**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______.

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