# 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. 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.

• 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.

• 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.