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Last updated on July 9th, 2025

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Improper Fractions

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Around 1600 BC, Ancient Egyptians first used fractions, which makes fractions an old concept. There are different types of fractions: In an improper fraction, the numerator is always greater than the denominator, for example, 8/5, 15/13. In this article, we will be discussing improper fractions.

Improper Fractions for Canadian Students
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What are Improper Fractions?

Fractions are written in the form p/q, every fraction has two parts: that is the numerator and the denominator. A fraction where the numerator is greater than the denominator is known as an improper fraction. For example, 9/5, where 9 is the numerator and 5 is the denominator. 

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Difference Between Improper and Proper Fractions

As we discussed, there are different types of fractions. In this section, let's talk about 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.
  • A fraction where the numerator is less than its denominator is a proper 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, 4/3, 6/5, 9/2
  • For example, 1/2, 8/11, 7/9
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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/q where a = whole number, p, q are integers, q≠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. That is the quotient (remainder/denominator). 

 

Step 3: Arrange the values as in step 2. 

 

For example, to convert 8/5 to a mixed fraction 

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

So, 8/5 can be written as 1 3/5

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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 product from step 1 to the numerator 

 

Step 3: The sum from step 2 is the numerator, and the denominator will be the same as in the mixed fraction

 

Now let’s see how to convert 2 3/5 to an improper fraction

 

Step 1: Multiplying the denominator by the whole number, that is, 5 × 2 = 10

 

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

 

Step 3: 2 3/5 can be written as 13/5

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How to Convert Improper Fractions to Decimals

The most common way to represent a part of a whole is by using fractions and decimals. For dividing the numerator by the denominator, convert the improper fraction to a decimal. For example, let’s convert 11/5 to a decimal. 

 

Dividing 11 by 5, that is, 11 ÷ 5 = 2.2

So, 11/5 in decimal can be written as 2.2. 

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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. 

 

Let’s solve the improper fraction: 7/5 + 6/5 

As both the fractions have the same denominator, so, we add the numerators. That is 7 + 5 = 12, so 7/5 + 6/5 = 13/5.

It can be written as 2 3/5 

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Real-world applications of Improper Fractions

In our everyday life, we use fractions in different fields such as finance, cooking, construction, and so on. 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 $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 ½ mile. 
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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.

Mistake 1

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Error when converting an improper fraction to a mixed fraction

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Miscalculation when converting an improper fraction to a mixed fraction is common among students. The error can be caused by skipping the steps while converting or by mixing up the remainder and quotient. So, to avoid this error, students should remember that to convert an improper fraction to a mixed fraction, first, we divide the numerator by the denominator. Then the quotient will become the whole number, and the remainder will be the numerator, and the denominator will be the same.

Mistake 2

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Errors while simplifying the fractions

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When simplifying the fraction, students cancel out the fraction without common factors. Sometimes students tend to simplify the one part that is either the numerator or the denominator, which is wrong. So, always remember that the fraction can only be simplified if both the numerator and denominator have a common factor.

Mistake 3

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Solving improper fractions with different denominators

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Students sometimes add improper fractions with different denominators without finding the common denominator. So when adding or subtracting a fraction, it is to find the equivalent fraction with a common denominator.

Mistake 4

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Confusing with improper fraction with a proper fraction

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Mostly, students make mistakes in calculating improper fractions and proper fractions. In most of these cases, students make errors in operations. To avoid such mistakes, a few points need to be remembered like numerator in improper fractions is always greater than denominator, and numerator in proper fraction is always smaller than denominator.

Mistake 5

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Making errors when working on word problems

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When working on word problems, students misidentify the whole and the part, which can lead to errors. So, to avoid errors, students should read the question carefully and determine the units, and also they can make a simple sketch to identify the relationship between the parts and the whole.

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Solved Examples of Improper Fractions

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Problem 1

Convert 18/5 to a mixed fraction

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18/5 in mixed fraction can be expressed as 3 3/5

Explanation

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

That is 18 ÷ 5 = 3.6, here the quotient is 3 and the remainder is 3
So, 18/5 can be expressed as 3 3/5

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Max, the Girl Character from BrightChamps

Problem 2

Convert 3 3/5 to an improper fraction

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 An improper fraction, 3 3/5 can be expressed as 18/5

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 × 3 = 15, then we add the sum and numerator, 15 + 3 = 18. So the new numerator is 18, so 3 3/5 can be expressed as 18/5

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Problem 3

Find the sum of 7/3 + 8/3

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The sum of 7/3 + 8/3 = 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 7/3 + 8/3 = 15/3, which can be simplified as 5.

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Max, the Girl Character from BrightChamps

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.

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For 4 batches of cookies, Emma needs 20/3 cups or 6 2/3 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, 5/3 × 4 = 20/3

Which can be expressed as 6 2/3 cups.

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Problem 5

Simplify 24/8

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 24/8 can be simplified as 3

Explanation

As 8 is a factor of 24, we can divide 24 ÷ 8 = 3

So, 24/8 can be simplified as 3

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FAQs on Improper Fractions

1.What is an improper fraction?

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

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3.What are the types of fractions?

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

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5.What is a mixed fraction?

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6.How can children in Canada use numbers in everyday life to understand Improper Fractions?

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7.What are some fun ways kids in Canada can practice Improper Fractions with numbers?

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8.What role do numbers and Improper Fractions play in helping children in Canada develop problem-solving skills?

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9.How can families in Canada create number-rich environments to improve Improper Fractions skills?

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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.

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Fun Fact

: She loves to read number jokes and games.

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