Improper Fractions - Definition, Conversions, Examples

A fraction is a way to show one or more parts of a whole. Like if a chocolate bar is split into 4 parts and you eat 1, that’s written as ¼. In this fraction, 1 is the numerator (the number of parts taken ), and 4 is the denominator (the total number of equal parts).

Fractions are categorized as proper or improper, depending on the relationship between the numerator and the denominator.  In this blog, we will understand the concept of improper fractions in detail with real-life examples.

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What Is an Improper Fraction With Example

Let’s begin by understanding what is improper fraction is with an example. A fraction is split into two main parts:

• Numerator – the top part of the fraction, representing the number of parts taken

• Denominator – the bottom part, representing the total number of equal parts

In most fractions, the numerator is less than the denominator. These are called proper fractions. For example, 2/5 is a proper fraction because 2 is smaller than 5.

But in some fractions, the numerator is equal to or greater than the denominator. These are called improper fractions.

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Improper fraction example:

• 5/4

• 9/3

• 11/6

In each of these, the numerator (top number) is either equal to or larger than the denominator (bottom number). This means they represent values that are greater than or equal to 1.

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Definition of Improper Fraction

The definition of improper fraction states that a fraction is called improper when its numerator is greater than or equal to its denominator. This means the value of the fraction is either equal to or greater than one.

For example:

• 5/4 is an improper fraction because 5 > 4

• 10/3 is an improper fraction because 10 > 3

• 9/7​ is also an improper fraction because 9  > 7

This kind of fraction often represents amounts that are more than a whole and can be converted into mixed fractions for better clarity in reading or usage.

How to Convert Improper to Mixed Fractions?

Improper fractions and mixed fractions represent the same value but in two different forms.

An improper fraction has a numerator that is equal to or greater than the denominator. For example, 17/5, 9/4​, and 10/3 are improper fractions.

A mixed fraction is a number made up of a whole number and a proper fraction. It is written in the form:

whole number + proper fraction, such as 3 25 ​, 4 13 or 6 38

Steps to Convert Improper Fractions to Mixed Fractions

To convert an  improper fraction into a mixed fraction, follow the steps explained below:

Step 1: Divide the numerator by the denominator.
Step 2: The quotient (the answer from division) becomes the whole number part.
Step 3: The remainder becomes the new numerator.
Step 4: Keep the same denominator.

Now you have a mixed fraction.

Let’s now understand the above step to convert an improper to a mixed fraction with an example.

Example: Convert 29/7 into a mixed fraction

Step 1: Divide 29 by 7 → 29 ÷ 7 = 4 with a remainder of 1

Step 2: The quotient is 4 → this is the whole number

Step 3: The remainder is 1 → this becomes the new numerator

Step 4: Denominator stays 7

So, 29/7= 4 71 

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How to Convert Mixed Fractions to Improper Fractions?

We can convert mixed fractions into improper fractions using a simple method discussed below.

Let’s say the mixed fraction is written as w (n/d), where:

• w is the whole number,

• n is the numerator,

• d is the denominator.

To convert this into an improper fraction, follow these steps:

Step 1: Multiply the whole number (w) by the denominator (d)
w × d

Step 2: Add the numerator (n) to that result
 (w × d) + n

Step 3: Place the total from Step 2 over the original denominator (d)
 Improper fraction = [(w × d) + n] / d

Example: Convert 4 37 ​ into an improper fraction.

4 × 7 = 28

28 + 3 = 31

Final answer = 31/7

Example of Improper Fraction in Real Life

To better understand the concept, let’s consider an example of improper fraction in daily life.

You are baking cookies. One tray holds 8 cookies. You bake 26 cookies in total. How many trays do you use?

That’s 26/8.

Since 26 is greater than 8, this is an improper fraction.

Converting it  into mixed fraction gives 3 28 , which simplifies to 3 14.

So, you would need  3 14 trays to bake all 26 cookies.

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Improper Fraction Solved Examples 

Example 1: Identify the improper fractions from the following: 

14/9, 6/11, 17/8, 3/5, 12/6

Solution: An improper fraction has a numerator greater than or equal to the denominator. So, the improper fractions are:

14/9, 17/8, 12/6

Example 2:  Write 25/7 as a mixed fraction.

Solution: Divide the numerator by the denominator:

25 ÷ 7 = 3 quotient, remainder 4

So, the whole number is 3, the remainder becomes the new numerator, and the denominator stays the same.

Therefore, 25/7 = 3 47

Example 3: Convert a mixed fraction to an improper fraction

Write 2 59 as an improper fraction.

Solution: Multiply the whole number and the denominator: 2 × 9 = 18

Add the numerator: 18 + 5 = 23

Keep the same denominator
So, 2 59 =  239 

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