Rational Numbers-NCERT Solutions

NCERT SOLUTIONS FOR RATIONAL NUMBERS
Exercise 1.1

Question 1:
Using appropriate properties Find:
(i)       
(ii)      
Solution:
(i)       

          
(ii)      

          

Question 2:
Write the additive inverse of each of the following:
(i)       
(ii)      
(iii)    
(iv)    
(v)       
Solution:
(i)       
(ii)      
(iii)    
(iv)    
(v)       

Question 3:
Verify that –(–x) = x for.
(i)       
(ii)      
Solution:
(i)       
          The additive inverse of
          
          The equality
          represents that the additive inverse of
           or it can be said that
          
(ii)      
          The additive inverse of
          
          This equality represents that
          the additive inverse of
          i.e., –(–x)=x

Question 4:
Find the multiplicative inverse of the following.
(i)       -13
(ii)      
(iii)    
(iv)    
(v)       
(vi)       -1
Solution:
(i)       
(ii)      
(iii)    
(iv)    
(v)       
(vi)       

Question 5:
Name the property under multiplication used in each of the following:
(i)       
(ii)      
(iii)    
Solution:
(i)       
           1 is the multiplicative identity.
(ii)      Commutativity
(iii)    Multiplicative inverse

Question 6:
Multiply by the reciprocal of
Solution:                        

Question 7:
Tell what property allows you to compute
       
Solution:
Associativity

Question 8:
Is the multiplicative inverse of Why or why not?
Solution:
If it is the multiplicative inverse, then the product should be 1.
           However, here, the product is not 1 as
           

Question 9:
Is 0.3 the multiplicative inverse of Why or why not?
Solution:
           
           Here, the product is 1. Hence, 0.3 is the multiplicative inverse of

Question 10:
Write:-
(i)       The rational number that does not have a reciprocal.
(ii)      The rational numbers that are equal to their reciprocals.
(iii)    The rational number that is equal to its negative.
Solution:
(i)       0 is a rational number but its reciprocal is not defined.
(ii)      1 and –1are the rational numbers that are equal to their reciprocals.
(iii)    0 is the rational number that is equal to its negative.

Question 11:
Fill in the blanks.
(i)       Zero has _________ reciprocal.
(ii)      The numbers _________ and _________ are their own reciprocals.
(iii)    The reciprocal of –5 is _________.
(iv)    Reciprocal of where x ≠ 0 is _________.
(v)       The product of two rational numbers is always a _________.
(vi)       The reciprocal of a positive rational number is _________.
Solution:
(i)       Zero has no reciprocal.
(ii)      The numbers 1, and –1 are their own reciprocals.
(iii)    The reciprocal of –5 is
(iv)    The reciprocal of where x ≠ 0 is x.
(v)       Rational number
(vi)       Positive Rational number
Exercise 1.2

Question 1:
Represent these numbers on the number line:
(i)       
(ii)      
Solution:
(i)        can be represented on the number line as follows.
(ii)       can be represented on the number line as follows.

Question 2:
Represent on the number line.
Solution:
can be represented on the number line as follows.

Question 3:
Write five rational numbers which are smaller than 2.
Solution:
2 can be represented as
Therefore, five rational numbers smaller than 2 are:
              

Question 4:
Find ten rational numbers between
Solution:
can be represented as respectively.
Therefore, ten rational numbers between are
              

Question 5:
Find five rational numbers between
(i)       
(ii)      
(iii)    
Solution:
(i)        can be represented as respectively.
Therefore, five rational numbers between are
(ii)       can be represented as respectively Therefore, five rational numbers
                  between are:
            
(iii)     can be represented as respectively.
Therefore, five rational numbers between and
            

Question 6:
Write five rational numbers greater than –2.
Solution:
–2 can be represented as
Therefore, five rational numbers greater than –2 are
            

Question 7:
Find ten rational numbers between
            
Solution:
can be represented as
Therefore, ten rational numbers between are
             NCERT SOLUTIONS FOR RATIONAL NUMBERS