**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.

=

=

=

=

**(ii) **

Sol. (by commutativity)

=

= =

=

=

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

**(i**)

Sol.

**(ii) **

Sol.

**(iii) **

Sol.

**(iv) **

Sol. Since

**(v) **

Sol. Since

**3. Verify that for (i) **

**(ii)**

**Sol. (i)** We have

**,**

The additive inverse of ** ** is

The same equality

**
. **

**(ii) **We have ** ,**

The additive inverse of

**is since**

The same equality , shows that the additive inverse of

**
.**

**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

**(ii)**

Sol. Since , so multiplicative inverse of –

**(iii)**

Sol. Multiplicative inverse of is 5 , because

**(iv)**

Sol.

Since ,so multiplicative inverse of

**(v)**

Sol

Since

**(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,

**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

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

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

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