Understanding Mixed Numbers in Mathematics

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.