RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Class 8: RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

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Exercise: 1.5


Question 1: Multiply:

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Answer :

(i) RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(ii) RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(iii)  RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(iv) RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(v) RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(vi) RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(vii) RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(viii) RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Question 2: Multiply:

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Answer :

(i) RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(ii) RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(iii) RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(iv) RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(v) RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(vi) RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Question 3: Simplify each of the following and express the result as a rational number in standard form:

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Answer :

(i)  RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(ii) RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(iii) RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(iv) RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(v) RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(vi) RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(vii) RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(viii) RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Question 4: Simplify:

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Answer : 

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

= 23/12

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

= 25/8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

= 2/3

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

= 20/12 = 5/3

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

= 19/5

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

= 483/30

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

= 239/126

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

= -417/160

Question 5: Simplify:

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Answer :

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

= 47/12

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

= 94/42 = 47/21

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

= -204/30 = -34/5

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

= -177/ 286


Exercise: 1.6


Question 1: Verify the property: x × y = y × x by taking:

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Answer :

We have to verify that x×y=y×x. 

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Hence verified. 

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Hence verified. 

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Hence verified. 

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Hence verified. 

Question 2: Verify the property: x × (y × z) = (x × y) × z by taking:

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Answer :

We have to verify that x×(y×z)=(x×y)×z.

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

x×(y×z)=RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(x×y)×z= RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Hence verified. 

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

x×(y×z)= RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(x×y)×z= RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Hence verified. 

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

x×(y×z)= RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(x×y)×z= RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Hence verified.

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

x×(y×z)= RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(x×y)×z= RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Hence verified. 

Question 3: Verify the property: x × (y + z) = x × y + x × z by taking:

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Answer :

We have to verify that  x×(y+z)=x×y+x×z. 

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

x×(y+z)= RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

x×y+x×z= RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

= -1/26

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Hence verified. 

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

x×(y+z)= RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 = RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

x×y+x×z= RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

= 13/5

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Hence verified. 

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

x×(y+z)= RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

x×y+x×z= RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

= 2/3

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Hence verified .

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

x×(y+z)= RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

x×y+x×z= RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

= 1

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Hence verified. 

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

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Answer :

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(ii) RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(iii) RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(iv)  RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8


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

(ii) −7

(iii) 12/5

(iv) −7/9

(v) −3/−5

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(ix) −1
(x) 0/3
(xi) 1 

Answer :
(i) Multiplicative inverse (reciprocal) of 9 =1/9
(ii) Multiplicative inverse (reciprocal) of −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 RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(vii) Multiplicative inverse (reciprocal) of RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(viii) Multiplicative inverse (reciprocal) of RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(ix) Multiplicative inverse (reciprocal) of RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(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:

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

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 


Question 7: Fill in the blanks:
(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.

(xi) Reciprocal of RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8
(xii) (17 × 12)−1 = 17−1 × .....
Answer :
(i) Positive
(ii) Negative
(iii) Positive
(iv) Positive
(v) Negative
(vi) No
(vii) 1
(viii) -1 and 1
(ix) a
(x) not
(xi) a
(xii) 12112-1 

Question 8: Fill in the blanks:

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Answer :

(i) −4

x×y=y×x  (commutativity) 

(ii) 5/11
 x×y=y×x  (commutativity) 
(iii) 3/4 ; 1/2
x×(y+z)=x×y+x×z  (distributivity of multiplication over addition) 
(iv) 5/7
x×(y×z)=(x×y)×z  (associativity of multiplication )

                                                  Exercise: 1.7


Question 1: Divide:

(i) 1 by 1/2
(ii) 5 by −5/7(iii) −3/4 by 9/−16
(iv) −7/8 by −21/16
(v) 7/−4 by 63/64
(vi) 0 by −7/5
(vii) −3/4 by −6
(viii) 2/3 by −7/12
(ix) −4 by −3/5
(x) −3/13 by −4/65

Answer :

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Question 2: Find the value and express as a rational number in standard form:

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Answer 2:

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Question 3: The product of two rational numbers is 15. If one of the numbers is −10, find the other.
Answer 3:

Let the other number be x.

∴ x×(−10)=15 

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

So, the other number is -3/2.
Question 4: The product of two rational numbers is -8/9. If one of the numbers is -4/15, find the other.

Answer 4: Let the other number be x. 

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

or x= 10/3

Thus, the other number is 10/3.
Question 5: By what number should we multiply -1/6-16 so that the product may be -23/9?
Answer 5: Let the number be x. 

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8
Therefore, the other number is 46/3.

Question 6: By what number should we multiply -15/28-1528 so that the product may be -5/7?-57?

Answer 6: Let the other number be x. 

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

or x= 4/3

Thus, the other number is 4/3.
Question 7: By what number should we multiply -8/13 so that the product may be 24?

Answer 7: Let the number be x. 

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

or x=39 

Thus, the number is −39.
Question 8: By what number should -3/434 be multiplied in order to produce 2/3?23?
Answer 8:
Let the other number that should be multiplied with -3/4 to produce2/3 be x. 

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Thus, the number is -8/9.

Question 9: Find (x + y) ÷ (x − y), if

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Answer 9:

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8


RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Question 10: The cost of RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 metres of rope is Rs RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8. Find its cost per metre.

Answer 10:  The cost of RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 metres of rope is Rs RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8.Cost per metre = RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

= 153/92

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Question 11: The cost of RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 metres of cloth is Rs RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8Find the cost of cloth per metre.
Answer 11:  The cost of RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 metres of cloth is Rs. RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8∴ Cost per metre
=RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8= 129/4
RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8Thus, RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 or Rs 32.25 is the cost of cloth per metre.  Question 12: By what number should -33/16 be divided to get -11/4?
Answer 12: Let the number be x.
RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8Thus, the number is 3/4.

Question 13: Divide the sum of -13/5-135 and 12/7127 by the product of -31/7 and -1/2.-317 and -12.

Answer 13:

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

= -2/5

Question 14: Divide the sum of 65/12 and 12/7 by their difference.

Answer 14:

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

= 599/311
Question 15: If 24 trousers of equal size can be prepared in 54 metres of cloth, what length of cloth is required for each trouser?

Answer 15: Cloth needed to prepare 24 trousers=54 m
∴ Length of the cloth required for each trousers= 54÷24= 54/24 = 9/4 m = RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 metres


                                              Exercise: 1.8


Question 1: Find a rational number between −3 and 1.

Answer 1: Rational number between −3 and 1 =

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 -2/2 = -1
Question 2:  Find any five rational numbers less than 2.

Answer 2:

We can write:RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Integers less than 10 are 0, 1, 2, 3, 4, 5 ... 9.

Hence, five rational numbers less than 2 are 0/5, 1/5, 2/5, 3/5,and 4/5 .
Question 3: Find two rational numbers between −2/9 and 5/9.-29 and 59.

Answer 3:
Since both the fractions (−2/9 and 5/9) have the same denominator, the integers between the numerators(−2 and 5) are −1, 0, 1, 2, 3, 4.Hence, two rational numbers between −2/9 and 5/9 are 0/9 or 0 and 1/9.
Question 4: Find two rational numbers between 1/5 and 1/2.15 and 12
Answer 4: Rational number between1/5 and1/2 =  RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Rational number between 1/5 and7/20 =RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8


Therefore, two rational numbers between 1/5 and 1/2 are 7/20 and 11/40.
Question 5: Find ten rational numbers between 1/4 and 1/2.14 and 12.
Answer 5: The L.C.M of the denominators (2 and 4) is 4.

So, we can write 1/4 as it is. 

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

As the integers between the numerators 1 and 2 of both the fractions are not sufficient, we will multiply the fractions by 20. 

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Between 20 and 40, there are 19 integers. They are 21, 22, 23, 24, 25, 26, 27....39, 40.

Thus, 21/40,22/40,23/40,24/40,25/40,...................38/40 and 39/40 are the fractions.We can take any 10 of these. 

Question 6: Find ten rational numbers between -2/5 and1/2. and 12.
Answer 6:

L.C.M of the denominators (2 and  5) is 10.

We can write: 

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Since the integers between the numerators (−4 and 5 ) of both the fractions are not sufficient, we will multiply the ractions are not sufficient, we will multiply the fractions by 2.

RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

There are 17 integers between −8 and 10, which are −7,−6,−5,−4...................8, 9.These can be written as: 

−7/20, −6/20, −5/20, −4/20, −3/20,................... 8/20 and 9/20

We can take any 10 of these. 


Question 7: Find ten rational numbers Between 3/5 and 3/4.
Answer 7: The L.C.M of the denominators 5 and 4 of both the fractions is 20.We can write: RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8
Since the integers between the numerators 12 and 15 are not sufficient, we will multiply both the fractions by 5.
RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8
There are 14 integers between 60 and 75. They are 61, 62, 63.......73 and 74. Therefore, 60/100,61/100,62/100..........73/100 and74/100 are the 14 fractions. We can take any 10 of these.

The document RD Sharma Solutions (Ex -1. 5, 1.6, 1.7 & 1.8): Rational Numbers Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 is a part of the Class 8 Course RD Sharma Solutions for Class 8 Mathematics.
All you need of Class 8 at this link: Class 8

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