What are Improper Fractions? Definition With Examples

Fractions are often referred to as numbers between numbers. Fractions are numerical values that represent a part or a portion of a whole. For example, look at the pizza below.

This pizza has been cut into 4 equal parts. So each piece of the pizza represents 1 out of 4 equal parts. So mathematically, we can represent each piece as  $\frac{1}{4}$. This number is called a fraction. 

The number below the bar that represents the total number of equal parts that the whole is divided into is called the denominator.

And the number on the top that represents the number of equal parts we are considering is called the numerator. 

What is an improper fraction?

Before discussing improper fraction, we first need to understand proper fractions.

Proper fractions: Fractions for which the numerator is less than the denominator are called proper fractions. For example, if you order a pizza and cut it into 4 equal parts, and then eat one slice out of it, the remaining pizza can be expressed as $\frac{3}{4}$ of the whole pizza. Here, since 3 is less than 4, the fraction is a proper fraction.

Improper fractions: Improper fractions are defined as fractions for which the numerator is greater than the denominator. Let us take an example of improper fraction, imagine you order a pizza that has 4 slices. Your friends eat all 4 slices. And you realize you didn’t get any. You order another pizza. After eating 1 slice from it, you realize you are done eating. So, how much of the pizza did your friends and you have in all?

Your friends first had all 4 slices of 1 pizza, and then you had 1 slice of the same size from the second pizza.

So, the total pizza eaten is $\frac{5}{4}$ slices of pizza. And that’s an improper fraction with a numerator greater than the denominator. 

Mixed numbers: Mixed numbers are just another way of writing fractions greater than a whole. A mixed number has a whole part and a fractional part, which is actually a proper fraction.

Let’s take the same example from above. You and your friends ate one whole pizza and one-fourth of a pizza. As a mixed fraction, we can write this as $1$ and $\frac{1}{4}$ of a pizza or $1\frac{1}{4}$ of a pizza.

Fraction Conversion

Improper Fraction to Mixed Number

An improper fraction can be converted to a mixed fraction and a mixed fraction can be converted to an improper fraction.

Let’s say we want to convert the fraction $\frac{7}{2}$ into a mixed number. 

Step 1: Find the quotient and the remainder by dividing the numerator with the denominator.

Step 2: The quotient will be the number of wholes for the mixed number. The remainder will be the numerator of the fractional part and the denominator will remain the same.

So, the mixed number form of $\frac{7}{2}$will be:

Mixed Number to Improper Fraction

Any mixed number can be converted into an improper fraction.

Let’s say we want to convert the mixed number $1\frac{3}{4}$ into an improper fraction. 

Step 1: Multiply the denominator with the whole. And then add the numerator to the product.

Step 2: Keep the denominator same and solve for the numerator.

Therefore, the improper fraction for the mixed number $1\frac{3}{4}$ will be $\frac{7}{4}$. 

Solved Examples

Example 1. Identify the improper fractions:

$\frac{1}{5}$, $2\frac{7}{5}$, $\frac{3}{2}$, $\frac{1}{3}$, $\frac{5}{4}$, $6 \frac{1}{6}$

Solution: $\frac{2}{3}$ and $\frac{5}{4}$ are improper fractions as the value of the numerator is greater than the value of the denominator for both of these fractions.

Example 2. Write $4\frac{2}{7}$ as an improper fraction.

Solution: Converting $4\frac{2}{7}$ into an improper fraction,

$4 \frac{2}{7}$ = $\frac{(7\times4) + 2}{7}$ = $\frac{30}{7}$

Example 3. Write $2\frac{9}{6}$ as an improper fraction.

Solution: While dividing 29 by 6, the quotient and remainder are 4 and 5 respectively.
So  $\frac{29}{6}$ written as a mixed number is $ 4 \frac{5}{6}$ .

Converting $3\frac{1}{5}$ to an improper fraction:

Practice Problems

Frequently Asked Questions