Types of fractions – Definition and examples

In this article, we will understand different types of fractions with the help of some examples and learn how to identify them.

Types of fractions

Fractions are classified into three types based on the properties of numerator and denominator, these are:

1. Proper fraction
2. Improper fractions
3. Mixed fraction

Group of fractions are classified into 2 types: 

1. Like fractions
2. Unlike fractions 

Further, there are two more types of fractions:

1. Equivalent fractions
2. Unit fractions

Now let us understand each type of fraction with examples.

Proper fractions

A fraction is a proper fraction if it has the following properties:

1. Numerator < Denominator.
2. Value of fraction is less than 1.

Examples:

a \frac{1}{7}

b \frac{2}{5}

c \frac{2}{35}

d \frac{3}{8}

Improper fractions

A fraction is an improper fraction if it has the following properties:

1. Numerator > Denominator.
2. Value of fraction is more than 1.

Examples:

a \frac{8}{7}

b \frac{11}{5}

c \frac{36}{35}

d \frac{99}{8}

Mixed fraction

A fraction is a mixed fraction if it has the following properties:

1. It consists of a whole number and a proper fraction.
2. Value of fraction is more than 1. 

A mixed fraction can also be written in the form of an improper fraction and vice-versa.

Examples:

a. 2 \frac{1}{7}

2 is a whole number and \frac{1}{7}is a fraction.

b. 1\frac{2}{5}

1 is a whole number and \frac{2}{5} is a fraction.

c. 3 \frac{2}{35}

3  is a whole number and \frac{2}{35} is a fraction.

Like fractions

A group of fractions are like fractions if they have the  following properties:

1. Denominators of all the fractions in the group are equal.
2. The fractions may be proper or improper.

Examples: 

a \frac{1}{7}, \frac{6}{7}, \frac{5}{7}, \frac{11}{7}, \frac{10}{7}, \frac{3}{7}

The denominator 7 is common.

b. \frac{2}{5}, \frac{3}{5}, \frac{5}{5}, \frac{12}{5}, \frac{6}{5}, \frac{1}{5}

The denominator 5 is common.

Unlike fractions

A group of fractions are unlike fractions if they have the following properties:

1. Denominators of all the fractions in the group are not equal.
2. The fractions may be proper or improper.

Examples: 

a. \frac{1}{7}, \frac{6}{8}, \frac{5}{9}, \frac{11}{7}, \frac{10}{21}, \frac{3}{7}

The denominator of all fractions is not equal.

b. \frac{2}{5}, \frac{3}{2}, \frac{5}{8}, \frac{12}{5}, \frac{6}{15}, \frac{1}{5}

The denominator of all fractions is not equal.

Equivalent fractions

All the fractions giving the same value after simplification are known as equivalent fractions.

Examples: 

a. \frac{1}{2}, \frac{3}{6}, \frac{5}{10}, \frac{12}{24}

All the fractions become \frac{1}{2} after simplification.

b. \frac{2}{3}, \frac{4}{6}, \frac{6}{9}, \frac{12}{18}

All the fractions become \frac{2}{3} after simplification.

Multiplying both the numerator and denominator with the same number gives us an equivalent fraction of the given fraction. 

Converting mixed fraction into an improper fraction

A mixed fraction is written in the form of  ” a\frac{b}{c} “

a = whole number
b = numerator
c = denominator

The improper fraction form of this mixed fraction is written as \frac{(a \times c)+b}{c}.

Converting improper fraction into a mixed fraction

An improper fraction is written in the form of \frac{p}{q}(where p>q)

p = numerator
q = denominator

We have to then divide numerator by denominator

Then the mixed fraction form of this improper fraction is written as:

 ” Quotient\frac{Remainder}{ Divisor } ” 

Solved Examples

1. Convert 1 \frac{1}{7}into an improper fraction.

1 \frac{1}{7}

• a = 1
• b = 1
• c = 7

Improper fraction form of 1 \frac{1}{7} =\frac{(a \times c)+b}{c}=\frac{(1 \times 7)+1}{7}=\frac{8}{7}

2. Convert \frac{12}{5}into a mixed fraction.

\frac{12}{5} is an improper fraction. Where:

• p = 12
• q = 5

When we divide 12 by 5, we get:

• Quotient = 2
• Remainder = 2
• Divisor = 5

Mixed fraction form of \frac{12}{5} = Quotient \frac{remainder}{divisor} = 2\frac{2}{5}

3. Find four equivalent fractions of \frac{3}{8}.

We have to multiply both the numerator and denominator with the same number to find an equivalent fraction of the given fraction.

• Multiplying 3 with numerator and denominator: 

• Multiplying 5 with numerator and denominator:

• Multiplying 2 with numerator and denominator:
  

• Multiplying 6 with numerator and denominator:

Hence \frac{9}{24}, \frac{15}{40}, \frac{6}{16}, \frac{18}{48}are four equivalent fractions of \frac{3}{8}.