Improper Fractions

A fraction in which the numerator is greater than the denominator is called an Improper Fraction. Fractions are types of numbers that are used to represent numbers between two whole numbers. Suppose we have to find the number between 2 and 3 then using the concept of fractions we can find the number between 2 and 3 as 5/2. Fractions were used in ancient India and Egypt around 2000 BC and evolved from then. Fractions are highly useful in our daily life. Fractions are of generally two types. The improper fraction and the proper fraction.

In this article, we will learn about, Improper Fractions in Maths, their examples, and others in detail along with a brief introduction about fractions.

Improper Fractions Definition

Improper Fractions in Maths are the fractions whose numerators are greater than the denominator. For Example, 4/5, 9/4, 23/5, etc.

We know that fractions are numbers that are written in the form where two numbers are written in the division from as,

Numerator/Denominator

where the Numerator is the number that is the Dividend and the Denominator is Divisor. On the basis of Numerator and Denominator fractions are of two types. That is,

• Proper Fraction: Fraction where Numerator is less than Denominator. (Numerator < Denominator). Example, 2/5, 3/7, etc.
• Improper Fraction: Fraction where Numerator is greater than Denominator. (Numerator > Denominator). Example, 12/5, 13/7, etc.

Here, in this article, we will learn about Improper Fractions in detail.

What are Improper Fractions?

An improper fraction is one in which the numerator is higher than or greater than the denominator, such as 7/3 and 12/5. Here we see that in the fraction shown in the example the numerators 7 and 12 are greater than the denominators 3 and 5. Thus, they are improper fractions.

So for Improper fractions,

Numerator > Denominator

“Are Improper Fractions Rational Numbers”

If a numerator is greater than denominator in fraction then the improper fraction will be rational number.

• Example: We have fraction 5/4 its a improper fraction as here numerator is greater than denominator. After dividing 5 by 4 , the result will be 1.25 which is a terminating after decimal , therefore its an rational number.

Improper Fraction To Mixed Fraction

We know that any improper fraction can be easily written as mixed fractions or mixed number. A mixed fraction is a type of fraction that is written in the form of a(b/c) and is read as “a whole b by c“. Some examples of mixed fractions are 4(2/3), 6(3/5), etc.

We can easily change mixed fractions into improper fractions by following the method.

Suppose we have to find the improper fraction of mixed fraction a(b/c) then the steps to follow are,

Step 1: Multiply the denominator(c) of the mixed fraction with the whole number(a) as, a×c

Step 2: Add the value of the numerator with the multiple obtained in Step 1 as, (a×c) + b

Step 3: Simplify (a×c) + b and write it as a numerator where the denominator is c the fraction so obtained is the required fraction.

Study the example for more help.

Example: Change 11(3/5) into an improper fraction.

Solution:

= 11(3/5)

= {(11×5) + 3}/5

= 58/5

How to Convert Improper Fractions to Mixed Numbers?

Improper fractions and mixed fractions are the two ways of representing the same number and so they are equivalent and thus converting improper fraction to mixed number, we can convert them to each other very easily. To change improper fraction to mixed fraction use the steps discussed below,

Step 1: As we know that in improper fractions the numerator is always greater than the denominator. Divide the numerator by the denominator value.

Step 2: In the division process obtain the quotient and remainder.

Step 3: Arrange all the values obtained in Step 2 as,

Fraction in Mixed Form = Quotient(Remainder/Denominator)

The same can be understood by studying the example added below:

Example: Convert 17/4 into a mixed fraction.

Solution:

We have 17/4

Dividing the fraction we get,

17 = 4×4 + 1

• Quotient = 4
• Remainder = 1

In Mixde Fraction Form,

= 4(1/4)

This is the required mixed fraction form.

The image for the same is added below:

Converting Improper Fractions to Decimals

Improper fractions can easily be converted to decimal value by simply dividing the fractions. The modulus of the improper fractions is always greater than 1. In converting the improper fraction into decimal we divide the given numerator with the denominator value to get the required decimal value. An example added below will help us to better understand the same.

Example: Convert improper fraction 13/2 into decimal.

Solution:

= 13/2

Dividing 13 by 2 we get,

= 6.5

This is the required decimal value.

Solving Improper Fractions

Improper fractions are easily solved as we solve normal fractions to add or subtract improper fractions if they are like fractions then we simply simplify the numerator value without changing the denominator value and for unlike fractions we take the LCM of numerator to simplify further.

Now learn about the Addition and subtraction of Improper Fractions in detail.

Addition of Improper Fractions

Improper fraction adding is achieved using two cases, which are

• Case 1: Addition of Improper Like Fractions
• Case 2: Addition of Improper Unlike Fractions

Now let’s learn the same in detail,

Addition of Improper-Like Fractions

In the case of improper-like fractions, we simply add the numerator of the two fractions taking the denominator as constant.

For example, add 11/3 and 5/3.

Solution:

= 11/3 + 5/3

= (11 + 5)/3

= 16/3

Addition of Improper Unlike Fractions

In the case of improper unlike fractions, we add the fraction by first making them Like fractions by finding their LCM and then simplifying it normally.

For example, Add 4/3 and 5/4.

Solution:

= 4/3 + 5/4

LCM of 3, 4 = 12

= 16/12 + 15/12

= (16 + 15)/12

= 31/12

Learn more about Addition of Fractions

Subtraction of Improper Fractions

Subtraction of Improper Fractions can be done for two cases, which are

• Case 1: Subtraction of Improper-Like Fractions
• Case 2: Subtraction of Improper Unlike Fractions

Learn, Subtraction of Fractions

Now let’s learn the same in detail,

Subtraction of Improper-Like Fractions

In the case of improper-like fractions, we simply subtract the numerator of the two fractions taking the denominator as constant.

For example, subtract 11/3 and 5/3.

Solution:

= 11/3 – 5/3

= (11 – 5)/3

= 6/3 = 2/1

= 2

Subtraction of Improper Unlike Fractions

In the case of improper unlike fractions, we subtract the fraction by first making them Like fractions by finding their LCM and then simplifying it normally.

For example, subtract 4/3 and 5/4.

Solution:

= 4/3 – 5/4

LCM of 3, 4 = 12

= 16/12 – 15/12

= (16 – 15)/12

= 1/12

Multiplication and division of Improper fractions is achieved as we solve the normal fractions.

Read More,

• Equivalent Fractions
• Comparing Fractions
• Multiplying Fractions

Improper Fractions Examples

Example 1: Multiply 11 by 5/3

Solution:

= 11 × 5/3

= 11/1 × 5/3

= (11 × 5) / (3 × 1)

= 55 / 3

Example 2: Subtract 14/5 and 5/4.

Solution:

= 14/5 – 5/4

LCM of 5, 4 = 20

= 56/20 – 25/20

= (56 – 25)/20

= 31/20

Example 3: Add 4/3 and 5/4.

Solution:

= 5/3 + 5/4

LCM of 3, 4 = 12

= 20/12 + 15/12

= (20 + 15)/12

= 35/12

Example 4: Change 7(1/3) into an improper fraction.

Solution:

= 7(1/3)

= (7×3 + 1)/3

= 22/3

FAQs on Improper Fractions

1. What is an Improper Fraction?

An improper fraction is a type of fraction in which the numerator value of the fraction is greater than the denominator value of the fraction. We write improper fractions as a/b where a > b.

2. What are Examples of Improper Fractions?

Various examples of the Improper fractions are, 11/3, 4/2, 5/2, -17/7, -8/3, etc.

3. What is Difference between Proper Fraction and Improper Fraction?

The difference between a proper fraction and an improper fraction is learned using the table added below,

Proper Fractions	Improper Fractions
For proper fractions, the numerator value is smaller than the denominator value, i.e. (Numerator < Denominator)	For improper fractions, the numerator value is greater than the denominator value, i.e. (Numerator > Denominator)
Examples of proper fractions are 11/13, 4/5, 1/2, 2/3, etc.	Examples of improper fractions are 15/13, 14/5, 11/2, 12/7, etc.

4. Identify Improper Fractions out of 13/5, 3, 2/9, 4/2, 4/5.

 An improper fraction is one in which the numerator is higher than or greater than the denominator. 

Here improper functions are: 13/5, 4/2, 3.