Rs Aggarwal Solutions: Exercise 1D - Rational Numbers | Mathematics (Maths) Class 8 PDF Download

Q.1. Find each of the following products:
(i)
(ii)

(iii)
(iv)
(v)

(vi)
(vii)
(viii)
(ix)
(x)
(xi)

(xii)

Ans.
(i)

(ii)

(iii)

Simplifying the above rational number, we get:

(iv)

Simplifying the above rational number, we get:

(v)

Simplifying the above rational number, we get:

(vi)

Simplifying the above rational number, we get:

(vii)

Simplifying the above rational number, we get:

(viii)

Simplifying the above rational number, we get:

(ix)

Simplifying the above rational number, we get:

(x)

Simplifying the above rational number, we get: 

(xi)

Simplifying the above rational number, we get:

(xii)

Simplifying the above rational number, we get:


Q.2. Verify each of the following:

(i)
(ii)
(iii)

(iv)
Ans.
(i)



Simplifying, we get:


Simplifying, we get:

LHS = RHS
(ii)


(iii)


Simplifying, we get:


Simplifying, we get:

LHS = RHS
(iv)


Simplifying, we get:


Simplifying, we get:

LHS = RHS

Q.3. Verify each of the following:
(i)
(ii)
(iii)
Ans.
(i)




(ii)




(iii)





Q.4. Fill in the blanks:
(i)
(ii)
(iii)

(iv)
Ans.
(i)

(ii)

(iii)
 

(iv)
 

Q.5. Find the multiplicative inverse (i.e., reciprocal) of:
(i)
(ii)
(iii)
(iv) 18
(v) −16
(vi)
(vii) −1
(viii)
(ix)
(x)
Ans.
(i) Reciprocal of
(ii) Reciprocal of
(iii) Reciprocal of
(iv) Reciprocal of 18 is
(v) Reciprocal of - 16 is
(vi) Reciprocal of

(vii) Reciprocal of −1 is −1.
(viii) Reciprocal of  does not exist as

(ix) Reciprocal of
(x) Reciprocal of

Q.6. Find the value of:
(i)
(ii)
(iii) (−7)⁻¹
(iv)
Ans.
We know that  a⁻¹ = 1/a or a⁻¹×a=1
(i)

(ii)

(iii)

(iv) 


Q.7. Verify the following:
(i)
(ii)
(iii)
(iv)
Ans.
(i)



(ii)



(iii)





(iv)



Q.8. Name the property of multiplication illustrated by each of the following statements:
(i)
(ii)
(iii)
(iv)
(v)
(vi)  
Ans.
(i) Commutative property
(ii) Associative property
(iii) Distributive property
(iv) Property of multiplicative identity
(v) Property of multiplicative inverse
(vi) Multiplicative property of 0

Q.9. Fill in the blanks:
(i) The product of a rational number and its reciprocal is .......
(ii) Zero has ....... reciprocal.
(iii) The numbers ....... and ....... are their own reciprocals.
(iv) zero is ....... the reciprocal of any number.
(v) The reciprocal of a, where a ≠ 0, is .......
(vi) The reciprocal of  1/a, where a ≠ 0, is .......

(vii) The reciprocal of a positive rational rational number is .......
(viii) The reciprocal of a negative rational number is .......
Ans.
(i) 1
(ii) no
(iii) 1; -1
(iv) not
(v) 1/a
(vi) a
(vii) positive
(viii) negative