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 xÂ  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:Â 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:Â 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:Â 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 theÂ  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.

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