In this chapter, we will try to understand the basic concepts of fractions with examples.

After reading the chapter, you will be able to identify the fraction number and can understand its significance and application in real life.

## What are fractions ?

In mathematics, **a fraction is use to represent the part / portion of whole number or objects.**

In other words, a fractions signifies the** part of a selected object**. The selected object can be a whole number or a real life entity.

### Components of fraction number

The fraction is** made of two numbers**.

The number present in the top is called **numerator.**

The number in the bottom is called **denominator.**

Both the numerator and denominator are separated by division symbol ” / “.

The numbers like \mathtt{\frac{2}{3} ,\ \frac{3}{5} ,\frac{11}{4} \ \&\ \frac{8}{13}} are examples of fraction number.

### Significance of fraction number

To understand the significance and meaning of fraction number, we have to select an imaginary object.

Let us consider below rectangle for reference.

#### Analyzing fraction 1/2 with respect to rectangle

Here** fraction 1/2** signifies the **half portion of above rectangle figure**.

We can understand this using given numerator and denominator.

Here, **Denominator = 2.**

It tells that the object is divided into two parts.

Also,** Numerator = 1**

It tells that out of two parts, we are selecting one part.

The fraction 1/2 is shown by below image, painted in red color.

Conclusion: Fraction 1/2 is basically half of any given object.

#### Analyzing fraction 3/4 with respect to rectangle

Here, **denominator = 4**

It means that the rectangle is divided into 4 equal parts.

And,** numerator = 3**

It means that out of four equal parts, three parts are selected.

The representation of fraction 3/4 is shown by below image by red color.

**Note**: Instead of rectangle, there can be different object or number. You can use the fraction to signify the part of given object.

### Case study related to fraction number

John ordered a cheese pizza for dinner. He **divides the pizza into 5 equal parts**. He **ate 4 pieces of pizza **and **kept remaining one piece in refrigerator for next day**. Represent part of pizza eaten during dinner using fraction.**Solution**

The pizza is divided into five equal parts. It means the **denominator of fraction is 5**.

At dinner, John ate four of the pieces. I means the **numerator is 4.**

So the **fraction becomes 4 / 5.**

Given below is the representation of fraction 4/5 with red color.

Hence, John ate 4/5 of the Pizza.

### Value of Fraction

The exact value of any given fraction can be found by** dividing numerator by denominator.**

The value of fraction can be integer or decimal number, depending on the type of fraction.

**For example;**

Find the value of fraction 3 / 5**Solution**

Simply divide numerator by denominator, we get;

\mathtt{\frac{3}{5} \Longrightarrow \ 0.6}

Hence, 0.6 is the exact value of given fraction.

**Example 02**

Find the value of fraction 84 / 7

**Solution**

Divide numerator by denominator.

\mathtt{\frac{84}{7} \Longrightarrow \ 12}

Hence, **12 is the value of given fraction.**

You can find the value of any given fraction using this technique.

### Fraction as a Ratio

The **fraction can be represented as ratio**, that is, fractions can be used to compare one group of objects with another.

Some examples of fractions as a ratio are:

In the above examples, the ratio of cars to scooters can be expressed as 2 : 3

This ratio can also be expressed in the form of fraction 2/3, it all mean the same thing.

### Can integers be written in form of fractions ?

Yes!!

All the integers like 2, 19, -31 have one in the denominator.

If we explicitly show the denominator, these numbers can be represented in the form of fractions.

For example;

\mathtt{23\Longrightarrow \frac{23}{1}}\\\ \\ \mathtt{-16\Longrightarrow \frac{-16}{1}}\\\ \\ \mathtt{500\ \Longrightarrow \frac{500}{1}}