Math Examples of Properties of Rational Numbers

We have a rational  number r  =   4/5, then additive inverse of r is -4/5,                                             because it produces 0  as  a  result,  4/5 + (-4/5 ) = 0.             This is an example which shows the additive inverse of simple rational number.      

2 can be written as 2/1 as a rational number, now its reciprocal is 1/2.

Multiplying rational number 2 with it’s reciprocal.

2/1*1/2 = 1,

  Dividing rational number 2 with it’s reciprocal. 2/1÷1/2 = 2/1*2/1 = 4,   Adding rational number 2 with its reciprocal. 2/1+1/2 = (4+1)/2 = 5/2,   Subtracting rational number 2 with its reciprocal. 2/1-1/2 = (4-1)/2 = 3/2

The denominators of the given Numbers are 10, 16, 18,16.

The LCM of 10, 16, 18,16 will be ( 2 x 5 x 2 x 2 x 2 x 3 x 3 ) = 720,   Now, the expression will be ( 72 + 90 + 120 + 225 )/720 = 507/720,   Hence, the final sum will be 507/720.   The results will always be same regardless of the arrangement of the Fractions.

  The denominators of the given Numbers are 10, 16, 18,16.   The LCM of 10, 16, 18,16 will be ( 2 x 5 x 2 x 2 x 2 x 3 x 3 ) = 720   Now, the expression will be ( 288 + 540 + 120 + 675 )/720 = 1623/720,   Hence, the final sum will be 1623/720.   The results will always be same regardless of the arrangement of the Fractions.

The reciprocal of 2/5 is 5/2, as in reciprocal we interchange the value of numerator with denominator and vice-versa. 

Solution:  Reciprocal of 8/9 is 9/8   If we Multiply Rational Number '8/9' with it’s reciprocal, we get:  => 8/9*9/8, => 1.    If we perform division operation on the given rational number and its reciprocal, we get:  => 8/9÷9/8, => 8/9*8/9, => 64/81.     If we do addition of  both rational number and its reciprocal then we get:  => 8/9+9/8, => (64+81)/72, => 145/72.     On subtracting reciprocal of given rational number we get: =>8/9–9/8, => (64-81)/72, => -17/72.

Reciprocal of 10/3 = 3/10, 

If we Multiply Rational Number '10/3' with it’s reciprocal, we get: => 10/3*3/10,   => 1.    If we perform division operation on the given rational number and its reciprocal then we get:       => 10/3÷3/10, => 10/3*10/3,   => 100/9.    If we do addition of  both rational number and its reciprocal then we get: 

=> 10/3+3/10,

=> (100+9)/30,

=> 109/30.    On subtracting reciprocal of given rational number we get: => 10/3-3/10,   => (100-9)/6,   => 91/30. 

Step 1: Write the given rational number in p/q form, on doing so, we get: 

p/q=-3/4,    Step 2: For multiplicative inverse we write the reciprocal rational number,     p/q = q/p = 4/-3,    Step 3:  Now, we multiply both the terms,   Multiplicative Inverse = p/q x q/p, = -3/4 x 4/-3, =1. 

Step 1: First of all we will write the given rational number in the form 'p/q', 

p/q=4/5,    Step 2: For multiplicative Inverse we have to write the reciprocal of the given rational number. The reciprocal can be written as:      =>  p/q = q/p = 5/4,   Step 3:  Now, we will multiply both the Rational Numbers, on doing so we get,  Multiplicative Inverse = p/q x q/p,  = 4/5 x 5/4,  = 20/20 =1.

 

Given Rational number is decimal number q= 4/10, then additive inverse of q is -(4/10), 

because result  is:          => 4/10 + (-4/10) = 0/10,   => 0/10 = 0. 

The given Integer 3 is a Rational number as it can be represented as: 3/1 

then according to additive inverse we get. 

p = -3/1,  because it produces '0' as a result:        3/1 + (-3/1) = 0.              This  example shows the additive inverse of the integer number. 

 

In the multiplication operation multiply the numerator of all Fractions together and denominator of all fractions together.

i.e. ( 3 x 12 x 11 )/( 7 x 8 x 13 ) = 396/728.   Hence, the final result of multiplication will be 396/728.    

In the multiplication operation multiply the numerator of all Fractions together and denominator of all fractions together.

i.e. ( 14 x 12 x 16 )/( 11 x 7 x 19 ) = 2688/1463,   Hence, the final result of multiplication will be 2688/1463,   The results will always be same regardless of the arrangement of the fractions.  

In the multiplication operation multiply the numerator of all Fractions together and denominator of all fractions together.

i.e. ( -5 x -7 x 11 )/( 9 x 12 x 18 ) = 385/1944.   Hence, the final result of multiplication will be 385/1944.   The results will always be same regardless of the arrangement of the fractions.

The denominators of the given Numbers are 9, 12, 18.

The LCM of 9, 12, 18 will be ( 3 x 3 x 2 x 2 ) = 36,   Therefore the expression become: ( ( -20 ) + ( -21 ) + 22 )/36 = -19/36,   Hence, the final sum will be -19/36,   The results will always be same regardless of the arrangement of the Fractions.