**Download NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 – Rational Numbers**

**NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1 , has been designed by the NCERT to test the knowledge of the student on the following topics : **

**1.1 Introduction**

**1.2 Properties of Rational Numbers**

**1.2.1 Closure**

Closure Property of Whole numbers

Closure Property of Integers

Closure Property of Rational Numbers

(a) Addition

(b) Subtraction

(c) Multiplication

(d) Division

**1.2.2 Commutativity**Commutative Property of Whole Numbers

Commutative Property of Integers

Commutative Property of Rational Numbers

(a) Addition

(b) Subtraction

(c) Multiplication

(d) Division**1.2.3 Associativity**

Associative Property of Whole Numbers

Associative Property of Integers

Associative Property of Rational Numbers

(a) Addition

(b) Subtraction

(c) Multiplication

(d) Division**1.2.4 The role of zero (0)****1.2.5 The role of 1****1.2.6 Negative of a number****1.2.7 Reciprocal****1.2.8 Distributivity of multiplication over addition for rational numbers**

**Problems and Solutions – Rational Numbers Class 8 –**** Exercise 1.1 **

**1. Using appropriate properties find.**

**1. **

**2. **

**Solution:**

**1.**

= (By Commutativity property of Rational Numbers)

= (By Distributivity property of Rational Numbers)

=

= = = 2

**2. **

= (By Commutativity property of Rational Numbers)

=

=

= =

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

**(i) **

**(ii) **

**(iii) **

**(iv) **

**(v) **

**Solution:**

**Additive inverse of a number is another number, which when added to the original numbers gives the result as “0”.**

**(i)** The additive inverse of is because + = 0

**(ii)** The additive inverse of is because + = 0

**(iii)** The additive inverse of is because + = 0

**(iv)** The additive inverse of is because + = 0

**(v)** The additive inverse of is because + = 0

**3. Verify that – (– x) = x for**

**(i) x = **

**(ii) x = –**

**Solution:**

**(i)** We are given that , x =

The additive inverse of x = is -x =

Since + = 0

This can be written as − =

So, -(-x) = x

**(ii)** x =

The additive inverse of x = is -x =

Since + = 0

This can be written as − =

So, -(-x) = x

**4. Find the multiplicative inverse of the following.**

**(i) -13**

**(ii) **

**(iii) **

**(iv) **

**(v) **

**(vi) -1**

**(i)** The multiplicative inverse of – 13 is

**(ii) **The multiplicative inverse of is

**(iii) **The multiplicative inverse of is 5.

**(iv) ** =

The multiplicative inverse of is

**(v) ** -1 x = .

The multiplicative inverse of -1 x is

**(vi)** The multiplicative inverse of – 1 is **–** 1

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

**(i) x 1 = 1 x = **

**(ii) x = x **

**(iii) x = 1**

**Solution:**

**(i)** 1 is Multiplicative Identity

**(ii) **Commutative property

**(iii) **Reciprocal or multiplicative inverse

**6. Multiply by the reciprocal of **

**Solution:** The reciprocal of is

x =

**7. Tell what property allows you to compute **

**Solution:** By associative property we can compute

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

**Solution: **No, is not the multiplicative inverse of .

is a mixed fraction. It can be written as The multiplicative inverse of is . So the multiplicative inverse of is

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

**Solution: **0.3 is the multiplicative inverse of .

is a mixed fraction. It can be written as The multiplicative inverse of is , which is 0.3 when converted to decimal.

**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.**

**Solution:**

(i) 0 is the rational number that does not have a reciprocal, since reciprocal of any number x is where x ≠0

(ii) 1 and -1 are rational numbers that are equal to their reciprocals because = -1 and = 1

(iii) 0 is the rational number equal to its negative because −0 =0

**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 , where x ≠ 0 is ________.**

**(v) The product of two rational numbers is always a _______.**

**Solution:**

(i) No { since reciprocal of any number x is where x ≠0}

(ii) 1, −1 {since = -1 and = 1}

(iii) − { since reciprocal of any number x is where x ≠0}

(iv) x { since reciprocal of any number x is where x ≠0 and vicecersa}

(v) Rational number

(vi) Positive { since reciprocal of any number x is where x ≠0}

**The next Exercise for** **NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.2 – Rational Numbers can be accessed by clicking here.**

**Download NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.1**

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