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A common fraction is written in the form , where a and b both are integers and b ≠ 0.  Here, a is numerator and b is denominator. Common fractions are also known as vulgar or simple fractions.    

To understand the concept of fractions better, look at the following video.

These numbers like and etc. are known as fractions. Both these fractions have 1 as the numerator. Their denominators are 2 and 4 respectively. Fractions are used to represent a part of a whole.

The fractions can be categorized into 3 types. They are

  1. Proper Fraction

  2. Improper Fraction

  3. Mixed Fraction

To understand each type of fraction, look at the following video.

Important points to note

  • If both the numerator and denominator of a fraction are equal, then the value of the fraction is 1. For example, .

  • We know that an improper fraction is always greater than 1 and a proper fraction is always less than 1. Therefore, we can say that any improper fraction is always greater than any proper fraction. For example, the improper fraction is greater than the proper fraction.

A mixed fraction can be converted into an improper fraction and vice-versa. Let us start with the conversion of improper fraction into mixed fraction.

It can be easily understood with the help of an example. Let us convert the improper fractioninto mixed fraction. For this, we have to follow these steps.

Step 1: Divide the numerator by the denominator of the improper fraction to obtain the quotient and remainder.

The numerator and denominator of the fraction are 34 and 15 respectively. Now, the division process can be done as

In the above division process, the quotient = 2 and the remainder = 4.

Step 2: The improper fraction can then be expressed as a mixed fraction by writing it in the form of


For the improper fraction, we have the denominator as 15, the remainder as 4, and the quotient as 2.

Therefore, we can write the improper fraction as a mixed fraction as .

Let us now try and convert a mixed frac…

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