Mixed Fractions

Mixed Fractions are one of the three types of fractions. It is also called Improper fractions. We will study mixed fractions in details in this article like the definition of mixed fractions, Conversion of the improper fraction to proper fraction and vice versa.

Definition of a Mixed Fraction:

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

Example2(1/7), where 2 is a whole number and 1/7 is a fraction.

Mixed Fractions Definition

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 function 15/7 is changed to a Mixedfraction – 2 (1/7)

Converting Improper Fraction to Mixed Fractions

Some more examples of mixed fractions 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).
\(7\times 2\) =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 the same i.e 7.
  • Step 4: The Improper fraction obtained is : 15/7.

Converting Mixed Fraction to Improper Fractions

How to Add Mixed Fractions?

When it comes to adding Improper or mixed 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 difference 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 Mixed fractions with the same Denominators.

Example: 6/4 + 5/4

Adding Mixed fractions 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)

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

Subtracting mixed fractions with the same Denominators. Example: 6/4 + 5/4 Subtracting Mixed fractions 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

How to Multiply Mixed Fractions?

Example: 2(⅚)  × 3 (½)

Solution:

Step 1: Convert the mixed fraction 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 fraction. =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 three types of fractions.

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.

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Practise This Question

If the graph of the equation 4x + 3y = 12 cuts the coordinate axes at A and B, then hypotenuse of right angle triangle AOB is of length