Fractions are used to describe a part of a whole. On this page, we will learn all about fractions and related results like how to simplify fractions.
Definition
Definition of a Fraction: A portion of a whole is called a fraction.
Mathematically, a fraction is always represented as p/q where p, q are integers and q is non-zero.
p:= Numerator
q:= Denominator.
Depending upon which is bigger between p and q we have different types of fractions which we will learn below.
Types of Fractions
Depending upon which one is bigger among the numerator and the denominator of a fraction, we have different types of fractions. We list them in the table below.
| Types | Description |
|---|---|
| Like and Unlike Fractions | Two fractions are called like (or similar fractions) if they have the same denominator. Otherwise, they are unlike fractions (dissimilar fractions). For example, 3/4 and 1/4 are like fractions whereas 3/4 and 1/2 are unlike fractions. |
| Proper and Improper Fractions | A fraction is called a 1. proper fraction if numerator < denominator. 2. improper fraction if numerator > denominator. For example, 1/2 is a proper fraction whereas 3/2 is an improper fraction. |
| Mixed Fractions | A mixed fraction is a combination of a whole number and a proper fraction. For example, 1½ is a combination of the whole number 1 and the proper fraction ½, so it is a mixed fraction. |
| Equivalent Fractions | Two fractions are said to be equivalent if they represent the same value. For example, 1/2 and 2/4 both have the value 0.5, so they are equivalent fractions. |
| Unit Fractions | A fraction is called the unit fraction if it has the numerator 1. |
How to Simplify Fractions
Lets learn step-by-step process how to simplify a fraction to its simples form. To simplify the fraction $\dfrac{p}{q}$ in its simplest form, we will below steps:
Step 1: First, calculate the g.c.d (greatest common divisor) of p and q.
Step 2: Lets write d = g.c.d (p,q).
Step 3: Divide both p and q by their gcd d.
Step 4: The resulting fraction $\dfrac{p \div d}{q \div d}$ will be the simplest form of the given fraction $\dfrac{p}{q}$.
Examples
The fraction 6/8 simplified is equal to 3/4.