Proper and Improper Fractions: Definition, Examples, Differences

The concepts of proper and improper fractions are based on which one between the numerator and the denominator is bigger. In this article, we will learn about proper fractions and improper fractions with their definitions, examples, and properties. Note that

Any fraction has the form a/b for some b≠0. Here a is the numerator and b is the denominator of the fraction.

Proper Fraction Definition

A fraction is called a proper fraction if the numerator is less than the denominator of the fraction.

$\dfrac{1}{2}, \dfrac{3}{4}, \dfrac{5}{7}, \cdots$ are examples of proper fractions. But, there are fractions that are not proper. For example, $\dfrac{4}{3}$ is not a proper fraction as 4>3 that is the numerator is bigger than the denominator. These fractions are known as improper fractions which we learn now.

Improper Fraction Definition

Definition of improper fractions: A fraction is called a proper fraction if the numerator is greater than the denominator of the fraction.

For example, $\dfrac{3}{2}, \dfrac{5}{4}, \dfrac{11}{7}, \cdots$ are improper fractions.

How to Add Proper/Improper Fractions?

The addition of proper or improper fractions will be done according to the rule as follows. Note that any proper or improper fractions are always of the form $\dfrac{a}{b}$. And we can add two such fractions $\dfrac{a}{b}$ and $\dfrac{x}{y}$ as given below:

$\dfrac{a}{b}+\dfrac{x}{y}=\dfrac{ay+bx}{by}$.

For example, let’s add $\dfrac{1}{2}$ and $\dfrac{4}{3}$. We have

$\dfrac{1}{2}+\dfrac{4}{3}$

= $\dfrac{1 \times 3+4 \times 2}{2 \times 3}$

= $\dfrac{3+8}{6}$

= $\dfrac{11}{6}$.

Improper Fraction to Mixed Fraction

Now we will learn about how to convert improper fractions into mixed fractions. To do so the below steps have to be followed.

Step 1: At first, we will divide the numerator by the denominator.

Step 2: The quotient will be the whole number associated with the desired mixed fractions.

Step 3: The remainder will be the numerator of the fractional part associated with the desired mixed fractions.

Step 4: The divisor will be the denominator of the fractional part associated with the desired mixed fractions.

For example, we will convert $\dfrac{11}{10}$ into a mixed fraction.

We have $11=10\times 1 +1$

$\therefore \dfrac{11}{10}=1 \dfrac{1}{10}$.

So the improper fraction $\dfrac{11}{10}$ is converted into the mixed fraction $1 \dfrac{1}{10}$.

Also Read:

Simple and Compound Fractions

Similar and Dissimilar Fractions

Differences between Proper & Improper Fraction

The proper and improper fractions are different in nature. Their differences are listed in the table below.

Proper Fraction	Improper Fraction
The numerator is less than the denominator.	The numerator is greater than the denominator.
1/2, 3/4 are examples of proper fractions.	3/2, 4/3 are examples of improper fractions.
The value of a proper fraction is always less than 1.	The value of an improper fraction is always greater than or equal to 1.

Question-Answer on Proper and Improper Fractions

Question 1: Is $\dfrac{4}{7}$ a proper fraction?

Answer:

Here numerator= 4 and denominator= 7. As 4<7, the numerator is less than the denominator. Thus, $\dfrac{4}{7}$ is a proper fraction.

Question 2: Is $\dfrac{7}{4}$ a proper fraction?

Answer:

Here numerator= 7 and denominator= 4. Thus, the numerator is bigger than the denominator and so $\dfrac{7}{4}$ is an improper fraction.

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