The document RD Sharma Solutions - Chapter 1 - Rational Numbers (Ex -1. 6), Class 8, Maths Class 8 Notes | EduRev is a part of the Class 8 Course RD Sharma Solutions for Class 8 Mathematics.

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**Question 1: Verify the property: x Ã— y = y Ã— x by taking:**

**Answer :**

We have to verify that xÃ—y=yÃ—x.** **

Hence verified.** **

Hence verified.** **

Hence verified.

Hence verified.

**Question 2: Verify the property: x Ã— (y Ã— z) = (x Ã— y) Ã— z by taking:**

**Answer :**

We have to verify that xÃ—(yÃ—z)=(xÃ—y)Ã—z.

xÃ—(yÃ—z)=

(xÃ—y)Ã—z=

Hence verified.

xÃ—(yÃ—z)=

(xÃ—y)Ã—z=

Hence verified.

xÃ—(yÃ—z)=

(xÃ—y)Ã—z=

Hence verified.

xÃ—(yÃ—z)=

(xÃ—y)Ã—z=

Hence verified.

**Question 3: Verify the property: x Ã— (y + z) = x Ã— y + x Ã— z by taking:**

**Answer :**

We have to verify that xÃ—(y+z)=xÃ—y+xÃ—z.

xÃ—(y+z)=

xÃ—y+xÃ—z=

= -1/26

Hence verified.

xÃ—(y+z)= =

xÃ—y+xÃ—z=

= 13/5

Hence verified.

xÃ—(y+z)=

xÃ—y+xÃ—z=

= 2/3

Hence verified .

xÃ—(y+z)=

xÃ—y+xÃ—z=

= 1

Hence verified.

**Question 4: Use the distributivity of multiplication of rational numbers over their addition to simplify:**

**Answer :**

(ii)

(iii)

(iv)

**Question 5: Find the multiplicative inverse (reciprocal) of each of the following rational numbers:****(i) 9**

**(ii) âˆ’7**

**(iii) 12/5**

**(iv) âˆ’7/9**

**(v) âˆ’3/âˆ’5**

**(ix) âˆ’1(x) 0/3(xi) 1 **

**Answer :**(i) Multiplicative inverse (reciprocal) of 9 =1/9

(ii) Multiplicative inverse (reciprocal) of âˆ’7 = -1/7

(iii) Multiplicative inverse (reciprocal) of 12/5 = 5/12

(iv) Multiplicative inverse (reciprocal) of -7/9 = -9/7

(v) Multiplicative inverse (reciprocal) of -3/-5 = -5/-3 or 5/3

(vi) Multiplicative inverse (reciprocal) of

(vii) Multiplicative inverse (reciprocal) of

(viii) Multiplicative inverse (reciprocal) of

(ix) Multiplicative inverse (reciprocal) of

(x) Multiplicative inverse (reciprocal) of 0/3 = 3/0 = Undefined

(ix) Multiplicative inverse (reciprocal) of 1 = 1/1 = 1

**Question 6: Name the property of multiplication of rational numbers illustrated by the following statements:**

**Answer :**

**(i) Commutative property(ii) Commutative property(iii) Distributivity of multiplication over addition(iv) Associativity of multiplication(v) Existence of identity for multiplication(vi) Existence of multiplicative inverse(vii) Multiplication by 0(viii) Distributive property **

(i) The product of two positive rational numbers is always .....

(ii) The product of a positive rational number and a negative rational number is always .....

(iii) The product of two negative rational numbers is always .....

(iv) The reciprocal of a positive rational number is .....

(v) The reciprocal of a negative rational number is .....

(vi) Zero has ..... reciprocal.

(vii) The product of a rational number and its reciprocal is .....

(viii) The numbers ..... and ..... are their own reciprocals.

(ix) If a is reciprocal of b, then the reciprocal of b is .....

(x) The number 0 is ..... the reciprocal of any number.

(i) Positive

(ii) Negative

(iii) Positive

(iv) Positive

(v) Negative

(vi) No

(vii) 1

(viii) -1 and 1

(ix)

(x) not

(xi)

(xii) 12âˆ’1

**Question 8: Fill in the blanks:**

**Answer :**

(i) âˆ’4

xÃ—y=yÃ—x (commutativity)** **

(ii) 5/11

xÃ—y=yÃ—x (commutativity)

(iii) 3/4 ; 1/2

xÃ—(y+z)=xÃ—y+xÃ—z (distributivity of multiplication over addition)

(iv) 5/7

xÃ—(yÃ—z)=(xÃ—y)Ã—z (associativity of multiplication )