Difference between Proper and Improper Fractions

Proper and improper fractions are the two main types of 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 fractions are 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:

Read More,

• Comparing Fractions 
• Multiplication of Fractions 
• Division of Fractions

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/ 12

The addition of 3/4 and 4/3 is 25/12.