Types of Fractions

In Maths, there are three major types of fractions. They are proper fractions, improper fractions and mixed fractions. Fractions are those terms which have numerator and denominator. Based on these two terms we define its types.

Fractions are the terms used to determine the parts of a whole object. For example, a pizza is divided into four pieces, so each piece of it is represented as 1/4th of the pizza. Here 1 is the numerator and 4 is the denominator.

Based on numerator and denominator, apart from these three major types of fractions, there are three more types of fractions namely like & unlike fractions and equivalent fractions. Hence, there are in total six types of fractions such as:

1. Proper fraction
2. Improper fraction
3. Mixed fraction
4. Like fractions
5. Unlike fractions
6. Equivalent fractions

Note: The first three fractions are defined for a single fraction but the other three fractions, determine the comparison between two or more fractions.

In real-life scenarios all the measured quantities cannot be an absolute whole number, we may have to deal with parts and portions of whole things, and this is where the concept of fraction comes into the picture.

Different Types of Fraction

A fraction is considered to be the ratio of two numbers. The upper number is called Numerator, and the lower part is known as the Denominator. When a whole of something is divided into the number of parts, then each part is referred to as a fraction. A typical example of how the concept of fraction works is illustrated in the below figure.

Consider another example, a WHOLE pizza is divided into EIGHT PIECES that form the fraction, where one piece of the whole pizza is represented as 1/8, where 1 is the numerator and 8 is the denominator.

Proper Fraction

A fraction where the numerator is less than the denominator, then it is known as a proper fraction.

i.e., Numerator < Denominator

For example,

Note:

• The value of proper fraction after further simplification is always less than 1.

Improper Fraction

A fraction where the numerator is greater than the denominator, then it is known as an improper fraction.

i.e., Numerator > Denominator

For example,

Note:

• All the natural numbers can be represented in the form of fractions, where the denominator is always equal to 1.
• The simplification of improper fraction results in the value which is equal or greater than 1, but not less than 1.

Mixed Fraction

A mixed fraction is the combination of a natural number and fraction. It is basically an improper fraction.

Note:

• Mixed fractions can always be converted into a fraction.
• An improper fraction can be converted into a mixed fraction.
• A mixed fraction is always greater than 1.

Like Fractions

The fractions which have the same denominators are called like fractions.

For example 1/2, 3/2, 5/2, 7/2 are like fractions.

The simplification of such fractions is easy, as all the denominators here are the same. Suppose we need to add all the above like fractions, then;

1/2 + 3/2 + 5/2 + 7/2 = (1+3+5+7)/2 = 16/2 = 8

Unlike Fractions

The fractions which have unequal denominators or different denominators are called, unlike fractions.

For example 1/2, 1/3, 1/4, 1/5, are unlike fractions.

Simplication for such fractions is a little lengthy method since we need to factorise the denominator first and then simplify them (in case of addition and subtraction).

• Suppose, we have to add 1/2 and 1/3. Then first we will find the LCM of 2 and 3 which is equal to 6.
• Now we need to multiply 1/2 by 3 and 1/3 by 2, both in numerator and denominator.
• The fractions become 3/6 and 2/6.
• Now if we add 3/6 and 2/6, we get;
• 3/6+2/6 = 5/6

Equivalent Fractions

When two or more fractions have the same result after simplification for which they represent the same portion of the whole, then such fractions are equal to each other and are called equivalent fractions.

For example, 1/2 and 2/4 are equivalent.

1/3 and 3/9 are equivalent.

Examples

Let us see some examples here based on the fraction’s types.

• Examples of Proper Fractions:  2/3, 2/4, 2/5, 1/2. 4/7, 7/9, etc. (Numerator < Denominator)
• Examples of Improper Fractions: 3/2, 4/2, 5/2, 7/4, 9/7, 8/5, etc. (Numerator > Denominator)
• Examples of Mixed Fractions:  etc. (Combination of whole numbers, proper and improper fractions)

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