Difference between Proper Fraction and Improper Fraction

The key difference between proper fraction and improper fraction in mathematics is that a proper fraction has a numerator that is smaller than its denominator, while an improper fraction has a numerator that is equal to or greater than its denominator.

Proper Fractions Vs Improper Fractions

In proper fractions, such as 1/4, 3/5, and 2/7, the numerator (the number above the fraction line) is smaller than the denominator (the number below the fraction line). These fractions represent a part of a whole or a value less than 1. For example, 1/4 represents one out of four equal parts.

In contrast, improper fractions, such as 5/4, 7/3, and 9/2, have a numerator that is equal to or greater than the denominator. These fractions represent a whole or a value equal to or greater than 1. For example, 5/4 represents five equal parts, where each part is larger than one whole unit.

Characteristic	Proper Fraction	Improper Fraction
Numerator vs. Denominator	Numerator is smaller than denominator.	Numerator is equal to or greater than denominator.
Representation	Represents a part of a whole or a value less than 1.	Represents a whole or a value equal to or greater than 1.
Value Range	The value of the fraction is between 0 and 1.	The value of the fraction is equal to or greater than 1.
Examples	1/4, 3/5, 2/7.	5/4, 7/3, 9/2.
Visual Representation
Additional Examples	2/9, 3/8, 1/3.	4/4 (which simplifies to 1), 8/5, 6/6.