Mixed Number

Dhristi JEE 2022-24

Introduction to Mixed Number

In mathematics, a number is an object used to count, measure, and label. A mixed number is a form of fraction and a whole number. Different types of numbers are used in mathematics.


In this article, we will learn about mixed numbers such as definition, changing of the improper fraction to a mixed fraction, and so on. One can quickly learn about every operation of Mixed numbers. Those are

  • Addition

  • Subtraction

  • Multiplication

  • Division


Read the complete article to understand the concept of mixed numbers.

What is a Mixed Number?

When a whole number and proper function combine and are represented in a new way, it is called a Mixed Number.


 It is generally used to represent a number between any two whole numbers.

Example of Mixed Number  

The diagram below represents a fraction that is greater than 1 but less than 2. Thus, it is a mixed number. That fraction which is more significant than one, but less than two is considered a mixed number.


The student will understand more about the mixed number when they know some examples. Some examples are    2 ½,  3 ⅔ etc.  

What is the Meaning of Mixed Fraction ?

In mathematics, a Mixed Number is the combination of a whole number and a fraction. The numerator and denominator are part of the proper fraction that makes the mixed number. [D8]  It is two-part in a fraction that helps to make the mixed number. Those are

  • Denominator

  • Numerator


So, a mixed number is partly a whole number and partly a fraction.

What is a Mixed Numeral?

A mixed numeral expresses the exact same information as an integer written next to a fraction that is less than one. The mixed numeral is the combination and fractional presentation of a whole number and valid number.


So, for example, 5⅓ is the mixed numeral equivalent of 16/3.

The Formula of Mixed Fraction 

One must flow the given steps one after another to convert an improper fraction to a mixed fraction, which is called the mixed fraction formula. Consider the number 7/3.

  • Step 1: Divide the numerator of the fraction with its denominator. That is 7/3.

  • Step 2: The integer part that the student will get in the answer will be considered the integer part of the fraction. 2 is an integer in this case.

  • Step 3: The denominator in the fraction will not change. It will be considered as the same given in the first. That is 3.

  • Step 4: After applying all the steps correctly, an improper fraction that is 7/3 will change into a Mixed fraction that is 2⅓


Pictorial representation of mixed number 2⅓

How to Add Mixed Fractions? 

We can either add the same denominators for both the fractions or the denominators can differ too. Here we have given a stepwise method to add the improper fraction with the same or different denominators. One can easily follow the given steps below to get the correct result.


Note: Before applying any arithmetic operations such as addition, subtraction, multiplication, etc., we need to change the mixed fractions to improper fractions.

Adding With the Same Denominators

Add: 6/4 + 5/4

  • Step 1: Keep the denominator of the fractions the same as given the question. In that case which is 4.

  • Step 2: Add the numerators of the fractions correctly.In that case which is 6+5=11.

  • Step 3: You can get your answer in improper fractions. In that case, change it with Mixed Fraction. In that case 11/4  = 2(¾).


So, We have 2 (¾) holes.

Adding With the Different Denominators

Add: 8/6 + 12/8

  • Step  1: Calculate the LCM of the denominators of the given fraction. That is 24, LCM of 6 and 8.

  • Step 2: In the next step, Multiply denominators of fractions and numerators of both fractions with a number such that they have the LCM as their new denominator. That is 8/6 by 4 and 12/8 by 3.

  • Step 3: Add the new numerator properly and keep the denominator the same. That is 32 / 24 + 36 / 24  = 68/24 =17/6

  • Step 4: You can get your answer in improper fractions. In that case, change it with Mixed Fraction. That is 2 (⅚).

Subtracting Mixed Fractions:

Here’s a step-wise explanation of how to Subtract the improper fraction with the Same or Different Denominators. Subtracting with the same Denominators.

Example: 6/4 – 5/4

Step 1: Keep the denominator ‘4’ the same.


Step 2: Subtract the numerators ‘6’ -’5’ = 1.


Step 3: If the obtained answer is in the improper form then convert it into a mixed fraction. i.e. ¼

Subtracting With the Different Denominator

Subtract 12/8 – 8/6

Step 1: Find the LCM of the denominators, i.e. the LCM of 8 and 6 is 24


Step 2: Multiply denominators and numerators of both fractions with a number such that they have the LCM as their new denominator.Multiply the numerator and denominator of  8/6 by 4 and 12/8 by 3.


Step 3: Subtract the numerator and keep the denominators the same as it is.36 / 24 – 32/24 = 4/24


Step 4: If the obtained answer is in an improper form then convert it into Mixed Fraction. 4/24 = 1/6.

Multiplication of Mixed Fractions

Example: 2(⅚)  × 3(½)

Step 1: Convert the given mixed fraction into an improper fraction. 17/6 × 7/2


Step 2: Multiply the numerators of both the fractions together and in similar way denominators of both the fractions together. (17 × 7)/(6 × 2)


Step 3: Now convert the fraction into the simplest form or Mixed fraction = 119/12 or 9(11/12).


Facts: Mixed number is also known as mixed fractions.


FAQs on Mixed Number

1. What is a Mixed Fraction?

All the fractions can be broken into two-parts.  Those are numerator and denominator. Those whose number of the numerator is more extensive than their denominator is an improper fraction. In that case, students must multiply the numerator by the denominator. After that, they will get a particular form of a fraction. That would be called a mixed fraction.


Example: 17/6 is an improper fraction. After dividing the numerator with the denominator, the student will get 2 (⅚). That is a mixed fraction.

2. How can we Convert an Improper Fraction to a Mixed Number?

To convert an improper fraction into a mixed number first divide the numerator by the denominator. After that write down the whole number result. In the next step use the remainder as the new numerator over the denominator.

3. What is the Mixed Number of 15/2?

Mixed number of 15/2 is 7½ because when we divide 15 by 2 we will get 7 as quotient and 1 as remainder.

4. What is a fraction? Type of fraction.

Fraction is a numeral quantity in mathematics. Fraction is not considered as a whole number. A fraction presents a part of a whole number. Fractions have a numerator and denominator. Example: 2/3, 3/5, 5/7 e.t.c


There are three types of fractions. Those are Proper fraction, Improper Fraction, and Mixed fraction.


Those fractions with a greater denominator than the numerator are called proper fractions. Example: 2/3


Those fractions that have greater numerators than denominators are called Improper fractions. Example: 7/4


 A mixed fraction is the modified form of an Improper fraction. Example: 2 (⅚).

5. How to add the same denominator mixed fraction?

Any student can add mixed fractions easily. They have to follow the steps and can get the result. Steps are -

Step 1: Keep the denominator of the fractions the same as given the question.

Step 2: Add the numerators of the fractions correctly.

Step 3: You can get your answer in improper fractions.

6. How to add different denominator mixed fractions?

Step  1: Calculate the LCM of the denominators of the given fraction.

Step 2: In the next step, Multiply denominators of fractions and numerators of both fractions with a number such that they have the LCM as their new denominator.

Step 3: Add the new numerator properly and keep the denominator the same.

Step 4: You can get your answer in improper fractions. In that case, change it with Mixed Fraction.

7. How Vedantu helps to gain knowledge about Mixed fractions?

In Vedantu, students can get all the necessary material to study Mixed Fractions. This includes the link that is available on this page. Other than these, students can also easily get all the study materials for all their classes, free of cost in Vedantu. Students can also download the Vedantu app which will help them to get their study materials faster.

Comment