NCERT Solutions for Class 8 maths Chapter 1 : rational Numbers Exercise 1.1

Question 1:  
Using appropriate properties find:


Answer

1. Using commutativity property of rational number
   Now using Distributivity property
   
   
   (ii) Using commutativity property of rational numbers
   
      Now using Distributivity property
   
   

Question 2    
Write the additive inverse of each of the following:

1. 2/8
2. -5/9
3. -6/-5
4.  2/-9
5. 19/-6

Answer:
(i) 2/8
Additive inverse = -2/8
(ii) -5/9
Additive inverse = 5/9
(iii) -6/-5 =6/5
Additive inverse = -6/5
(iv)  2/-9=-2/9
Additive inverse =2/9
(v) 19/-6=  -19/6
Additive inverse =19/6
Question 3
Verify that - ( - x) = x for.
(i) x =11/15 (ii) x=-13/17
Answer:

1.  x=11/15 Additive inverse
       -x=-11/15  As   (11/15)   + (-11/15) =0
   The above   also represent that additive inverse of (-11/15) is (11/15) or we can say that
   - (-11/15)=11/15
   Or x=-(-x)
   

x=-13/17
Additive inverse
    -x=-13/17  As   (-13/17)  + (13/17) =0
The above also represent that additive inverse of (13/17) is (-13/17)) or we can say that
- (13/17) = -13/17
Or x=-(-x)
Question 4
Find the multiplicative inverse of the following.

1. -13
2. -13/19
3.  1/5
4. -5/8 X -3/7
5. -1 X -2/5
6.  - 1

Answer

1. -13 Multiplicative inverse =-1/13
   
2. -13/19 Multiplicative inverse =-19/13
   
3. 1/5 Multiplicative inverse =5
   
4. -5/8 X -3/7 =15/56 Multiplicative inverse =56/15
   
5. -1 X -2/5 =2/5 Multiplicative inverse =5/2
   

-1
Multiplicative inverse =-1
Question 5  :
Name the property under multiplication used in each of the following:

Answer:

1. 1 is the multiplicative identity
2. Commutatively
3. Multiplicative inverse

Question 6:  
Multiply 6/13 by the reciprocal of -7/16
Answer
Reciprocal of -7/16= -16/7
So (6/13) X (  -16/7) =-96/91
Question 7  Tell what property allows you to compute

Answer:
Associativity

Question 8  
Is   8/9 the multiplicative inverse of
Why or why not?
Answer:

=-9/8
Now
(8/9) X   (-9/8)   = -1
So it is not the multiplicative inverse
Question 9   Is 0.3 the multiplicative inverse  of

 Why or why not?

Answer:

=10/3
Now
(3/10) X   (10/3)  =1
So it is the multiplicative inverse
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.

Answer:

1. 0
2. 1 and -1
3. 0

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 (1/x)   where is x ≠ 0 __________.
(v) The product of two rational numbers is always a __________.
(vi) The reciprocal of a positive rational number is __________.

Answer:

1. No
2. 1 and -1
3.  -1/5
4. X
5. Rational Number
6. Positive rational number

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