**Download NCERT Solutions for Class 8 Maths Chapter 1 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:**

**(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)** 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}

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

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