In this chapter we will extensively look at different type of fractions in mathematics with solved examples.

After reading the chapter you will be able to identify the fraction type just by looking at the number.

## Classification of Fractions

There are** 8 types of fractions** in number system;

(a) **Like fraction**

(b) **Unlike fraction**

(c) **Proper fraction**

(d) **Improper fraction**

(e) **Mixed fraction**

(f) **Equivalent fraction**

(g) **Decimal fraction**

(h) **Vulgar fraction**

We will discuss each of the fraction in detail with examples.

Given below is the image representation of different fraction types for your reference.

### Like Fraction

Two or more **fractions having the same denominator** are called **Like fractions**.

Note that in Like fractions, the **numerator value can be different **but the denominator digit of given fractions must be same.

**Note**: Identifying like fractions are important as doing math operations like addition / subtraction is easier on these numbers.

#### Examples of Like fraction

(a) Consider the below fraction numbers.

\mathtt{\Longrightarrow \ \frac{1}{7} ,\ \frac{3}{7} ,\ \frac{15}{7} \ \&\ \frac{32}{7}}

Since all the numbers have same denominators, they are like fractions.

(b) Examine below set of numbers.

\mathtt{\Longrightarrow \ \frac{1}{5} ,\ \frac{2}{10} ,\ \frac{3}{15} \ \&\ \frac{5}{25}}

Here all numbers have different denominators, hence **they are not like fractions**.

Note that if you simplify the numbers, you will get the same fraction 1/5. This means that these fractions have same values. These types of fractions are called equivalent fractions.

### Unlike fractions

If the given group of **fractions have different denominators**, then they are called** unlike fractions**.

While analyzing fractions, you **simply have to observe the denominators** and make a call if it is like or unlike fraction.

**Note: **The process of addition/subtraction of unlike fraction is different and complex than the like fractions.

#### Examples of Unlike fractions

Consider the below fractions.

\mathtt{\Longrightarrow \ \frac{6}{9} ,\ \frac{11}{7} ,\ \frac{2}{3} \ \&\ \frac{8}{9}}

Note that all the given numbers have different denominators. Hence, they are unlike fractions.

### Proper Fractions

The fraction in which the **numerator is less than the denominator** are called **proper fraction**.

The value of proper fraction after simplification is **always less than 1**

#### Examples of Proper Fraction

Consider the **Fraction 2 / 3**

Since the denominator is greater than numerator, the given fraction is a proper fraction.

Similarly, \mathtt{\ \frac{1}{5} ,\ \frac{8}{13} ,\ \frac{31}{32} \ \&\ \frac{9}{20}} are all examples of proper fraction.

### Improper Fractions

The fraction in which the **numerator is greater than the denominator** are called **improper fraction**.

The simplification of improper fraction result in the value which is** equal or greater than 1**,but not less than 1.

#### Examples of Improper fractions

Consider the **fraction 8 / 3.**

Since** numerator is greater than the denominator**, the above fraction is am improper fraction.

Similarly, fractions \mathtt{\frac{5}{2} ,\ \frac{12}{9} ,\ \frac{16}{5} \ \&\ \frac{51}{25}} are all examples of improper fractions.

**Note:**

⟹ All the whole numbers like1, 4, 78, and 124 are improper because all the numbers have 1 in their denominator.

⟹ We can convert improper fraction to mixed fraction and vice versa.

### Mixed Fractions

The fraction which is **combination of both whole number and fraction** is called a **mixed fraction**.

The value of mixed fraction is **always equal or greater than 1**.

These are basically improper fraction which are converted into mixed number for better representation.

#### Examples of Mixed fraction

Consider the mixed fraction \mathtt{2\frac{1}{3} \ }

The above number is made of whole number 2 and fraction 1/3.

Similarly, the numbers \mathtt{6\frac{2}{5} ,\ 11\frac{3}{10} ,\ 3\frac{1}{3} \ \&\ 11\frac{3}{7}} are all examples of mixed numbers.

### Equivalent Fraction

Two or more numbers are equivalent fractions if** on simplification they gives the same value**.

To identify the equivalent fractions, one should have good division skills.

**For example**, consider the fractions \mathtt{\ \frac{1}{3} ,\ \frac{4}{12} \ \&\ \frac{9}{27}} **First Fraction** ⟹ 1/3

Further simplification is not possible.

**Second Fraction** ⟹ 4 / 12

Divide numerator and denominator by 4.

\mathtt{=\ \frac{4\div 4}{12\div 4}}\\\ \\ \mathtt{=\ \frac{1}{3}}

Upon simplification, we get value 1/3.

**Third Fraction** ⟹ 9 / 27

Divide numerator and denominator by 9

\mathtt{=\ \frac{9\div 9}{27\div 9}}\\\ \\ \mathtt{=\ \frac{1}{3}}

Hence, all the fraction gives number 1/3 upon simplification.

**So all the given numbers are equivalent fractions**.

### Decimal Fractions

A fraction whose denominator is any of the number 10, 100, 1000 etc. is called a **decimal fraction**

Numbers like \mathtt{\frac{1}{10} ,\ \frac{5}{100} \ ,\frac{25}{10000} \ etc.} are all examples of decimal fractions.

### Vulgar Fraction

A fraction those denominator is a whole number other than any of the number 10, 100, 1000 etc. is called a **vulgar fraction**.

Numbers like \mathtt{\frac{1}{20} ,\ \frac{11}{35} \ ,\frac{36}{256} \&\frac{101}{4500}} are examples of Vulgar fractions.