Fractions are divided into three categories in mathematics: proper fractions, improper fractions, and mixed fractions. A fraction has a numerator and denominator. If the numerator is less than the denominator, the fraction is called a Proper Fraction. A Proper Fraction value is always less than one.

Fraction is categorised based on the numerical value of the numerator and the denominator. For example, 1/6, 1/8, 18/25, etc., are categorised as proper fractions. This article will learn more about proper fraction definitions, types, and examples.

Proper Fraction Definition

The proper fraction is the fraction where the upper part (numerator) is lesser than the lower part (denominator).

1. Numerator- The numerator is the number on the upper part of the fraction, and it presents the number of the parts we are studying.
2. Denominator- The number on the lower part of the fraction presents equal parts, divided into the whole.

Proper Fraction Examples

3/7 is the fraction, where ‘3’ is the numerator, and ‘7’ is the denominator.

Few more examples of Proper Fractions:

• 1/8
• 3/11
• 5/9

In the above examples, the upper part is the numerator, which is smaller than the lower part denominator.

So, it is a way to divide or cut any object into smaller parts. For example, if you divide a pr of chocolate into two equal parts, it would be known as two halves.

It can signify it mathematically as

12+12=1

This interpretation is called a Fraction. We can divide the chocolate bar into more pieces too.

Addition of Proper Fractions

If the denominators of two proper fractions are the same, it is easier to add the fractions. We need to add the numerators of the fractions as the denominators are the same.
For eg: 1/8 + 3/8 can be easily added by adding the numerators.
The total of 1/8 + 3/8 equals 4/8.

But if the denominators of the fractions are different, then we use the LCM (Least Common Multiple) of the denominators. We rewrite the fractions as equivalent fractions using the LCM as the common denominator.

For example, to add 1/3 + 3/5, we take the LCM of the denominators. The LCM of 3 and 5 is 15. Then, we will multiply both the fractions with such a number (in this case, 5 and 3 respectively) so that the denominators become equal. This results in (5 + 15)/15 = 20/15.

Substraction of Proper Fractions

Subtracting proper fractions is comparable to adding them together. If we need to find the difference between two similar fractions, we subtract the numerators while keeping the same denominator.
For example, The difference between 5/9 and 3/9, for example, is 2/9.

But to subtract unlike fractions, we use the LCM (Least Common Multiple) of the denominators to rewrite the fractions as equivalent fractions with the LCM as the common denominator. We subtract the numerators and write the result on the common denominator when all the denominators are the same.

For example, to subtract 7/9 from 2/4, we use the LCM of the denominators. 9 and 4 have an LCM of 36. Now we multiply both fractions by the same number (in this case, 4 and 9), bringing the denominators to the same value. As a result, (28 – 18)/36 = 10/36 is obtained.

Types of Fraction

There are three (3) types of fractions–

1. Proper Fraction/ Common Fraction- Numerator is less than a denominator.
2. Improper Fraction- Numerator is more or equal to a denominator.
3. Mixed Fraction- A combination of Proper Fractions and Whole Number.

Difference between Proper Fraction and Improper Fraction

Let us look at some of the differences between proper fractions and improper fractions in the table below:

Proper Fraction	Improper Fraction
Proper fractions are those in which the numerator is less than the denominator.	An improper fraction is one in which the numerator is greater than or equal to the denominator.
A proper fraction value is always less than 1.	An improper fraction value is either equal to or greater than 1.
Examples: 2/3, 6/7, 1/9	Examples: 3/2, 4/3, 5/5

Solved Examples

Solve the problems on proper fraction mentioned below:

Example 1- Is 1/3 a proper fraction?

Ans- Yes,⅓ is a proper fraction because ‘1’ is the numerator in this fraction, which is less than the denominator ‘3’.

Example 2- Is 7/5 a proper fraction?

Sol- No, 7/5 is not a proper fraction because ‘7’ is the numerator, which is more than the denominator ‘5’. This fraction is an improper fraction.

Example 3- Is 2/9 a proper fraction?

Ans- Yes, 2/9 is a proper fraction because ‘2’ is the numerator in this fraction, which is less than the denominator ‘9’.

FAQs

Check the Frequently Asked Questions related to the articles below:

Ques 1- What are examples of proper fraction? Ans- A proper fraction has a numerator less than the denominator. For example, 1/3, 3/7, 5/9, etc., are proper fractions.

Ques 2- Can a proper fraction be negative? Ans- Yes, the proper fraction can be negative or positive.

Ques 3- Is 3/4 a proper fraction? Ans- Yes, ¾ is a proper fraction because ‘3’ is a numerator, which is less than a denominator ‘4’.

We conclude that if the numerator is less than the denominator, it would only be a proper fraction. Otherwise, it will be considered in another type of fraction.