Improper Fractions
2026-02-28 17:11 Diff
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Last updated on December 8, 2025

Fractions are used to represent parts of a whole using a numerator and a denominator. The fraction in which the numerator is greater than or equal to the denominator is improper. Examples like 8/5 or 16/15 show values that are one or more; let’s learn them in detail.

What are Improper Fractions?

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Fraction are written in the form p/q, where p is the numerator and q is the denominator. Based on the numerator and denominator, fractions are of two types: proper and improper. When the numerator is greater than the denominator, the fraction is called an improper fraction. For example, \(9\over5\) has a numerator larger than its denominator, so it is an improper fraction.

Difference Between Improper and Proper Fractions

In this section, we will discuss the difference between improper and proper fractions.

Improper Fraction Proper Fraction
  • A fraction where the numerator is greater than its denominator is an improper fraction.
  • An improper fraction represents one or more whole units.
     
  • A proper fraction represents a smaller part of a whole.
     
  • The value of an improper fraction is greater than 1.
     
  • The value of a proper fraction is always less than 1.
  • For example, \({4\over 3}, {6\over 5}, {9\over2}\)
  • For example, \({1\over 2}, {8\over 11}, {7\over9}\)
     

How to Convert Improper Fractions to Mixed Fractions?

A whole number and a proper fraction make a mixed fraction. It is written as  \(a{p\over q}\) where a = whole number, p, q are integers, \(q \neq 0\). Converting improper fractions to mixed fractions is referred below:

Step 1: First, we divide the numerator by the denominator.
 

Step 2: When converting an improper fraction to a mixed fraction, we consider the quotient as the whole number of the mixed fraction, and the remainder as the numerator and denominator will be the same for the proper fraction. The mixed fraction is written as the quotient, followed by the proper fraction: quotient \((remainder ÷ denominator)\).
 

Step 3: Arrange the values as in step 2. 

For example, to convert \(8 \over 5\) to a mixed fraction 

Dividing 8 by 5, the quotient is 1 and the remainder is 3

So, \(8 \over 5\) can be written as \({1}{3\over5}\)

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How to Convert Mixed Fraction to Improper Fraction

As we learned how to convert an improper fraction to a mixed fraction, now let’s discuss the conversion of the mixed fraction to an improper fraction in the following steps -

Step 1:  First, multiply the denominator by the whole number of the mixed fraction.
 

Step 2: Then add the result from Step 1 to the numerator. 

Step 3: The sum from Step 2 becomes the numerator, and the denominator remains the same as in the mixed fraction.
 

Now let’s see how to convert \({2}{3\over 5}\)to an improper fraction.
 

Step 1: Multiplying the denominator by the whole number, that is, \(5 \times 2 = 10\).
 

Step 2: Adding the product in Step 1 with the numerator, that is, \(10 + 3 = 13\).
 

Step 3: \({2} {3\over 5}\) can be written as \(13\over 5\).
 

How to Convert Improper Fractions to Decimals

Fractions and decimals are the most common ways to represent parts of a whole. For dividing the numerator by the denominator, convert the improper fraction to a decimal. For example, let’s convert \(11\over 5\) to a decimal. 

Dividing 11 by 5, that is, \(11 \div 5 = 2.2\)

So, \(11\over 5\) in decimal can be written as 2.2. 

How to Solve Improper Fractions?

Solving the improper fraction means performing the arithmetic operations, and the answer is simplified further and written as a mixed fraction. There are four basic arithmetic operations: addition, subtraction, multiplication, and division. 

Operation Example Addition \({7\over 5} + {6\over 5} = {{7 + 6}\over 5} = {13\over 5} = {{2}{3\over5}}\) Subtraction \({7\over 5} - {6\over 5} = {{7 - 6}\over 5} = {1\over 5} \) Multiplication \({7\over 5} \times {6 \over 5} = {{7 \times 6} \over {5 \times 5}} = {42\over 45} = {1 {17\over 25}}\)

Division 

 \({7\over 5} \div {6 \over 5} = {{7 \over 5} \times {5 \over 6}} = {35\over 30} = {7\over 6} = {{1}{1\over 6}}\)

Tips and Tricks to Master Improper Fractions

Students often consider fractions as tricky. To master improper fractions, we will learn a few tips and tricks. It helps students to convert, simplify, and use improper fractions in real life. 

  • Understand the concept of the improper fraction, that is, an improper fraction is a fraction where the numerator is equal to or greater than the denominator. 
     
  • When converting the improper fraction to a mixed number, remember: \({mixed number} = {numerator\over denominator} = {{quotient} {remainder\over denominator}}  \)
     
  • To convert a mixed number to an improper fraction, first multiply the whole number by the denominator, then ass the numerator. 
     
  • Simplify the fraction whenever possible, so after calculation, check if the fraction can be simplified, whether the numerator and denominator have any common factors or not. 
     
  • Memorize that if the numerator is greater than the denominator, then it's an improper fraction, and if the numerator is smaller than the denominator, then it's a proper fraction.
     
  • Teachers can use visual aids such as pie charts, bar models, or fraction strips to show that improper fractions are larger than a whole. 
     
  • Parents can help students learn improper fractions by connecting them to real-life examples, such as cutting pizzas, measuring cups, or sharing chocolate bars. 
    Make learning fun with fraction cards, matching games, or online fraction apps. Ask students to convert improper fractions to mixed numbers during the game. 
     

Common Mistakes and How to Avoid Them in Improper Fractions

When working on fractions, students make errors because it is a confusing topic. Most students tend to repeat the same mistakes, so to master improper fractions, let’s learn a few common mistakes and ways to avoid them.

Real-World applications of Improper Fractions

In our everyday life, we use fractions in different fields such as finance, cooking, construction, and more. These are the few real-life applications of fractions.

  • To split the bills among the friends, we use fractions. That is, if the total cost is $15 and there are 5 people, the bill per person is \(\frac{15}{5} = 3 \).  
  • In cooking, to adjust the ingredients according to the number of servings, we use fractions. 
  • In construction, to measure the materials, floor, and so on, we use fractions.
  • To represent the distances in road signs, we use fractions such as \(1 \over 2\) mile. 
     
  • To share quantities we use the improper fraction, for example, when dividing pizza, cakes, or any item into unequal portions. 

Problem 1

Convert 18/5 to a mixed fraction

Okay, lets begin

\(18 \over 5\) in mixed fraction can be expressed as \({3} {3\over 5}\).

Explanation

To convert an improper fraction to a mixed fraction, we first divide the numerator by the denominator.

Dividing 18 by 5, the quotient is 3 and the remainder is 3.
So, \(18\over 5\) can be expressed as \(3 {3\over 5}\).

Well explained 👍

Problem 2

Convert 3 3/5 to an improper fraction

Okay, lets begin

 An improper fraction, \(3 {3\over 5}\) can be expressed as \(18\over 5\).

Explanation

To convert a mixed fraction to an improper fraction, we first find the product of the denominator and the whole number.

That is  \(5 \times 3 = 15\), then we add the sum and numerator,   \(15 + 3 = 18\). So the new numerator is 18, so \(3 {3\over 5}\) can be expressed as \(18\over 5\).

Well explained 👍

Problem 3

Find the sum of 7/3 + 8/3

Okay, lets begin

The sum of \({7\over 3} + {8 \over 3} = 5\).

Explanation

As the denominators of both the fractions are the same, we add the numerators to find the sum of the fractions.

That is, \(7 + 8 = 15\),

so \({{7\over 3} + {8\over 3} = {15\over 3}}\), which can be simplified as 5.

Well explained 👍

Problem 4

Emma is baking cookies for a school fundraiser. Each batch of cookies requires 5/3​ cups of sugar. She wants to make 4 batches, so calculate the total sugar needed.

Okay, lets begin

For 4 batches of cookies, Emma needs \(20\over3 \) cups or \(6 {2\over3} \) cups of sugar.

Explanation

To find the number of cups of sugar required for 4 batches, we multiply the sugar required per batch by the number of batches.

Thus,\( {5\over 3} × 4 = {20\over3}\)

Which can be expressed as \({6} {2\over3}\) cups.

Well explained 👍

Problem 5

Simplify 24/8

Okay, lets begin

 \(24\over8\) can be simplified as 3.

Explanation

As 8 is a factor of 24, we can divide \(24 \div 8 = 3 \)
So, \(24\over 8\) can be simplified as 3.

Well explained 👍

FAQs on Improper Fractions

1.What is an improper fraction?

The improper fraction is a type of fraction where the numerator is greater than the denominator. For example, \({9\over5}, {8\over7}, {9\over4}. \)

2.What is 21/4 in a mixed fraction?

\(21\over 4\) can be expressed as \(5 {1\over4}\) a mixed fraction. When dividing 21 by 4, the quotient is 5 and the remainder is 1.  

3.What are the types of fractions?

4.What is 9 6/10 in an improper fraction

\({9 {6\over10}}\) can be written as \({96\over 10}\) which can be simplified as \({48\over 5}\). 

5.What is a mixed fraction?

A mixed fraction is a type of fraction that is a combination of a whole number and a fraction.

6.Why is it important for my child to learn improper fractions?

Learning improper fractions help students: 

  • To understand numbers greater than one. 
  • To perform arithmetic operations
  • Prepare for real-life applications like measuring ingredients, and diving items

7.How can I make learning improper fractions fun at home?

To make learning interactive and fun at home parents can use visual aids like fraction bars or pie chart, relate fractions to real-life activities like cooking, measuring, dividing toys, and make them practice simple problems daily.

Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.