How to compare an improper fraction and a proper fraction?

A proper fraction is a fraction whose numerator is smaller than its denominator and an improper fraction is a fraction whose numerator is greater than its denominator.

Answer: An improper fraction is always greater than a proper fraction {If N > D then it is an improper fraction and if D > N then it is a proper fraction}.

Let us try to compare an improper fraction and a proper fraction.

Explanation:

A fraction is in the format of Numerator/Denominator = N / D

• If N > D then it is an improper fraction 
  • examples: 5/3, 8/7, etc;
• If D > N then it is a proper fraction
  • examples: 1/2, 6/7, etc

Improper and proper fractions can be compared by converting them to like fractions. Let us consider an example:

Compare the proper fraction 4/5 and an improper fraction 3/2. 

LCM (2,5) = 10. Convert the fractions with denominator 10.

4/5 = 4×2/5×2 = 8/10; 3/2 = 3×5/2×5 = 15/10

Since 15 > 8 ⇒ 15/10 > 8/10 ⇒ 3/2 > 4/5

Please note that an improper fraction is always greater than 1 and a proper fraction is always less than 1. 

⇒ An improper fraction is always greater than a proper fraction.

So, an improper fraction is always greater than a proper fraction.