# Properties of Multiplication of Fractional Numbers

We have previously discussed about multiplication of fractional number. However there are few properties of multiplication of fractional numbers which can be applied in certain cases in order to make calculation easier and faster. These properties are helpful in better understanding of the concept and for the purpose of calculation as well.

Property I:

If two or more fractional numbers are multiplied then they can be multiplied in any order.

Examples:

1. 5/7  × 14/3

= (5 ×14)/(7 ×3)

= 70/21

= 10/3

Now if we change the order of the two fractional numbers we get,

14/3 × 5/7

= (14 ×5)/(3×7)

= 70/21

= 10/3

So, we can see that if the order of fractional numbers are changed it does not affect the result. That is the result remains unchanged.

2. 5/7  × 14/3 × 9/10

= (5 ×14 ×9)/(7 ×3×10 )

= 630/210

= 3

Now if we change the order of the three fractional numbers we get,

9/10×14/3 × 5/7

= (9 ×14×5)/(10×3×7 )

= 630/210

= 3

So, again we can see that if the order of fractional numbers are changed it does not affect the result. That is the result remains unchanged.

Property II: If any fractional number is multiplied by 1 the result is the fractional number itself.

Examples:

1. 9/5 × 1

= 9/5 × 1/1

= (9 × 1)/(5 × 1)

= 9/5

2. 7/3 ×1

= 7/3 × 1/1

= (7 ×1 )/(3 × 1)

= 7/3

So we can see here that in both the cases the answer is the fractional number itself when multiplied with 1

Property III: If any fractional number is multiplied by zero the result is zero.

Examples:

1. 8/5 × 0

= 0

2. 11/9 × 0

= 0

Here, in both the cases hence we can see that the result is zero when a fractional number is multiplied with zero.

Property IV: If any fractional number is multiplied by its reciprocal then the result is always 1

Examples:

1. 1/17  × 17/1

= (1 × 17)/(17 × 1)

= 17/17

= 1

2. 3/7 × 7/3

= (3 × 7)/(7 × 3)

= 21/21

= 1

So, here in both the examples we can see that when a fractional number is multiplied by its reciprocal the result is 1.

Using the properties of multiplication here are few examples

Solve the following and state the property used:

(i) 0 × 8/7 × 5/3 = ……..

(ii) 1/19 × ……. = 1

(iii) 5/11 × ……. = 0

(iv) 15/7 × 9/11= …… ×15/7

(v) 13/5 × 5/13 = ……..

(vi) 6/7 × 7/15 × 21/23 = 21/23 × 6/7 × ………

Solutions:

(i) 0

Property: When a fractional number is multiplied by zero the answer is always zero.

(ii) 19

Property: When a fractional number is multiplied by its reciprocal the result is always 1.

(iii) 0

Property: When a fractional number is multiplied by zero the answer is always zero.

(iv) 9/11

Property: If two or more fractional numbers are multiplied then they can be multiplied in any order.

(v) 1

Property: When a fractional number is multiplied by its reciprocal the result is always 1.

(vi) 7/15

Property: If two or more fractional numbers are multiplied then they can be multiplied in any order.