Proper Fraction and Improper Fraction

What is the difference between proper fraction and improper fraction?

Proper fraction:

The fractions 1/4, 3/8, 5/11, 9/13, 14/25, ………., etc., are the fractions where the numerators are smaller than the denominators.

A fraction is said to be a proper fraction when its numerator is smaller than its denominator.

For example:

1/2, 4/7, 5/9, 7/12, ………., 15/23, 17/25, etc., are called proper fractions.

Improper fraction:

The fractions 11/5, 23/9, 18/5, 3/2, 9/8, ………., etc., are the fractions where the denominators are smaller than the numerators.

A fraction is said to be an improper fraction when its denominator is smaller than its numerator.

An improper fraction is the sum of one or many whole number and one proper fraction

For example:

(i) 1 + 4/3 = 3/3 + 4/3 = (3 + 4)/3 = 7/3

(ii) 3 + 5/7 = (3 × 7)/7 + 5/7 = (21 + 5)/7 = 26/7

Similarly, 13/5, 27/9, 5/3, 17/2, 9/7, etc., are called improper fractions.

The explanations between the differences will help us to identify the proper fractions and the improper fractions.

Worksheet on Proper Fraction and Improper Fraction:

1. Which of the following are proper fractions?

(i) \(\frac{4}{3}\)

(ii) \(\frac{7}{11}\)

(iii) \(\frac{6}{19}\)

(iv) \(\frac{5}{11}\)

(v) \(\frac{15}{11}\)

(vi) \(\frac{14}{8}\)

(vii) \(\frac{12}{17}\)

(viii) \(\frac{23}{24}\)

(ix) \(\frac{9}{8}\)

(x) \(\frac{6}{2}\)


1. (ii), (iii), (iv), (vii), (viii) are proper fractions because numerator are less than denominators.

2. Which of the following are improper fractions?

(i) \(\frac{3}{14}\)

(ii) \(\frac{16}{15}\)

(iii) \(\frac{13}{16}\)

(iv) \(\frac{23}{11}\)

(v) \(\frac{28}{15}\)

(vi) \(\frac{19}{12}\)

(vii) \(\frac{11}{17}\)

(viii) \(\frac{15}{26}\)

(ix) \(\frac{5}{14}\)

(x) \(\frac{20}{11}\)


1. (ii), (iv), (v), (vi), (x) are improper fractions because numerator are greater than denominators.

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Related Concepts

Fraction as a Part of a Whole

Fraction as a Part of Collection

Greater or Smaller Fraction

Convert a Fraction to an Equivalent Fraction

Verify Equivalent Fractions

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3rd Grade Math Lessons

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