Proper Fractions

Before getting into the proper fractions, let us know what is a fraction? When the fraction is called the proper fraction? Fraction is defined as the part of the whole thing. Mathematically, a fraction is defined as the ratio of two numbers. The general form of a fraction is a/b such that b ≠ 0 and a, b are whole numbers; a is the numerator and b is the denominator. Fractions are categorized into various types based on the numerical value of numerator and denominator. Also, a fraction is called a proper fraction if the denominator is greater than the numerator and if the numerator is greater than the denominator, then it is an improper fraction.

Proper fractions

The figure above shows the fractions which are also proper fractions since the denominator is greater than the numerator.

Definition of Proper Fractions

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

  • 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, where 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:

\(\frac{3}{5}\) where 3 is a numerator less than 5, which is the denominator.

Proper fraction example

Few more Proper Fraction 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 / 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 the 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 know If the numerator and denominator of a fraction are multiplied by the same number, its value doesn’t change.

Proper Fractions Examples

Let’s Solve a few problems on Proper 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.

To learn more about fractions and operations on fractions, visit www.byjus.com. Also, download BYJU’S – The Learning App for personalised videos

Test your Knowledge on Proper Fractions

1 Comment

  1. Kunapareddy Manasri

    Super explanation

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