June 28, 2022

# NCERT-class-8-maths-chapter-1-exercise-1.1

Ncert Class 8 Maths Chapter 1 exercise 1.1

# NCERT solutions for class 8 maths| Chapter 1 Rational numbers

A  detailed and step-wise solutions to all the questions at the end of the chapter from the NCERT Maths book   are given below:

## Ncert-class-8-maths-chapter-1-exercise-1.1

1. Using appropriate properties find

(i)

Sol.    =        (by commutativity)

=            (by distributivity)

=

=

(ii)

Sol.                       (by commutativity)

=

=

=

=

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

(i)

Sol.   is the additive inverse of    because .

(ii)

Sol.    is the additive inverse of    because .

(iii)

Sol.  . So additive inverse of    is  .

(iv)

Sol. Since , so  additive inverse of    is   .

(v)

Sol. Since , so  additive inverse of    is  .

3. Verify that   for  (i)         (ii)

Sol. (i) We have ,

The additive inverse of   is   since .

The same equality  , shows that the additive inverse of   is    or , i.e.

(ii) We have  ,

The additive inverse of   is   since  .

The same equality  , shows that the additive inverse of   is     , i.e.  .

4. Find the multiplicative inverse of the following.

(i) – 13

Sol.  We say that a rational number is called the reciprocal or multiplicative inverse of another non-zero rational number
if .

Since  , so  multiplicative inverse of  -13 is   .

(ii)

Sol. Since  , so  multiplicative inverse of  – is   .

(iii)

Sol. Multiplicative inverse of    is 5 , because .

(iv)

Sol.

Since ,so multiplicative inverse of   is .

(v)

Sol

Since ,so multiplicative inverse of   is  .

(vi) – 1

Sol. Multiplicative inverse of -1 is  -1 , because (-1) x (-1) =1 .

5. Name the property under multiplication used in each of the following

(i)

Sol.  1 is the multiplicative identity.

(ii)

Sol. Commutativity of rational numbers.

(iii)

Sol. Multiplicative inverse .

6.  Multiply by the reciprocal of   .

Sol.  The reciprocal of   is   because .

Now the product of   and    = .

7. Tell what property allows you to compute  as .

Sol. Associativity of rational numbers.

8.  Is  the multiplicative inverse of ? Why or why not?

Sol.  No,    is not  the multiplicative inverse of   because their product is not 1.

9. Is 0.3 the multiplicative inverse of ? Why or why not?

Sol.  Yes, 0.3  is the multiplicative inverse of   because .

10. Write.

(i) The rational number that does not have a reciprocal.    Ans. 0

(ii) The rational numbers that are equal to their reciprocals.   Ans. 1 and -1

(iii) The rational number that is equal to its negative.  Ans.  0

11. Fill in the blanks.

(i) Zero has ____no____ reciprocal.

(ii) The numbers ___1_____ and __-1______ are their own reciprocals

(iii) The reciprocal of – 5 is ________.

(iv) Reciprocal of  where   is   ….……….

(v) The product of two rational numbers is always a ____rational number___.

(vi) The reciprocal of a positive rational number is __positive______. 