Last updated on July 9th, 2025
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.
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.
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 |
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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
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
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.
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
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.
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.
Convert 18/5 to a mixed fraction
18/5 in mixed fraction can be expressed as 3 3/5
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
Convert 3 3/5 to an improper fraction
An improper fraction, 3 3/5 can be expressed as 18/5
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
Find the sum of 7/3 + 8/3
The sum of 7/3 + 8/3 = 5
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.
Emma is baking cookies for a school fundraiser. Each batch of cookies requires 5/3 cups of sugar. She wants to make 4 batches.
For 4 batches of cookies, Emma needs 20/3 cups or 6 2/3 cups of sugar.
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.
Simplify 24/8
24/8 can be simplified as 3
As 8 is a factor of 24, we can divide 24 ÷ 8 = 3
So, 24/8 can be simplified as 3
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.
: She loves to read number jokes and games.