# Properties of Fractional Division | Division Properties of Fractional Numbers

This page will give all the information about the properties of the division of fractional numbers. Types of properties along with definitions and examples. A fraction is noting but the equal parts of a whole number, When we divide any number into equal parts, each part can be called a fraction. Fractions are usually represented in the form of $$\frac { x }{ y }$$, where x  is called a numerator, and y is known as a denominator. Refer to this entire module to know about different properties that are applicable to fractional division.

## Properties of Fractional Divison

There are various properties for fractional division. Each property is explained in detail by considering few examples as mentioned below

Property 1: A fractional number divided by 1 gives the fractional number itself.

This means whenever any fractional number is divided by 1 the result will be the same as the given number.

Example: Solve the equation dividing a whole number 1 with a faction number $$\frac { 2 }{ 4 }$$

Solution: We need to convert our given whole number 1 into a fractional number by simply just adding 1 as its denominator. which gives $$\frac { 1 }{ 1 }$$

The reciprocal of $$\frac { 1 }{ 1 }$$ will reamain same

Now we have to multiply both facrtions $$\frac { 1 }{ 1 } * \frac { 2 }{ 4 }$$

As we already know we can simplify this by multiplying numerators and denominators with each other $$\frac { 1 * 2 }{ 1 * 4 }$$

Which gives $$\frac { 2 }{ 4 }$$.

The result of dividing a whole number 1 with a facrtion $$\frac { 2 }{ 4 }$$ is $$\frac { 2 }{ 4 }$$.

Thus, Any given fractional number that is divided by 1 gives the resultant value as the same fractional number.

Property 2: A fractional number divided by zero(0) gives zero(0).

This means whenever any fractional number is divided by 0 the result will be zero.

Example: Solve the equation dividing a whole number 0 with a faction number $$\frac { 3 }{ 5 }$$

Solution: We need to convert our given whole number 0 into a fractional number by simply just adding 1 as its denominator but as we already know 0 divided by any number becomes 0.

The reciprocal 0 will be 0

Now we have to multiply $$\frac { 0 }{ 0 } * \frac { 3 }{ 5 }$$

As we already know we can simplify this by multiplying numerators and denominators with each other $$\frac { 0 * 3 }{ 0 * 5 }$$

Which gives $$\frac { 0 }{ 0 }$$.

The result of dividing a whole number 0 with a facrtion $$\frac { 3 }{ 5 }$$ is 0.

Thus, Any given fractional number that is divided by 0 gives the resultant value as 0.

Property 3: A fractional number divided by the same fractional number gives 1.

This means whenever any fractional number is divided by the same fractional number the result will be one.

Example: Solve the equation dividing a fractional number $$\frac {7}{5}$$ with the same faction number $$\frac {7}{5}$$

Solution: The reciprocal of $$\frac { 7 }{ 5 }$$ will be $$\frac { 5 }{ 7 }$$

Now we have to multiply both fractions $$\frac { 7 }{ 5 } * \frac { 5 }{ 7 }$$

As we already know we can simplify this by multiplying numerators and denominators with each other $$\frac { 7 * 5 }{ 5 * 7 }$$

Which gives $$\frac { 35 }{ 35 }$$

This can be simplifed as 1

The result of dividing a fractional number $$\frac { 7 }{ 5 }$$ with the  same facrtinal number $$\frac { 7 }{ 5}$$ is 1

Thus, Any given fractional number that is divided by the same fractional number gives the resultant value as 1.

### Example Problems on Division Properties of Fractional Numbers

Let us see few examples and find out which properties they are stating.

Example 1:

Solve the equation dividing a mixaed fractional number 3$$\frac {3}{5}$$ with the same mixed faction number 3$$\frac {3}{5}$$

Solution:

We need to convert our given Mixed fractional number into a simple fractional number by simply so 3$$\frac { 3 }{ 5 }$$ becomes $$\frac { 18 }{ 5 }$$

The reciprocal of $$\frac { 18 }{ 1 }$$ wiil be $$\frac { 5 }{ 18 }$$

Now we have to multiply both fractional numbers $$\frac { 18 }{ 5 } * \frac { 5 }{ 18 }$$

As we already know we can simplify this by multiplying numerators and denominators with each other $$\frac { 18 * 5 }{ 5 * 18 }$$

Which gives $$\frac { 90 }{ 90 }$$.

This can be simplified as 1

The result of dividing a mixed fractional number 3$$\frac { 3 }{ 5 }$$ with the same mixed fractional number 3$$\frac { 3 }{ 5}$$ is 1

This problem states our third property.

Example 2:

Solve the equation dividing a whole number 1 with a faction number 3$$\frac { 1 }{ 3 }$$

Solution:

We need to convert our given whole number 1 into a fractional number by simply just adding 1 as its denominator. which gives $$\frac { 1 }{ 1 }$$

The reciprocal of $$\frac { 1 }{ 1 }$$ will reamain same

We need to convert our given Mixed fractional number into a simple fractional number by simply so 8$$\frac { 2 }{ 3 }$$ becomes $$\frac { 26 }{ 3 }$$

Now we have to multiply both facrtions $$\frac { 1 }{ 1 } * \frac { 26 }{ 3 }$$

As we already know we can simplify this by multiplying numerators and denominators with each other $$\frac { 1 * 26 }{ 1 * 3 }$$

Which gives $$\frac { 26 }{ 3 }$$.

$$\frac { 26 }{ 3 }$$ can be repereted as mixed fractional number 8$$\frac { 2 }{ 3 }$$

The result of dividing a whole number 1 with a mixed facrtion 8$$\frac { 2 }{ 3 }$$ is 8$$\frac { 2 }{ 3 }$$

This problem states our first property.

Example 3:

Solve the equation dividing a whole number 0 with a faction number $$\frac { 6 }{ 5 }$$

Solution:

We need to convert our given whole number 0 into a fractional number by simply just adding 1 as its denominator but as we already know 0 divided by any number becomes 0.

The reciprocal 0 will be 0

Now we have to multiply $$\frac { 0 }{ 0 } * \frac { 6 }{ 5 }$$

As we already know we can simplify this by multiplying numerators and denominators with each other $$\frac { 0 * 6 }{ 0 * 5 }$$

Which gives $$\frac { 0 }{ 0 }$$.

The result of dividing a whole number 0 with a facrtion $$\frac { 6 }{ 5 }$$ is 0.

This problem states our second property.