Mixed Fractions

Mixed Fractions are one of the three types of fractions. It is also called Improper fractions. We will study these fractions in details in this article like its definition, changing of the improper fraction to proper fraction and vice versa. Also, we will learn here to perform operations like multiplying, dividing, adding and subtracting fractions.

Definition

It is a form of a fraction which is defined as the ones having a fraction and a whole number.

Example: 2(1/7), where 2 is a whole number and 1/7 is a fraction.

How to convert Improper fraction to a Mixed fraction?

  • Step 1: Divide the Fraction’s numerator with the denominator i.e 15/7.
  • Step 2: The integer part of the answer will be the integer part for a mixed fraction. i.e 2 is an integer.
  • Step 3: The Denominator will be the same as original, i.e 7.
  • Step 4: So, the improper fraction 15/7 is changed to a Mixed – 2 (1/7)

Some more examples of are 3(¼), 1 (2/9), 7(¾).

How to convert a Mixed fraction to an Improper Fraction?

  • Step 1: Multiply the denominator with the whole number integer. i.e Multiply 7 with 2 in the given example, 2(1/7).

7 × 2  =14

  • Step 2: Add the numerator of the Fraction to the result in step 1. i.e Add 1+ 14

=15.

  • Step 3: Keep the Denominator same i.e. 7.
  • Step 4: The Improper fraction obtained is: 15/7.

Addition

When it comes to adding Mixed or Improper fractions, we can have either the same denominators for both the fractions to be added or the denominators can differ too.

Here’s a step-wise method to add the improper fraction with same or different denominators.

Note: Change Mixed Fractions to Improper Fractions as shown above before applying any operations. (Addition, Subtraction, Multiplication).

Adding with the same Denominators.

Example: 6/4 + 5/4

 Adding with the different Denominators.

Example: 8/6 +12 /8
Step 1: Keep the denominator ‘4’ same. Step 1: Find the LCM between the denominators i.e The LCM of 6 and 8 is 24
Step 2: Add the numerators ‘6’ +’5’ =11. Step 2: Multiply both 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 with 4 and 12/8 with 3.
Step 3: If the answer is in improper form, Convert it into a mixed fraction. I.e 11/4  = 2 (¾) Step 3: Add the Numerator and keep the Denominators same.

32 / 24 + 36 / 24 = 68/24
So, We have 2 (¾) wholes. Step 4: If the answer is in Improper form, convert it into Mixed Fraction: 2 (⅚)

Subtraction

Here’s a step-wise explanation on how to Subtract the improper fraction with Same or different Denominators.

Subtracting with the same Denominators. Example: 6/4 + 5/4 Subtracting with the different Denominator 12/8 + 8/6
Step 1: Keep the denominator ‘4’ same. Step 1: Find the LCM between the denominators i.e The LCM of 8 and 6 is 24
Step 2: Subtract the numerators ‘6’ -’5’ =1. Step 2: Multiply both 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 with 4 and 12/8 with 3.
Step 3: If the answer is in improper form, Convert it into a mixed fraction. i.e. 1/4 Step 3: Subtract the Numerator and keep the Denominators same. 36 / 24 + 32/24 = 4/24
So, We have 1/4 wholes. Step 4:If the answer is in Improper form, convert it into Mixed Fraction. 4/24 = 1/6

Multiplication

Example: 2(⅚)  × 3 (½)

Solution:

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

Step 2: Multiply the numerators of both the fractions together and denominators of both the fractions together. {17 ×  7} {6 × 2}

Step 3: You can convert the fraction into the simplest form or Mixed one = 119 / 12 or 9 (11/12)

Definition of Fraction

The ratio of a whole number is called as a Fraction.

For Example, 15/7  is a fraction, where 15 is a numerator and 7 is a denominator. 7 is the number of parts into which the whole number divides.

A fraction can represent part of a whole.

Types of Fractions

There are basically three types of fractions. Below given table defines all the three of them.

Types of Fractions Explanation
Proper Fraction When the numerator is less than Denominator
Improper Fraction When the numerator is greater than or equal to the Denominator.
Mixed Fraction It is an improper function, which is written as a combination of a whole number and a fraction.