# Denominator

 1 Introduction to Denominator 2 Definition of Denominator 3 Denominator Examples 4 Denominator Calculator 5 Important Notes on Denominator 6 What is a Common Denominator? 7 Tips and Tricks 8 Solved Examples on Denominator 9 Practice Questions on Denominator 10 Maths Olympiad Sample Papers 11 Frequently Asked Questions (FAQs)

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## Introduction to Denominator

Denominator in Math can be defined as the bottom number in a fraction that shows the number of equal parts an item is divided into.

It is the divisor of a fraction.

The denominator lies below the line in a fraction.

Now the question arises, what is a Fraction?

Fractions represent a part of a whole or, more generally, any number of equal parts.

Mathematically, it is shown by the division of two numbers.

For example, $$\dfrac{1}{4}$$ is one part out of the four equal parts created from that one whole thing.

Here, 1 is the numerator and 4 is the denominator.

## Definition of Denominator

The definition of a denominator is the number below the horizontal line of the fraction that acts as the divisor of the numerator.

In other words, we can say that the denominator shows the total amount of parts that make up a whole.

It is not necessary that only numbers are expressed in the numerator and denominator form.

Variables are also expressed in the same form such as $$\dfrac{x}{y}$$, $$\dfrac{a}{b}$$, $$\dfrac{p}{q}$$, etc., where y, b and q are the denominators respectively as shown in the image below.

The fraction is shown using the symbol "/"

This symbol is known as the "fractional bar."

The number on the top is known as the  "numerator", and the number below is known as the "denominator".

## Denominator Examples

Some examples for denominators are:

#### Denominator

$$\dfrac{1}{3}$$

$$3$$

$$\dfrac{11}{20}$$

$$20$$

$$\dfrac{6}{x-2y}$$

$$x-2y$$

$$\dfrac{3x}{8y}$$

$$8y$$

$$\dfrac{i*j}{5}$$

$$5$$

$$\dfrac{p+3}{q+9}$$

$$q+9$$

### Denominator and Numerator

The denominator indicates how many of those parts make up a unit or a whole.

The numerator indicates the number of parts that we have selected out of the total number of equal parts.

Let us take an example to understand this better.

In the fraction $$\dfrac{3}{4}$$, the numerator 3 tells us that the fraction represents 3 equal parts, and the denominator 4 tells us that 4 parts make up a whole.

In the above image, we can observe that 3 parts are selected out of 5 equal parts that were created in a circle.

This can be represented as $$\dfrac{3}{5}$$

## Denominator Calculator

We can visualize the denominator using the following illustration.

Important Notes
1. A denominator must be an integer.
2. A denominator can never be zero because zero parts can never make up a whole.
3. The term denominator is widely used in the concepts of rational numbers, ratios and proportions, and division concepts.

## What is a Common Denominator?

When the denominators of two or more fractions are the same, they are known as common denominators.

For Example:

To find the sum or difference of two or more fractional numbers, we must replace them by other fractional numbers having the same denominator.

It is usually most convenient to consider the  Least Common Multiple (LCM) for the denominator.

Let us see some examples here:

• $$\dfrac{2}{2}$$ +$$\dfrac{3}{2}$$ =$$\dfrac{2+3}{2}$$ = $$\dfrac{5}{2}$$
• $$\dfrac{6}{7}$$ –$$\dfrac{2}{7}$$  =$$\dfrac{6-2}{7}$$ =$$\dfrac{4}{7}$$

Look at the simulation below to understand common denominator.

Tips and Tricks
1. The easiest way to find a common denominator for a pair of fractions is to multiply the numerator and denominator of each fraction by the denominator of the other.

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## Solved Examples on Denominator

 Example 1

Rita ordered a pizza at a restaurant.

Each piece of pizza represents a part of a whole.

The pizza is divided into 6 equal slices.

If she ate one slice, then what is the denominator of the fraction representing the amount she ate?

Solution:

Total number of slices of pizza = 6

Total number of the piece she ate = 1

The fraction of pizza she ate $$\dfrac{1}{6}$$

Here, 6 is the number that denotes the total number of slices of pizza.

 $$\therefore \text{The denominator is}$$ 6
 Example 2

A grandmother bought an apple for her grandchild.

If she cuts one piece of an apple.

What is the denominator of the fraction of the remaining apple?

Solution:

Total number of pieces of apple in a whole = 4

If 1 piece of an apple is cut then,

Total number of pieces of an apple left = 3

The fraction of remaining apple  =  $$\dfrac{3}{4}$$

So, the denominator is 4 the number that denotes the total number of pieces of apple.

 $$\therefore \text{The denominator is}$$ 4
 Example 3

There are two boys and three girls playing together.

Determine the fraction that represents the group of children.

What is the denominator of the fraction?

### Solution:

Total number of kids = 5

The fraction of boys who are playing = $$\dfrac{2}{5}$$

The fraction of girls who are playing = $$\dfrac{3}{5}$$

Here, 5 is the number that denotes the total number of kids.

 $$\therefore \text{The denominator is}$$ 5
 Example 4

In a class, the teacher asks the students to write their first and last names and count the number of letters in each.

She also asks them to count the number of vowels in each name, then shows them how to write a fraction that represents the vowels to total letters.

What is the denominator of the fraction representing the names?

Solution:

Let us assume that a student's name is HARRY JAMES.

Total number of letters in the first and last name = 10

The total number of vowels in the name = 3 ( Vowels are A, A, E)

The fraction of vowels to total letters =  $$\dfrac{3}{10}$$

 $$\therefore \text{The denominator is}$$ 10
 Example 5

On a school trip to the museum, a teacher shows the students a penny, nickel, dime, quarter, and other such coins.

She shows a quarter dollar coin and explains that each coin represents a specific part of 100 cents, which is equal to one dollar.

What is the value of the denominator for the quarter of a dollar?

Solution:

The fraction to indicate a quarter is one-fourth of a dollar =$$\dfrac{1}{4}$$

Thus, the denominator of the fraction = 4

 $$\therefore \text{The denominator is}$$ 4

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## Practice Questions

Here are a few activities for you to practice.

IMO (International Maths Olympiad) is a competitive exam in Mathematics conducted annually for school students. It encourages children to develop their math solving skills from a competition perspective.

## 1. What is a denominator?

Denominator in Math indicates the number of equal parts in which the whole thing has to be divided.

## 2. What is an example of a denominator?

The fraction $$\dfrac{4}{7}$$ has a top number 4 and a bottom number 7

Therefore,the denominator is 7

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