State True/False.The value of

−7

11

+
2

−5

+

−13

22

is equal to the value of

−7

11

+

2

−5

+

−13

22

.

Question

State True/False.The value of

−7
      
       11
     
     +
      2
      
       −5

+
    
     −13
    
     22

is equal to the value of

−7
    
     11
   
   +

2
      
       −5
     
     +
      
       −13
      
       22

.

Accepted Answer

Here, we have to find if

−7
      
       11
     
     +
      
       2
        
         −1

−5
        
         −1

+
    
     −13
    
     22
   
   =

−7
      
       11
     
     +
      
       −2
      5

+
    
     −13
    
     22

.Solving L.H.S first,

−7
      
       11
     
     +
      2
      
       −5

+
    
     −13
    
     22

and multiply and divide the expression by -1 to convert the sign of -5 to positive.

−7
      
       11
     
     +
      
       2
        
         −1

−5
        
         −1

+
    
     −13
    
     22
   
   =

−7
      
       11
     
     +
      
       −2
      5

+
    
     −13
    
     22

As the denominators of given rational numbers are different, so the LCM of 11 and 5 is 55.By using LCM as the common denominator,

−7
      
       11
     
     ×
      5
      5
     
     +
      
       −2
      5
     
     ×
      
       11
      
       11

+
    
     −13
    
     22
   
   =

−35
      
       55
     
     +
      
       −22
      
       55

+
    
     −13
    
     22

Adding,

−35+
          
           −22

55

+
      
       −13
      
       22
     
     =

−35−22
        
         55

+
      
       −13
      
       22

=
      
       −57
      
       55
     
     +
      
       −13
      
       22

Again taking L.C.M. of numbers 55 and 22. So the factors of

55=5×11
 . And factors of

22=2×11
 .

⇒2×5×11

=110

By using LCM as the common denominator,

−57
      
       55
     
     ×
      2
      2
     
     +
      
       −13
      
       22
     
     ×
      5
      5
     
     =
      
       −114
      
       110
     
     +
      
       −65
      
       110

=
      
       −114−65
      
       110

=
      
       −179
      
       110

Now, solving R.H.S,

−7
    
     11
   
   +

2
      
       −5
     
     +
      
       −13
      
       22

and multiply and divide the expression by -1 to convert the sign of -5 to positive.

−7
    
     11
   
   +

2
        
         −1

−5
        
         −1

+
      
       −13
      
       22

=
    
     −7
    
     11
   
   +

−2
      5
     
     +
      
       −13
      
       22

As the denominators of given rational numbers are different so the LCM of 5 and 22 is 110.By using LCM as the common denominator,

−7
    
     11
   
   +

−2
      5
     
     ×
      
       22
      
       22
     
     +
      
       −13
      
       22
     
     ×
      5
      5

=
    
     −7
    
     11
   
   +

−44
      
       110
     
     +
      
       −65
      
       110

Adding,

−7
      
       11
     
     +

−44+
          
           −65

110

=
      
       −7
      
       11
     
     +

−44−65
        
         110

=
      
       −7
      
       11
     
     +
      
       −109
      
       110

Again taking L.C.M. of numbers 11 and 110.So the factors of

11=1×11
 . And factors of

110=10×11
 .

⇒10×11

=110

By using LCM as the common denominator,

−7
      
       11
     
     ×
      
       10
      
       10
     
     +
      
       −109
      
       110
     
     ×
      1
      1
     
     =
      
       −70
      
       110
     
     +
      
       −109
      
       110

=
      
       −70−109
      
       110

=
      
       −179
      
       110

Thus,

−179
    
     110
   
   =
    
     −179
    
     110

.Therefore,

LHS=RHS
  . Therefore, the value of

−7
      
       11
     
     +
      2
      
       −5

+
    
     −13
    
     22

is equal to the value of

−7
    
     11
   
   +

2
      
       −5
     
     +
      
       −13
      
       22

.Thus, the given statement is true.Therefore, option (1) is correct.

State True/False.

The value of $− 7 11 + 2 − 5 + − 13 22$ is equal to the value of $− 7 11 + 2 − 5 + − 13 22$ .

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State True/False.The value of −7 11 + 2 −5 + −13 22 is equal to the value of −7 11 + 2 −5 + −13 22 .

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State True/False.

The value of $− 7 11 + 2 − 5 + − 13 22$ is equal to the value of $− 7 11 + 2 − 5 + − 13 22$ .