Mixed Number

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. Numbers are of different types. In this article, we will learn about mixed numbers such as definition, changing of the improper fraction to a mixed fraction, and so on. Also, we will learn how to write a mixed number and also perform operations like addition, subtraction, multiplication, and division of mixed numbers.

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


What is a Mixed Number?

A mixed number is a combination of a whole number, and a proper fraction together. It is generally used to represents a number between any two whole numbers.


Mixed Number Example

Given below diagram represents a fraction that is greater than 1 but less than 2. Thus, it is a mixed number.



Some other examples of mixed numbers are:

3 ½, 4 ⅖, 5 ½, 8 ⅔


Mixed Number Fractions

A fraction represented by its quotient and a remainder is a mixed number fraction. For example, 5½ is a mixed fraction, where 5 is the quotient, 1 is the remainder. So, the formula of mixed fraction is a combination of a whole number and a proper fraction.


What is the Definition of Mixed Fraction?

It is a form of a fraction that consists of a fraction and a whole number.

Example: 3 ½, where 3 is the whole number and ½ is a fraction.


Mixed Fraction Meaning

A mixed number is formed by the combination of three parts i.e a whole number, a numerator, and a denominator. The numerator and denominator are part of the proper fraction that makes the mixed number.



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


Mixed Numeral

A mixed numeral expresses the exact same information as an integer written next to a fraction that is less than one. So, for example, 5⅓ is the mixed numeral equivalent of 16/3.


Mixed Fraction Formula

Following are the steps to convert an Improper fraction to a mixed fraction, which is called the mixed fraction formula.

Consider the number 7/3.

(i) Divide the Fraction’s numerator with the denominator, i.e. 7/3.

(ii) The integer part of the answer will be the integer part for a mixed fraction, i.e. 2 is an integer.

(iii) The Denominator will be the same as the original, i.e 3.

(iv) So, the improper fraction 7/3 is changed to a Mixed fraction as 2⅓.

Pictorial representation of mixed number 2⅓.


Adding Mixed Fractions

We can either add the same denominators for both the fractions or the denominators can differ too.

Here we have given a step-wise method to add the improper fraction with the same or different denominators.

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 4 the same.

  • Step 2: Add the numerators 6 + 5 = 11.

  • Step 3: If the obtained answer is in an improper form then convert it into a mixed fraction, i.e. 11/4  = 2(¾).

So, We have 2 (¾) wholes.


Adding With the Different Denominators

Add: 8/6 + 12/8

  • Step 1: First find the LCM of the denominators i.e. the LCM of 6 and 8 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: Add the Numerator and keep the denominators the same as it is.

32 / 24 + 36 / 24 

 = 68/24 = 17/6

  • Step 4: If the obtained answer is in an improper form then convert it into Mixed Fraction: 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 (Frequently Asked Questions)

1. What is a Mixed Fraction?

Ans: A fraction represented with its quotient and a remainder is a mixed fraction. For example, 3½ is a mixed fraction, where 3 is the quotient, 1 is the remainder.

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

Ans: 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?

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