# Proper Fractions

## Definition of Proper Fractions:

When the numerator is less than the denominator, it is called a Proper function.

• If you want to describe a part of a whole, it is called a Fraction.
• Denominator – The number on the bottom of the fraction and it shows the number of equal parts the whole is divided into.
• Numerator – The numerator is the number on the top of the fraction and it shows the number of the parts we are considering.
• Example, in the fraction 5/6 it shows “5 of 6 equal parts.” 5 is the numerator, and 6 is the denominator.
• Example of a Proper Fraction:
$\frac{2}{6}$ where 2 is a numerator less than 6 which is the denominator.

• Few more Proper Function examples are :
$\frac{1}{9} , \frac{2}{7}, \frac{4}{9}$.

Note: In all the above examples, the number on the top (numerator) is smaller than the number at the bottom(denominator).

So, Basically, It is a way to divide or cut any object in smaller parts. Example If you divide a bar of chocolate into two equal parts, it would be called as two halves.

It can be denoted mathematically as

$\frac{1}{2} +\frac{1}{2}= 1$

This expression is called a Fraction. You may divide the chocolate bar into more pieces too.

## Types of fractions:

There are 3 types of fractions and an overview of them is given below:

 Types of Fractions Proper Fractions / Vulgar Fractions/Common Fractions Improper Fractions Mixed Fractions Property In this, the numerator is smaller than the Denominator. In this, the numerator is larger or equal than Denominator. It’s a combination of a whole number and a proper fraction. Example $\frac{2}{3}$ $\frac{2}{1} or \frac{5}{5}$ $5\frac{1}{2}$

Point to knowIf the numerator and denominator of a fraction are multiplied by the same number, its value doesn’t change.

Let’s Solve a few problems on Propper fractions:

 Question Answer Is $\frac{1}{2}$ a proper fraction? Yes, It is a proper fraction because the numerator 1 in this fraction is less than the denominator 2. Is $\frac{4}{2}$ a proper fraction? No, It is not a proper fraction because the numerator 4 in this fraction is more than the denominator 2. It is an improper fraction. Is $\frac{9}{8}$ a proper fraction? No, It is not a proper fraction because the numerator 9 in this fraction is more than the denominator 8. It is an improper fraction. Is $\frac{6}{5}$ a proper fraction? No, It is not a proper fraction because the numerator 6 in this fraction is more than the denominator 5. It is an improper fraction. Is $\frac{5}{9}$ a proper fraction? Yes, It is a proper fraction because the numerator 5 in this fraction is less than the denominator 9.