Proper Fractions

Last Updated : 23 Jul, 2025

A proper fraction is a type of fraction where the numerator is less than the denominator. This means the value of a proper fraction is always less than 1.

Examples of Proper Fractions are:
• 1/2​ (one-half)
• 3/4​ (three-quarters)
• 2/5​ (two-fifths)

file
Proper Fractions

Fractions which have values either equal or greater than 1 will always be Improper Fraction.
For Example:

  • 4/3 (four-thirds, which is an improper fraction)
  • 5/5 (five-fifths, which is equal to one)

Steps to Determine Proper Fractions

To identify whether any fraction is proper or not, first identify its numerator and denominator. Then, if

  • If the numerator is smaller than the denominator (e.g., 3/5​, 2/7​), it is a proper fraction.
  • If the numerator is equal to or greater than the denominator (e.g., 5/4, 7/4, 2/2​), it is not a proper fraction.

Let's consider an example for better understanding.

  • Fraction 22/25:
    • Numerator: 22
    • Denominator: 25
    • Comparison: Since 22 (numerator) is smaller than 25 (denominator), it is a proper fraction.
  • Fraction 13/11:
    • Numerator: 13
    • Denominator: 11
    • Comparison: Since 13 (numerator) is greater than 11 (denominator), it is not a proper fraction.

Operations on Proper Fractions

Proper fraction can be added, subtracted, multiplied or divided with each other similar to any other fractions. For any two fractions a/b and c/d, formulas of each operations are:

OperationFormulaExample
Addition

\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}

\frac{1}{3} + \frac{1}{6} = \frac{2 + 1}{6} = \frac{3}{6} = \frac{1}{2}

Subtraction

\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}

\frac{3}{4} - \frac{1}{4} = \frac{3 - 1}{4} = \frac{2}{4} = \frac{1}{2}

Multiplication

\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}

\frac{2}{3} \times \frac{3}{4} = \frac{6}{12} = \frac{1}{2}

Division

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}

\frac{2}{5} \div \frac{1}{2} = \frac{2}{5} \times \frac{2}{1} = \frac{4}{5}

Difference Between Proper and Improper Fraction

Some of the key difference between proper and improper fractions are:

FeatureProper FractionImproper Fraction
DefinitionNumerator is less than the denominator.Numerator is greater than or equal to the denominator.
ValueAlways less than 1.Equal to or greater than 1.
RepresentationCan be a part of a whole.Can represent a whole number or more.

Proper Fractions on Number line

Since the value of a proper fraction is less than 1, it is always placed between 0 and 1 on a number line. The whole part between 0 and 1 is divided into equal parts based on the denominator, and the numerator shows the fraction’s position. For example, to represent 3/4, divide the space between 0 and 1 into 4 parts, and the third part marks 3/4, in 2/5 the space between 0 and 1 is divided into 5 parts and the second part represents 2/5.

Proper-fractions-on-number-line

Read More:

Comment

Explore