That means the inverted divisor should be multiplied with the dividend. Let’s have a look at the below example.

Divide 12/5 by 16/3:

Numerator = 12/5

Denominator = 16/3

We can write the division of 12/5 by 16/3 as:

(12/5) ÷ (16/3)

= (12/5)/ (16/3)

Now, converting “÷” into “×” means that the divisor should be inverted and multiplied.

(12/5) × (3/16)

= (3/5) × (3/4)

= 9/20

Thus, the division 12/5 by 16/3 gives 9/20 as a result in fraction form.

### Division 3 Digits

In this section, you will learn how to divide a 3 digit number and division of numbers by a 3 digit number.

1) Perform division for 483 with 7 as a divisor.

Now, let’s have a look at the division of a number by a three digit number.

2) Compute: 580654 ÷ 112

## Division Examples

Below are the examples of division problems in maths.

Example 1:

What is the remainder when 6585 is divided by 13?

Solution:

From the given,

Dividend = 6585

Divisor = 13

Therefore, the remainder is equal to 7.

Example 2:

Divide 1764 by 11.

Solution:

From the given,

Dividend = 1764

Divisor = 11

Therefore, the division of 1764 by 11 gives the quotient as 160 by leaving the remainder 4.

### Division by Zero

The division of any number by zero is undefined. In this case, the result can be written as infinity. For example, 15/0 = ∞, i.e. undefined.

### Division Algorithm

Division of any expression, follows the division algorithm given below.

Dividend = Divisor × Quotient + Remainder

This algorithm helps in finding the missing numbers in the division problem.