December 8, 2023

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

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

,

since .

The same equality

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

(ii) We have  ,

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______. 