Different Types of Fractions – Proper, Improper, Mixed Fractions

Types of Fractions and their rules, methods, and formulae are defined here. Know the various types of fractions along with their usage in various situations. Refer to the terminology involved in fractions and also know the problems involved in it. Follow fraction rules and real-life scenarios of fractions. Check the below sections to find examples, rules, methods, etc.

Types of Fractions | What are Fractions?

Before going to know about types of fractions, first know what are fractions and how they work in real life. Fractions are derived from the Latin word “fractus” which means the number or quantity that represents the part or portion of the whole. In the language of layman, a fraction means a number that describes the size of the parts of a whole. Fractions are generally declared with the numerator displaying above the line and below the line, the denominator will be displayed. The terms numerators and denominators are also used in other fractions like mixed, complex, and compound.

Fractions can be written as the equal or same number of parts being counted which is called the numerator over the number or quantity of parts in whole which is called the denominator. There are three major types of fractions which are proper fractions, improper fractions, and mixed fractions. These fractions are divided based on numerator and denominator. Apart from these major fractions, there are also other fractions such as like fractions, unlike fractions, equivalent fractions, etc.

Proper, Improper, and Mixed fractions are defined as single fractions and the remaining fractions determine the comparison of fractions.

Fraction Definition and Terminology

The fraction is considered as the ratio between two numbers. Fractions are defined by a/b. a is called the numerator which means the equal number of parts that are counted. b is called the denominator which means a number of parts in the whole. The numerator and denominator are divided with a line. The line denoted the separation between the numerator and the denominator.

Fraction Types

There are various types of fractions available. We have listed a few of them and explained their definitions, examples in detail. They are as such

1. Proper Fraction:

A proper fraction is that where the value of the numerator is less than the value of the denominator

If you include a numerator, a denominator and a line in between, then it is called a fraction. Proper Fraction is defined as Numerator < Denominator. The value of the proper fraction is always less than 1.


1/2, 9/15,30/45 are the proper fractions

2. Improper Fraction:

An improper fraction is that where the value of the denominator is less than the value of the numerator. Improper fractions are defined as Numerator > Denominator. Each natural number can be written in fractions in which the denominator is always 1. For example: 20/1,40/1,35/1. The value of the improper fraction is always greater than 1.


3/2, 16/10,45/15 are the improper fractions

3. Mixed Fraction:

A mixed fraction is the combination of a natural number and a fraction. These fractions are improper fractions. Mixed fractions can easily be converted into improper fractions and also mixed fractions can also be converted to improper fractions. The mixed fraction is always greater than 1.


3 4/3, 4 5/4, 6 2/3

4. Like Fraction:

If the fractions have the same denominator, then they are called like fractions. For additional simplifications, we can easily make with the like fractions. Addition, Subtraction, Division and multiplication operations can be made easily on like factors.


1/2,3/2.5/2,7/2,9/2 are like fractions.

5. Unlike Fractions:

If the factors have different or unique denominators, then they are called, unlike fractions. Simplification of fractions is a lengthy process, therefore we factorize the denominators and then simplify the numerators.

Suppose that we have to add two fractions 1/2 and 1/3.

As the denominators are different, take the LCM of 2 and 3 is equal to 6.

Now, we multiply 1/2 and 1/3 by 2. Multiply it both in numerator and denominator.

Therefore, the fraction becomes 3/6 and 2/6

Now if add 3/6 and 2/6, we get 5/6


1/3,1/5,1/7 are unlike fractions

6. Equivalent Fractions:

When more fractions have a similar or same result even after simplification, they represent a similar portion of the whole. Those fractions are equal or similar to each other which are called equivalent fractions.


1/2 and 2/4 are equivalent to each other.

1/3 and 3/9 are also equivalent to each other.

How to Convert Improper Fractions into Mixed Fractions?

To convert an improper fraction into mixed fractions, the numerator is divided by the denominator, and the quotient is written as the whole number and the remainder as the numerator.


Convert the fraction 17/4 into a mixed fraction?


To solve the above problem, the steps undertaken are

  • Divide the numerator of the given fraction 17 by the denominator of the fraction 4.
  • After solving, the quotient is 4 and the remainder is 1.
  • Now, combine the whole number 4 with the fraction of 1/4.
  • Therefore, the mixed fraction is 4 1/4.

How to Convert Mixed Fraction to Proper Fraction?

The mixed fraction is converted to a proper fraction by multiplying the denominator of the fraction with the whole number and the product is added to the numerator.

The steps that are to be followed to convert mixed fraction as a proper fraction are:

  • Multiply the denominator with the whole number.
  • Suppose that 2 1/3 is an improper fraction.
  • In the above equation, 2 is the whole number and 3 is the denominator.
  • 2 * 3 = 6
  • Add the product of the numerator
  • 6 + 1 = 7
  • Now, after adding the product, numerator changes to 7 and denominator changes to 3.
  • Now, write the result as an improper fraction as 7/3

How to add Unlike Fractions?

To add the unlike fractions, first, we have to convert them to like fractions. The steps that are involved in adding the unlike fractions are:

  1. First, calculate the LCM of both the denominators.
  2. The result of LCM will be the denominator of fractions.
  3.  Now, we have to calculate the equivalent value of the 1st fraction. To calculate the equivalent, first, divide the LCM calculated in the previous step with the denominator of the 1st fraction. Now, multiply the numerator with the denominator value.
  4. In the same way, calculate the equivalent value of the second fraction. To find the equivalent value of the 2nd fraction, divide that LCM that is calculated in the first step by the denominator of the second fraction. Now multiply it with the numerator, therefore both the fractions have the same numerator.
  5. Finally, add both the values of the numerator as shown in the previous section.

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