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.

Also read,

- Properties of Multiplication of Fractional Numbers
- Properties of Divison
- Division of a Fractional Number

## 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.