Difference between Proper and Improper Fractions (original) (raw)
Last Updated : 23 Jul, 2025
**Proper and improper fractions are the two main typesof fractions based on the value of numerator and denominator. The key difference between them lies in the relationship between the numerator and the denominator.
Proper Fractions
**Proper fractionsare fractions where the **numerator is less than the denominator. This means that the **value of a proper fraction is always less than 1. Proper fractions represent parts of a whole, where the whole is divided into equal parts, and we are considering fewer parts than the total.
Examples of Proper Fractions
For example, the fraction 3/4 is a proper fraction
As the numerator (3) is less than the denominator (4). Other examples of proper fractions include 1/2, 5/8, and 7/10.
Improper fractions
**Improper fractions are fractions where the numerator is greater than or equal to the denominator. This means that the value of an improper fraction is always equal to or greater than 1. Improper fractions represent a quantity that is equal to or exceeds the whole.
Examples of Improper Fractions
For example, the fraction 7/4 is an improper fraction
As, the numerator (7) is greater than the denominator (4). Other examples of improper fractions include 9/8, 5/3, and 12/10.
Read more about **Types of Fractions.
Difference between Proper and Improper Fractions
The following table the key differences between proper and improper fractions are:
| Proper Fraction | Improper Fraction |
|---|---|
| A proper fraction is a type of fraction in which **numerator is less than its denominator. | An Improper fraction is a type of fraction in which numerator is greater than or equal to its denominator. |
| A proper fraction **cannot be represented as mixed fraction. | An Improper fraction **can be represented as mixed fraction. |
| The value of proper fraction is always less than 1 as its denominator is greater than its numerator. | The value of Improper fraction is always greater than or equal to 1 as its numerator is greater than or equal to its denominator |
| A proper fraction cannot be converted to an improper fraction. | An Improper fraction cannot be convert to a proper fraction. |
| A proper fraction **represents a smaller part of whole. | An Improper fraction **represents whole numbers and parts |
| Proper fractions are easier to understand for beginners. | An Improper fractions may be confusing to understand for beginners. |
| Proper fraction are less complex. | Improper fraction are more complex. |
| Example- 2/3 , 5/6, 4/6 , 7/9 etc. | Example- 4/3 , 5/2 , 3/3, 9/4 etc. |
**Read More,
Proper and Improper Fraction Solved Example Questions
**Example 1: 1 is which type of fraction?
**Solution:
1 is a type of Improper fraction. 1 can be represented as 1/1 which is a type of improper fraction.
An Improper fraction is a type of fraction in which numerator is greater than or equal to its denominator.
**Example 2: Change the improper fraction 7/2 into mixed fraction.
**Solution:
For changing 7/2 into mixed fraction, first perform division operation then represent it as :
Quotient(Remainder/Divisor)Where, quotient represent whole part (remainder/divisor) represent fractional part.
Now, 7 ÷ 2 = 3 as quotient and 1 as remainder.
7/2 in mixed fraction can be represent as 3(1/2).
**Example 3: Add: 3/4 and 4/3
**Solution:
3/4 is a type of proper fraction and 4/3 is a type of improper fraction.
We have to add both as denominator of given two fractions are different, we have to take LCM of denominators.
3/4 + 4/3,LCM of 3 and 4 is 12
= (9 + 16) / 12
= 25/ 12The addition of 3/4 and 4/3 is 25/12.