Fractions: Definition, Examples, Types, How to Simplify

A fraction is a part of a whole and it is represented in terms of the ratio of two numbers. In this article, we will learn about fractions with definition, examples, types, properties along with how to add, subtract, multiply and divide fractions.

Definition of a Fraction

A part of a whole is called a fraction that is is expressed as a ratio of two numbers. More specifically, a fraction is always of the form


where p, q are integers and q ≠ 0. The number p is called the numerator and the number q is called the denominator of the fraction p/q.

Types of Fractions

Depending upon which is bigger between the numerator and the denominator of a fraction, there are different types of fractions. These types are listed below.

How to Simplify Fractions

A fraction p/q can be simplified to its lowest terms by the following step-by-step method. First compute the gcd(p, q), call it d. The fraction p/q in its simplest form will be equal to $\dfrac{p \div d}{q \div d}$.

For more examples, click on below fractions to get their simplified reduced form.


Comparing Fractions

⅓ and ¾⅔ and ¾½ and ⅓
½ and ⅔

Mixed Number to Improper Fraction

We will learn to convert a mixed number to an improper fraction on this page “How to Write a Mixed Number as an Improper Fraction“.

The mixed number $a \dfrac{b}{c}$ as an improper fraction is given by $\dfrac{ac+b}{c}$. For example, $1 \dfrac{1}{2}$ converted to an improper fraction is equal to $\dfrac{1 \cdot 2 + 1}{2}=\dfrac{3}{2}$.

Improper Fraction to Mixed Number

To convert an improper fraction p/q (where p>q) to a mixed number, we need to divide the numerator p by the denominator q, and find the quotient and the remainder.

Let p = aq + b where 0≤ b < q. Then the improper fraction p/q when converted to a mixed number is equal to $a \dfrac{b}{q}$.


Q1: What is simplest form of a fraction?

Answer: A fraction in simplest form is its equivalent fraction which cannot be reduced further. More specifically, the simplest form of a fraction is defined to be its equivalent fraction whose numerator and denominator are relatively prime numbers, that is, they will not have any common factor other than 1. For example, the simplest form of the fraction 4/6 is equal to 2/3.