# Denominator

## Meaning of Denominator

The divisor of a fraction is called the denominator.

A Fraction is one part when a whole is divided into equal parts. Mathematically its is shown by the division of two numbers. Let’s go through some examples and you recall all the divisibility rules to make sure you understand the formulas easily.

For example:

1/4 is one part out of the four equal parts created from that one whole thing.

A fraction consists of two numbers. Symbolically it is represented by two numbers separated by a horizontal line. The number above the line is numerator, and the number below the line is the denominator.

For Example:

1 Numerator

4⟶ Denominator

Numerator and Denominator

The denominator indicates the number of equal parts in which the whole thing has to be divided.

The numerator indicates the number of divisions selected out of the total number of equal parts.

### What are Numerator and Denominator?

This would be better explained with the help of an Example.

3/4 is a fraction in which the denominator 4 represents that 4 equal divisions have to be made.

3 parts selected out of 4 equal parts created out from 1 circle can be represented as 3/4.

Diagrammatic representation of ¾ is as follows:

The diagram clearly shows three equal parts taken out when the whole circle is divided into four equal parts.

Least Common Denominator(LCD)

The least common denominator of two or more non-zero denominators is the smallest whole number that is divisible by each of the denominators.

### Methods to find LCD

1.Multiply both the denominators (when the denominators have no common multiple)

For Example:

There are two fractions as follows:-

⅓ and ⅕

3*5 = 15

Multiply both the fractions with the product (15) with the top as well as bottom:

⅓ * 15/15 = 5/15

⅕ * 15/15 = 3/15

Thus, we have a common denominator in both our fractions.

2.List the multiples of both denominators:

We have the two fractions: ⅓ and ⅙

3 = 3,6,9,12,18,21,24,27,30.

6=6,12,18,24,30,36,42,48,60.

The smallest common multiple that can be seen is 6.

So that is the LCD.

Rationalize the Denominator

The denominator of a fraction needs to be rationalized when it is an irrational number so that further calculations can be made easily on the fraction.

Irrational denominator includes the root numbers.

How to Rationalize The Denominator

Example 1. Monomial Denominator

$\frac{1}{\sqrt{3}}$ has an irrational denominator since it is a cube root of 3.

To remove the radical multiply the numerator and denominator by the $\sqrt{3}$, we have

$\frac{1}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}}{3}$

By multiplying the top and bottom with the, we have created the smallest possible perfect square in the denominator and removed the radical as per our requirement.

Example 2. Binomial Denominator:

When there are two terms in the denominator that make it irrational.

$\frac{3}{5 + \sqrt{3}}$

In this case, multiply the numerator and denominator with the conjugate of the denominator.

The conjugate means the same denominator but with the opposite sign.

The conjugate of $5 + \sqrt{3}$ is $5 – \sqrt{3}$, where the “+ sign “ is replaced with “- sign”.

To rationalize:

$\frac{3}{5 + \sqrt{3}} \times \frac{5 – \sqrt{3}}{5 – \sqrt{3}}$

$\frac{15 – 3\sqrt {3}}{5^{2} – (\sqrt{3})^{2}} = \frac{15 – 3\sqrt {3}}{28}$<

This was all about denominator and how to rationalize the fraction. Learn more about ratio and proportion, percentage, fractions etc. by visiting our site BYJU’S.