# Properties of Fractional Division

We are already learnt division of fractional numbers. It is basically multiplication of the first fraction with the reciprocal or multiplicative inverse of another fractional number. In case of finding the multiplicative inverse we actually interchange the numerator and denominators, where a proper fraction is converted into an improper fraction and an improper fraction is converted into a proper fraction. However, this topic deals with the properties of division. The understanding of the properties of division will help the students in better understanding of the concept of division and would lead to more in-depth knowledge along with the properties of multiplication learnt in previous topic as both the properties of division and multiplication are related.

The properties of division of fractional numbers are discussed below:

Property I:

When a fractional number is divided by itself the result is always 1.

Here are few examples to justify property 1:

1. 9/5 ÷ 9/5

= 9/5 × 5/9

= (9 ×5)/(9 ×5)

= 45/45

= 1

2. 15/7 ÷ 15/7

= 15/7 × 7/15

= (15 ×7)/(7 ×15)

= 105/105

= 1

Explanation:

From the examples we can see that any fraction divided by itself is 1. As the fraction is divided by the multiplicative inverse of itself when both the numerator and denominator gets reduced to lowest terms the answer is 1.

Property II:

If a non- zero fractional number is divided by 1 the result is the fractional number itself

Here are few examples to justify property 2:

1. 9/7 ÷ 1

= 9/7 × 1

= 9/7

2. 11/9 ÷ 1

= 11/9 ×1

= 11/9

Explanation:

From the example it is clear that fractional number divided by 1 is the fractional number itself. As the multiplicative inverse of 1 is 1 only. According to the rule of division,

Division = 1st fraction multiplied by the multiplicative inverse of the second fraction/ whole number.

Here the second number is 1 whose multiplicative inverse is also 1. Again according to the properties of multiplication anything multiplied by 1 is the number itself. Hence, fractional number divided by 1 is the fractional number itself.

Property III:

If zero is divided by a non-zero fractional number then the result is zero.

Here are few examples to justify property 3:

1. 0 ÷ 9/5

= 0 × 5/9

= 0

2. 0 ÷ 15/7

= 0 × 7/15

= 0

Explanation:

In the above two examples we can see that when zero is divided by a non-zero fractional number the result is always zero. As we can see that we are finding out the multiplicative inverse of the second fraction. After finding the multiplicative inverse of the second fraction it is actually multiplied with 0 any we know from the properties of multiplication that anything multiplied by zero is zero.

Hence in example (i)

0 ÷ 9/5  = 0

And in example (ii)

0 ÷ 15/7

= 0

Property IV:

As, fractional number cannot be divided by zero hence multiplicative inverse of 0 does not exists.

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