Dividing Fractions: Division of two fractions involves the process of multiplication of two fractions. Reciprocal of the denominator should be obtained and multiplied to the numerator. The transformation of the division problem to a multiplication problem has to be done carefully by inverting the divisor.

**Facts to be kept in mind while dividing fractions are as follows:**

- The first term which is to be divided is called dividend.
- The second term which is written after the sign of division is known as divisor.

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

## How to Divide Fractions

Division of fraction is the process of multiplying the reciprocal of the second fraction with the first fraction.

**Steps for Dividing Fractions:**

Step 1: Reciprocate the divisor.

Step 2: Change the division sign into multiplication.

Step 3: Cancel the common terms (if there are any) from numerator and denominator.

Step 4: Multiply all the remaining terms in numerator as well as in the denominator.

**Rules of division of fractions:**

- If mixed fraction present, needs to be converted into improper fraction
- Change the divisor sign to multiplication sign
- Multiply the first fraction by the inverted divisor fraction

Division of fractions will be carried out in the following steps as shown below.

Divide a/b ÷ c/d

Get the reciprocal of the second fraction by inverting the fraction and Change the sign to multiplication

a/b x d/c

Multiply the fraction and reduced it.

a/b x d/c = ad/bc.

## Dividing Fractions Examples

Few examples of division of fractions are given below:

Solution:

27/8 ÷ 3/4 = 27/8 x 4/3

= 9/2×1/1

= 9/2

Solution:

256/5÷ 16 = 256/5÷161

= 256/5 x 1/16

= 16/5

Solution:

Division 69 by 81

Keep the first fraction 6/9 as it is = 6/9

And then reciprocal the second fraction 8/1 = 1/8

Now multiply the both fractions = 6/9 x 1/8 = 6/72 = 3/36

Correct answer is 1/12

## How to Divide Fractions by Whole Numbers

The division on whole numbers is simple and easy. The whole numbers division may result in the whole numbers, finite numbers, and so on.

**How to Divide Fractions with Whole Numbers**

The following steps are used to solve a fraction with whole number:

- Step 1: Convert a whole number in to a fraction that is 7 is numerator and 1 is a denominator under 7, so you have 7/1.
- Step 2: To obtain the reciprocal of the newly converted fraction 71 , take reciprocal. Reciprocal means a fraction turned up, side down. So the reciprocal of 7/1 is 1/7. The reciprocal allows division into a multiplication.
- Step 3: Multiply the two denominators and two numerators. We have 4×1/3×7 = 4/21 .

**Divide Fractions with Whole Numbers Examples**

Solution:

Step 1: Convert a whole number in to a fraction part.

A whole number= 5

So, We get, 5/1

Step 2: Find reciprocal of a newly converted fraction.

Converted fraction = 5/1

Reciprocal = 1/5

Step 3: Multiply two denominator and two numerator

8/5 x 1/5

8×1/5×5

We get, 8/25 .

The Final answer is 8/25.

## Dividing Mixed Fractions

A mixed number or mixed fraction is the sum of a whole number and a proper fraction. This sum is implied without the use of any visible operator such as “+”, for example, in referring to two entire cakes and three quarters of another cake, the whole and fractional parts of the number are written next to each other: 2 + 3/4 = 2 3/4 .

Mixed number a b/c . Here,

a = Quotient.

b = Remainder

c = Divisor.

**How to Divide Mixed Fractions**

- Step 1: Convert the mixed fraction into normal fraction for both divisor and dividend
- Quotient Remainder/Divisor = (Quotient x Divisor) + Remainder/Divisor
- 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.

**Dividing Mixed Fractions (Numbers) Examples**

Below are the solved examples on how to divide mixed fractions or mixed numbers.

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,

606/348 = 606/6 ÷ 348/6

**Correct answer is 101/58**

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 = (3×11)+8/11

= 41/11

7 3/2 = (7×2)+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 = 41×2/11×17

**Correct answer is 82/187**

Solution:

Given , two mixed fractions 12 4/7, 27 2/3

We need to dividing the above fractions.

First we convert it into fractions.

12 4/7 = (12×7)+4/7

= 88/7

27 2/3 = (27×3)+2/3

= 83/3

12 4/7 ÷ 27 2/3 = 88/7 ÷ 83/3

Take a reciprocal for 83/3

Reciprocal of 83/3 = 3/83

Now multiply it with 88/7

12 4/7 ÷ 27 2/3 = 88/7 ÷ 88/3 = 88/7 x 3/83

88/7 x 3/83 = 88×3/7×83

**Correct answer is 264/581**

## Dividing Fractions Word Problems

Below there are some solved examples on how do you divide fractions:

Solution:

Keep the first fraction 34/6 as it is = 34/6

Reciprocate the second fraction 34/6 = 6/34

Now, multiply both the fractions = 34/6 x 6/34

**Correct answer is 1**

Solution:

Keep the first fraction 6/9 as it is = 6/9

Reciprocate the second fraction 8/2 = 2/8

Now, multiply both the fractions = 6/9 x 2/8 = 12/72

**Correct answer is 1/6**

Solution:

Keep the first fraction 1/4 as it is = 1/4

Reciprocate the second fraction 3/4 = 4/3

Now, multiply both the fractions = 1/4 x 4/3

**Correct answer is 1/3**