Types of Fractions
Before exploring the types of fractions, let us recall fractions. A fraction is nothing but a part of a whole thing. In many realtime situations, each and every quantity to be measured cannot be an absolute whole number. Hence, we may have to deal with parts of a whole or portions of a whole. This is where the concept of fraction turns in. In this lesson, let us learn about proper and improper fractions, mixed fractions, equivalent fractions, like and unlike fractions.
1.  What are Types of Fractions? 
2.  Improper Fraction to Mixed Fraction 
3.  Mixed Fraction to Improper Fraction 
4.  FAQs 
What are Types of Fractions?
A fraction is defined by two parts, the numerator, and the denominator. The numerator is the number on the top, while the number on the bottom is called the denominator. The numerator indicates the number of equal parts taken, whereas the denominator indicates the total number of equal parts in a whole.
Based on numerator and denominator, which are parts of a fraction, there are different types of fractions. A fraction can be classified under the following categories:
 Proper fraction
 Improper fraction
 Mixed fraction
Proper Fractions
A fraction whose numerator is less than its denominator is called a proper fraction. For example, 3/12 and 2/5 are the proper fractions because 3 < 12 and 2 < 5. Example: Sam got a bar of chocolate and divided it into 3 equal parts. He took 1 part and gave 2 parts to his sister, Sara. You represent Sam's portion as 1/3 and Sara's portion as 2/3. Both these fractions are considered proper fractions.
Improper Fractions
A fraction whose numerator is greater than or equals to its denominator is called the improper fraction. For example, 5/2 and 8/7 are improper fractions because 5 > 2 and 8 > 7. Example: Sam gets two pies ordered. He divides both the pies equally into 4 pieces each. There are 5 members in his family. Each of them takes a piece of the pie. This is represented as 5/4.
Mixed Fractions
A mixed fraction is a mix of a whole number and a proper fraction. Let's get back to the same example of Sam's pies. We will see how 5/4 can be expressed as a mixed fraction. 5/4 can also be represented as a whole and 1/4 which is equivalent to \(1 \dfrac{1}{4}\).
A group of fractions is classified as the following and these determine the comparison between two or more fractions.:
 Like fractions
 Unlike fractions
 Equivalent fractions
Like Fractions
If the denominators of two or more fractions are the same, then they are called the like fractions. For example 1/6, 2/6, 3/6, 5/6, etc. We can perform the addition and subtraction of fractions only on like fractions.
Unlike Fractions
If the denominators of two or more fractions are different, then the fractions are unlike fractions. For example 1/2, 1/3, 2/5, 3/6, etc. If the fractions are unlike while adding or subtracting the fractions, we convert them to like fractions.
Equivalent Fractions
Equivalent fractions are the fractions that have different numerators and different denominators but are equal to the same value. For example, 2/4, 3/6, 4/8 are all equal to 1/2. So, these fractions are equivalent fractions.
Improper Fraction to Mixed Fraction
To convert improper fractions to mixed fractions, we need to divide the numerator by the denominator. Then, we write it in the mixed number form by placing the quotient as the whole number, the remainder as the numerator and the divisor as the denominator. Let us go through the following example to understand this better. Let the improper fraction be 12/5. To convert it into a mixed fraction, we follow these steps:
 Divide 12 by 5
 On dividing, we obtain the quotient as 2 and the remainder as 2
 Quotient is the whole number part and the remainder 2 is written as 2/5
 Thus, the mixed fraction is represented as \(2\dfrac{2}{5}\)
Mixed Fraction to Improper Fraction
A mixed fraction is a mixture of a whole and a proper fraction. In order to convert a mixed fraction to an improper fraction, you need to multiply the denominator with the whole number part and then add the numerator to the product. The resultant will be the new numerator, whereas, the denominator remains the same. Let us go through the following example to understand this better. Let the mixed fraction be \(7\dfrac{3}{5}\). To convert into an improper fraction, we follow these steps:
Method 1:
 Rewrite 7 as a fraction with 5 as the denominator. So, we can write 7 = 35/5
 Add the fractions: 35/5 + 3/5 = 38/5
Method 2:
 Multiply the whole number 7 with the denominator 5. So, we get 7×5 = 35
 Add the product with the numerator: 35+3= 38
 Express it as a fraction with the denominator 5, that is, 38/5
Important Points
Given below are a few important points:
 An improper fraction is always greater than 1.
 A proper fraction is always less than 1.
 A mixed fraction is the combination of a whole number and a fraction.
 A mixed fraction can be converted into an improper fraction and vice versa. For example, \(2\dfrac{1}{2}\) = 5/2.
Thinking Out of the Box!
 Ron, Patrik, and Sam bought 2 cakes. How can they divide it evenly among themselves?
 Ria gets 2 pizzas and eats 3/4 of them. How much is left?
Solved Examples on Types of Fractions

Example 1: Classify the following as proper fractions or improper fractions: 3/7, 18/23, 51/26, 16/11
Solution:
The given fractions can be classified as:
 The fractions which have numerator < denominator are considered proper fractions. Therefore, 3/7, and 18/23 are proper fractions.
 The fractions which have numerator ≥ denominator are considered improper fractions. Therefore, 51/26, and 16/11 are improper fractions.

Example 2: Jack and Jane ordered 2 pizzas. They together ate 1 whole pizza and 2/6^{th} of the second pizza. What fraction of pizza have they eaten?
Solution:
Jack and Jane ate 1 + 2/6 pizzas, which can be represented as a mixed fraction, \(1\dfrac{2}{6}\). To represent an improper fraction, take LCM and add both the numbers, 1 and 2/6 ⇒ 8/6. Therefore, Jack and Jane ate \(1\dfrac{2}{6}\) or 8/6 pizzas.
FAQs on Types of Fractions
What are the Three Types of Fractions?
The three types of fractions, based on the numerator and the denominator are proper, improper, and mixed fractions.
How do you Solve Fractions?
Solving fractions or operations on two or given fractions can be performed in the following ways:
 Addition and subtraction are performed on like fractions (fractions with the same denominators). 1/3 + 4/3 = 5/3 = \(1\dfrac{2}{3}\) , 1 3/4 =1/4
 For unlike fractions, they are first converted into like fractions in order to add or subtract them. 1/3 + 1/2 = 5/6
 Multiplication of two given fractions is done by multiplying the numerators and the denominators. 1/3 ×1/2 = 1/6
 Division of one fraction by another is done by multiplying after taking the reciprocal of the second fraction. 1/3 ÷ 1/2 = 2/3
What are Proper Fractions?
The fraction that has the numerator less than the denominator is called a proper fraction. Example: 5/12, 3/8.
What are Two Parts of a Fraction?
A fraction has two parts, i.e. numerator and denominator. These are explained below:
 Numerator: The number on the top tells how many equal parts of the whole or collection are taken.
 Denominator: The number below the line which tells the whole or the total collection.
What is a Mixed Fraction?
A fraction represented as a combination of a whole and a proper fraction is a mixed fraction. For example, \(2\dfrac{1}{3}\) a mixed fraction, where 2 is the whole, 1/2 is the proper fraction.
How do you Know Fractions are Similar?
Two or more fractions having exactly the same denominator are like fractions. In other words, the fractions with the same numbers in the denominators are like fractions. For example, 1/7, 2/7, 5/7, 6/7 are all like fractions, with the denominator, that is, 7