RD Sharma Solutions (Ex 1.2): Rational Numbers | Mathematics (Maths) Class 8 PDF Download

Q.1. Verify commutativty of addition of rational numbers for each of the following pairs of rotional numbers:
(i)
(ii)
(iii)
(iv) 
(v)
(vi)
Ans.
Commutativity of the addition of rational numbers means that if   are two rational numbers, then
(i)
We have

Hence verified.
(ii) We have

Hence verified.
(iii)
 We have

Hence verified.
(iv)
We have

Hence verified.
(v)
We have 4 and

Hence verified.
(vi)
We have

Hence verified.

Q.2. Verify associativity of addition of rational numbers i.e., (x + y) + z = x + (y + z), when:
(i)
(ii)
(iii)
(iv)
Ans.
We have to verify that (x +y) +z = x + (y + z).
(i)


Hence verified.
(ii)



Hence verified.
(iii)


Hence verified.
(iv)



Hence verified.

Q.3. Write the additive inverse of each of the following rational numbers:
(i)
(ii)
(iii)
(iv)
Ans.
(i) Additive inverse is the negative of the given number.
So, additive inverse of
(ii) Additive inverse is the negative of the given number.
So, additive inverse of
(iii) Additive inverse is the negative of the given number.
So, additive inverse of
(iv) Additive inverse is the negative of the given number.
So, additive inverse of

Q.4. Write the negative (additive inverse) of each of the following:
(i)

(ii)
(iii)
(iv)
(v) 0
(vi) 1 
(vii) - 1
Ans.
(i) Negative of
(ii) Negative of
(iii) Negative of
(iv) Negative of
(v) Negative value of 0 is 0.
(vi) Negative of 1 is −1.
(vii) Negative of −1 is 1.

Q.5. Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number:
(i)
(ii)
(iii)
(iv)
Ans.
(i) We have:


(ii)
We have:

(iii)
We have:


(iv)
We have:



Q.6. Re-arrange suitably and find the sum in each of the following:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Ans.
(i)


(ii)


(iii)


(iv)


(v)

(vi)