Mixed Numbers: A mixed number (mixed fraction) can be explained as a fraction and a whole number. Any improper fraction could be expressed as mixed number and vice-versa. For changing a mixed number into an improper fraction, begin multiplying the whole number by the denominator and then add the numerator to get the result.

In this article we will learn about mixed fractions, definition, converting mixed fraction to Improper Fraction and, adding, subtracting, multiplying and dividing fractions along with examples.

## Table of Contents

## Mixed Fraction Definition

Mixed number (mixed fraction) is one of the form of fraction. Mixed number is also called as mixed fraction. Mixed numbers are defined the number which is having the fraction numbers and the whole numbers.

For example, 2 4/5 is a mixed fraction 2 is a whole number 4/5 .

**Examples:** 1 1/3, 2 1/4, 16 2/5.

One way Improper fraction convert to a mixed number is to divide the fraction’s numerator by its denominator. The integer part of the answer of division is the integer part of the mixed number. The denominator is the same as the original denominator. Another way Divide the numerator of fractions by its denominator and then convert the decimal portion of the answer to a fraction.

Examples: 4/3, 11/4, 7/7

- Fractions
- Simplify Fractions
- Adding Fractions
- Multiplying Fractions
- Subtracting Fractions
- Dividing Fractions
- Proper Fractions
- Improper Fractions
- Mixed Fractions
- Like Fractions
- Unlike Fractions
- Fraction Calculator
- Fraction Simplifier
- Mixed Fraction Calculator
- Convert Fraction to Decimal
- Convert Decimal to Fraction

## How to Convert Mixed fraction to Improper Fraction

**Follow these steps to convert mixed number (mixed fraction) to improper fraction:**

- The denominator of the mixed number is multiplied with the whole number of the mixed fraction.
- After the first step completed the numerator part is added with the multiplied value.
- The sum will become the improper fraction of numerator and the denominator is placed as it is given.
- The denominator of the mixed number will be same as the denominator of the improper fraction.

Example: Convert 4 2/5 to an improper fraction.

Multiply the whole number by the denominator: 4 × 5 = 20

Sum up the numerator to that: 20 + 2 = 22.

Then note down that above number as denominator, like this: 22/5

## How to Convert Improper Fraction to Mixed Fraction

**Following are the steps to convert an improper fraction to mixed fraction:**

- By Dividing the numerator with the denominator and then
- Write down the whole number answer
- Write down any remainder which we got above the denominator.

Example: Convert 11/4 to a mixed fraction.

Divide: 11 ÷ 4 = 2 with a remainder of 3

Take down the 2 and then write down the remainder (three) above the denominator (four), like this: 2 3/4

**When to Use Improper Fractions or Mixed Fractions**

For everyday use, people understand mixed fractions better. For example, It is comfortable to say “I had 2 1/4 cup of milk”, than “I had 9/4 cup of milk”.

## How to Add Mixed Fractions

**The following are the steps for adding mixed fractions:**

- Step 1: Change the given mixed fractions into improper fractions.
- Step 2: If the denominators are different, then convert the fractions to fractions with a common denominator.
- Step 3: Add the numerators and keep the denominator as same
- Step 4: If the sum is an improper fraction, convert it to a mixed number.
- Step 4: If possible, simplify the answer

**Adding Mixed Fractions Examples**

Question 1: Add the mixed number 5 1/2, 11 1/2

Solution:

Step 1: Change the mixed numbers into improper fractions

5 1/2 = (5×2)+5/2 = 1/2

11 1/2 = (11×2)+1/2 = 23/2

The improper fractions are 11/2, 23/2

Step 2: Here the denominators are same. So add the numerators

11/2 + 23/2 = 11+23/2 = 34/2

Step 3: Simplify

34/2 = 17

Correct answer is 17

Question 2: Add the mixed fractions 7 3/2 , 3 1/4

Solution:

Step 1: Change the mixed numbers into improper fractions

7 3/2 = (2×7)+3/2 = 17/2

3 1/4 = (4×3)+1/4 = 13/4

The improper fractions are 17/2, 13/4

Step 2: Here the denominators are different, take LCM.

LCM of 2, 4 = 4

17/2 = (17×2)/2×2 = 34/4

Step 3: Add the numerators

17/2 + 14/4 = 34/4 + 13/4

= 47/4

Step 4: Simplify and Express the answer as a mixed number

47/4 = 11 3/4

Correct answer is 11 3/4

Question 3: Multiply the following fraction and the mixed number 3/4 x 4 5/4

Correct answer is 1 19/20

Question 4: Multiply the following fraction and the mixed number 5/6 x 4 5/4

Correct answer is 4 9/24

Question 5 : Multiply the following fraction and the mixed number 6/7 x 5 8/5

Correct answer is 23/35

Question 6: Add the mixed fractions 2 8/12 , 5 1/2 , 11 1/4

Correct answer is 19 5/12

## How to Subtract Mixed Fractions

Subtracting mixed numbers can often be done by subtracting whole number from whole number and fraction from fraction. The subtraction is generally called as the arithmetic notation. In subtracting mixed fractions concept, before subtracting mixed fractions convert them into a proper fractions.

**Steps For Subtracting Mixed Fraction:**

- Step 1: Express the fractions as equivalent fractions having the lowest common denominator.
- Step 2: Subtract the numerators.
- Step 3: Reduce the answer to lowest terms, if necessary.
- Step 4: Again convert fraction to the mixed number.

**Subtracting Mixed Fractions Examples**

Question 1: Calculate the subtraction of mixed fraction is 9 5/9 – 6 2/9

Solution:

= 9 5/9 – 6 2/9

= 86/9 – 56/9

= (86 – 56)/9

= 30/9

Question 2: Calculate the subtraction of mixed fraction is 8 4/12 – 6 6/12

Solution:

= 8 4/12 – 6 6/12

= 100/12 – 78/12

= (100 – 78)/12

= 22/12

= 11/6

Question 3: Calculate the subtraction of mixed fraction is 6 1/8 – 8 2/4

Solution:

= 6 1/8 – 8 2/4

= 49/8 – 34/4

The denominator value is different so we take the LCM

The LCM value is 8.

= (49 * 1 – 34 * 2)/8

= (49 – 68)/(8)

= -19/8

## How to Multiply Mixed Fractions

In order to multiply two mixed fractions, first convert the mixed fractions into improper fractions. Then multiply the numerators together and multiply the denominators together. An improper fraction is a fraction in which the numerator is greater than the denominator.

**Steps for Multiplying Mixed Fractions**

Below are the steps to multiply mixed fractions:

- Step 1: Convert mixed fractions to improper fractions.
- Step 2: Multiply numerators together and multiply the denominators together.
- Step 3: Again convert improper fraction to mixed fractions.
- Step 4: If possible simplify the result obtained in Step 3 and write the final answer.

**Multiplying Mixed Fractions Examples**

Example 1: Multiply the mixed fractions: 3 4/5 and 2 3/6

Solution:

Step 1: Convert given fractions to improper fractions

3 4/5 = 19/5

2 3/6 = 15/6

Step 2: Multiply the numerators and then denominators

19/5 x 15/6 = 285/30

Step 3: Simplify 285/30.

285/30 = 19/2 (Divided numerator and denominator by 15)

9 1/2 (By converting in mixed number)

Correct answer is 3 4/5 x 2 3/6 = 9 1/2

Example 2: Solve 1 3/4 x 2 2/3

Solution:

Step 1: Convert given fractions to improper fractions

1 3/4 = 7/4

2 2/3 = 8/3

Step 2: Multiply the numerators and then denominators

7/4 x 8/3 = 56/12

= 14/3 (By simplifying)

= 4 2/3 (By converting in mixed number)

Correct Answer is 1 3/4 x 2 2/3 = 4 2/3

## How to Divide Mixed Fractions

**Steps for Dividing Mixed Fractions:**

- Step 1: Convert the mixed fraction into normal fraction for both divisor and dividend
- Step 2: Now take a reciprocal of the divisor.
- Step 3: Multiply the reciprocal fraction with the dividend fraction.
- Step 4: If it is possible, we can simplify it further.

**Below are the solved examples on how to divide mixed fractions**

Solution:

Given , two mixed fractions 8 5/12, 4 5/6

We need to dividing the above fractions.

First we convert it into fractions.

8 5/12 = (12×8)+5/12 = 101/12

4 5/6 = (4×6)+5/6 = 29/6

8 5/12 ÷ 4 5/6 = 101/12 ÷ 29/6

Take a reciprocal for 29/6

Reciprocal of 29/6 = 6/29

Now multiply it with 101/12

8 5/12 ÷ 4 5/6 = 101/12 ÷ 29/6 = 101/12 x 6/29

= 606/348

We can simplify it further.

Divide by 6 on both numerator and denominator,

606348 = 606/6 / 348/6

Correct answer is 10/158

Solution:

Given , two mixed fractions 3 8/11, 7 3/2

We need to dividing the above fractions.

First we convert it into fractions.

3 8/11 = 41/11

7 3/2 = 17/2

3 8/11 ÷ 7 3/2 = 41/11 ÷ 17/2

Take a reciprocal for 17/2

Reciprocal of 17/2 = 2/17

Now multiply it with 41/11

3 8/11 ÷ 7 3/2 = 41/11 ÷ 17/2 = 41/11 x 2/17

41/11 x 2/17 = 82/187

Correct answer is 82/187

Question 3: Dividing the mixed fractions 12 4/7 ÷ 2 72/3

Solution:

Given , two mixed fractions 12 4/7 , 2 72/3

We need to dividing the above fractions.

First we convert it into fractions.

12 4/7 = 88/7

2 72/3 = 83/3

12 4/7 ÷ 2 72/3 = 88/7 ÷ 83/3

Take a reciprocal for 83/3

Reciprocal of 833 = 3/83

Now multiply it with 88/7

12 4/7 ÷ 2 72/3 = 88/7 ÷ 83/3 = 88/7 x 3/83

88/7 x 3/83 = 264/581

Correct answer is 264/581

## How to Solve Mixed Fractions? – Examples

**Below are the Mixed fraction examples:**

Question 1: Convert 13/3 into a mixed fraction.

Solution:

First Divide 13 ÷ 3 = 4 with a remainder of 1

Write down the 4 and then write down the remainder (1) above the denominator (3)

= 4 1/3

Question 2: Convert 12/5 into a mixed fraction.

Solution:

First Divide 12 ÷ 5 = 2 with a remainder 2

Write down the 2 and then write down the remainder (2) above the denominator (5)

= 2 2/5 this is improper fraction.

Question 3: Convert 21/4 into a mixed fraction.

Solution:

First Divide 21 ÷ 4 = 5 with a remainder 1

Write down the 5 and then write down the remainder (1) above the denominator (4)

= 5 1/4 this is improper fraction.

Question 4: Convert 1 3/5 to an improper fraction.

Solution:

Multiply the whole number by the denominator: 1 × 5 = 5

Add the numerator to that: 5 + 3 = 8

Then write that down above the denominator, like this: = 8/5

Question 5: Convert 3 2/5 to an improper fraction.

Solution:

Multiply the whole number by the denominator: 3 × 5 = 15

Add the numerator to that: 15 + 2 = 17

Then write that down above the denominator, like this:= 17/5

Question 6: Convert 5 6/7 to an improper fraction.

Solution:

Multiply the whole number by the denominator: 5 × 7 = 35

Add the numerator to that: 35 + 6 = 41

Then write that down above the denominator, like this:= 41/7