Improper Fractions
Fractions were first used in Ancient Egypt around 1600 BC, which makes the concept quite old. Fractions are of different types. When the numerator is smaller than the denominator i.e. 1/2, it is a proper fraction. However, when the denominator is smaller than the numerator, then it is an improper fraction. An example of this is 16/15.
An improper fraction is one type of fraction in which the numerator is equal to or greater than the denominator. Its value is always one or greater than one. Improper fractions are usually written in mixed number form, in a simplified manner, as mixed fractions are easier to comprehend.
What is an Improper Fraction?
An improper fraction is a type of fraction where the numerator is greater than or equal to the denominator. For example, 5/2 and 8/5, are improper fractions.
Every fraction has two parts, numerator, and denominator. In mathematics, there are two main types of fractions based on the values of numerator and denominator, and those are proper fractions and improper fractions. Let's learn about all the types of fractions in the next section.
Improper Fraction and Mixed Fraction
An improper fraction is a fraction whose numerator is greater than or equal to its denominator. For example, 9/4, 4/3 are improper fractions. Numerically, an improper fraction always equals to or greater than 1. On the other hand, a mixed fraction is a fraction that is written as a combination of a natural number and a proper fraction. It is a simplified form of an improper fraction. For example, \( 21\dfrac{4}{5}, 16\dfrac{2}{3}\) are mixed fractions. Numerically, a mixed fraction is always greater than 1. Also, any mixed fraction is an improper fraction.
Generally, in real life, mixed fractions are easier to interpret and compare, as compared to improper fractions. We can easily convert any improper fraction to a mixed number or mixed fraction to an improper fraction by following some basic steps that you will study in later sections on this page.
Converting Improper Fractions to Decimals
Fractions and decimals are two ways to represent numbers. Improper fractions can be converted to decimals easily by dividing the numerator with the denominator. Let’s look at a quick and easy example of how we can convert improper fractions to decimals. Let’s consider the following example.
Example: Convert the given improper fraction to a decimal: 10/4
Solution: The first step is to divide 10 by 4. When we do so, we will get: 10 ÷ 4 = 2.5
Here, 10/4 is an improper fraction and 2.5 is a decimal. Similarly, the value of 3/2 is 1.5 in decimals and 5/2 is 2.5 in decimals. When we convert an improper fraction to decimal, the decimal value is always greater than 1.
Converting Improper Fraction to Mixed Fraction
The denominator of the mixed fraction form of an improper fraction is always the same as that of the original fraction. A mixed fraction is considered as the simplified form of improper fractions, that is why it is important to learn this conversion. For converting an improper fraction to a mixed fraction, we have to follow the belowlisted steps:
 Step 1 Divide the numerator with the denominator.
 Step 2 You will get values of quotient and remainder.
 Step 3 Arrange those values of the quotient, remainder, and divisor in the following manner to express a fraction as a mixed number: \(Quotient\dfrac{Remainder}{Divisor}\)
Let’s look at a quick and easy example of how we can convert improper fractions to mixed fractions. Let’s say you have an improper fraction, 13/4. The first step is to divide 13 by 4. We get 3 as the quotient with a remainder of 1. Next, we will place 1 as the numerator, 4 as the denominator, and 3 as the whole number. Thus, we get the mixed fraction: \( 3\dfrac{1}{4}\)
Similarly, let’s solve another example. Here, we have an improper fraction 9/2. On dividing 9 by 2, we get 4 as the quotient with a remainder of 1. Again, we will repeat the same process. We will place 1 as the numerator, 2 as the denominator, and 4 is the whole number. Thus, we get the mixed fraction: \(4\dfrac{1}{2}\).
How to solve Improper Fractions?
Solving improper fractions mean to perform arithmetic operations on them and simplify the value of the answer so obtained. There are mainly four arithmetic operators in mathematics and those are addition, subtraction, multiplication, and division. Solving an improper fraction is the same as solving any other proper fraction, the only difference is that, here, we have to simplify the answer and write it in mixed number.
Let's solve the improper fraction: 4/3 + 7/3
Step 1: We have the same denominator for both the fractions. Therefore, we will directly add the numerators 4 and 7. We get 11. Thus, on adding, we get the improper fraction: 11/3.
Step 2: Simplifying the improper fraction (dividing 11 by 3), we will get 3 as a whole, 2 as a numerator, and 3 as the denominator.
The answer is \(3\dfrac{2}{3}\).
Solved Examples

Example 1:
Samuel is baking a cake. The recipe says that the cake needs two and onehalf cups of flour. He accidentally poured four and onesixth cups of flour into the bowl. Find out the quantity of flour Samuel must take out of the bowl.
Solution:
From the question, we know that the quantity of flour needed is \(2\dfrac{1}{2}\) cups and the quantity of flour poured is \(4\dfrac{1}{6}\) cups. We have to find out how much flour should be taken out of the bowl. We can find this by subtracting \(2\dfrac{1}{2}\) from \(4\dfrac{1}{6}\). Before doing so, we have to make the denominator equal.
By using the concept of LCM, we know that the LCM of 2 and 6 is 6. Thus, \(2\dfrac{1}{2}\) becomes \(2\dfrac{3}{6}\)
\( 4\dfrac{1}{6}\ –\ 2\dfrac{3}{6}\). We get \(1\dfrac{4}{6}\) as the result. On simplifying \(1\dfrac{4}{6}\), we get \(1\dfrac{2}{3}\) which is the answer.
Therefore, Samuel must take out \(1\dfrac{2}{3}\) cups of flour.

Example 2:
There are fivefourth liters of plain milk in the refrigerator. There is also oneeighth liters of chocolate milk. Calculate how much more plain milk is there in the refrigerator compared to chocolate milk.
Solution:
To find out the extra quantity of plain milk, we have to subtract the quantity of chocolate milk from the total quantity of plain milk. We have to find (5/4  1/8).
Before subtracting, we have to make the denominator equal by using the LCM method. We know the LCM of 4 and 8 is 8. So, now we have 10/8  1/8
Therefore, the answer is (101)/8, i.e 9/8, which can be simplified as \(1\dfrac{1}{8}\).
FAQs on Improper Fractions
Are Whole Numbers Examples of Improper Fraction?
Yes, whole numbers are examples of improper fractions, as we can write any whole number in the form of a fraction in which the numerator is greater than the denominator. For example, 3= 3/1, 5= 5/1, etc.
How can we Add Improper Fractions?
The addition of two like improper fractions is done by adding the values of their numerator and writing the common denominator as the denominator of the sum obtained. While, in the case of two, unlike improper fractions, we first take the LCM of the denominators and convert them into like fractions. Then, we add those two fractions. Let's take an example of two improper fractions 5/4 and 7/4.
 Step 1: We have the same denominator in these fractions 5/4 + 7/4. Therefore, we will simply add the numerators 5 and 7. We get 12 as the sum of the numerator. Thus, on adding, we have 12/4.
 Step 2: Simplifying the improper fraction (dividing 12 by 4), we get 3 as the answer.
How do we Simplify an Improper Fraction?
Simplification of improper fractions means finding the lowest value of the fraction by dividing the numerator with the denominator. Let us take an example to understand how to simplify an improper fraction. Consider the fraction 100/5. By dividing 100 by 5, we get 20 as the answer. Thus, 100/5 = 20 in the simplified form.
How to Subtract Improper Fractions?
Subtraction of two like improper fractions is done by subtracting the values of their numerator and writing the common denominator as the denominator of the difference obtained. While, in the case of two unlike improper fractions, we first take the LCM of the denominators and convert them into like fractions. Then, we subtract those two fractions.
How to Convert Improper Fraction to Mixed Numbers?
Improper fractions are converted to mixed fractions by dividing the numerator with the denominator and write the answer in this form: \(Quotient\dfrac{Remainder}{Divisor}\).
How to Multiply Improper Fractions?
The numerator and denominator of an improper fraction are multiplied with the numerator and denominator of the other fraction to find the product. After multiplying, we simplify the fraction so obtained. In this way, we multiply two improper fractions.