Learn how to divide a number by another number. The division is a basic arithmetic operation apart from addition, subtraction and multiplication. The division is the reverse process of multiplication. This method is represented by the symbol ‘÷’ or ‘/’. In this method, when a number x is divided by another y, we get an output result that equals to third number z, such as;

x ÷ y = z

Where x is the dividend, y is the divisor and z is the quotient.

Here, we will learn to divide the numbers, fractions, decimals, polynomials, with examples.

How to Divide Numbers Step By Step

Division method is nothing but the inverse of multiplication. In multiplication, we multiply the numbers into multiples but in the division, we divide the numbers into parts. Let us learn first how to divide a number with the help of examples.

Example: Divide 2 by number 4.

Solution: 2÷4 = 2/4

Since, both the number, 2 and 4 are the multiples of 2. Therefore, we can cancel out the common factor 2 from both numerator and denominator, to get;

2/4 = (2 × 1)/(2 × 2)

= ½ = 0.5

This was the case when the digits were single. Now let us solve a case of double digits.

Example: Divide 22 by 11.

Solution: 22÷11 = 22/11

Since, 22 and 11 both are multiples of 11, therefore;

22/11 = (2×11)/(1×11)

Cancelling the common terms from both numerator and denominator, we get;

22/11 = 2

Now, let us consider a case of a three-digit number.

Example: Divide 204 by 144.

Solution: 204÷144 = 204/144

Both the numbers 204 and 144 are the multiples of 12. Therefore,

204/144 = (12×17)/(12×12)

By cancelling the like terms.

= 17/12

How to Divide Decimals

To understand how to divide decimal numbers, we have to follow the below-given steps;

• Step 1: Convert the decimals into equivalent fractions.
• Step 2: Cancel the like terms from numerator and denominator.
• Step 3: Write the final answer in fraction or decimal.

Let us understand the above steps with the help of an example.

Example: Divide the decimals 0.14 and 0.07.

Solution: First we have to write the decimals into fractions.

0.14 = 14/100

0.07 = 7/100

Now divide both the fractions.

(14/100)÷(7/100)

= 14÷7

= 2

How to Divide Fractions

To divide the fractions, we need to simplify the fractions first and then divide them. Another method is to reverse the divisor and multiply with the dividend, as shown in the below example.

Example: Divide 15/8 by 5/2.

Solution: Given 15/8 and 5/2 are the two fractions.

Now,

(15/8)÷(5/2) = (15/8) × (2/5)

= (15 × 2)/(8 × 5)

= ¾

= 0.75

How to Divide Polynomials

Polynomials are expressions which consist of unknown variables. Thus, we need to follow the steps to perform division on polynomials.

• First, we have to write the polynomials into division form, i.e.numerator and denominator
• Then cancel the like or common terms.
• Now, perform the division like fractions.

Example: Divide x²y³ by xy³.

Solution: x²y³/xy³

In both numerator and denominator, xy³ is the common term. So cancelling the like terms we get;

x²y³/xy³ = x

How to Divide Numbers with Decimals

While dividing numbers with decimals, we can observe the decimal point in the divisor. As we know, there should not be decimals in the divisor. Hence, we need to remove the divisor’s decimal point by adding as many zeros to the dividend as there are digits after the decimal point.

Example: Divide 5 by 2.5.

Solution:

5/2.5 = 50/25 = 2/1 = 2

In this way, we can divide whole numbers by decimals.