The document RD Sharma Solutions - Chapter 1 - Rational Numbers (Ex - 1.2), 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 commutativity of addition of rational numbers for each of the following pairs of rational numbers:**

**(i) -11/5 and 4/7**

**(ii) 4/9 ****and 7/-12****49 and 7-12**

**(iii) -3/5 and -2/-15**

**(iv) 2/-7 and 12/-35**

**(v) 4 and -3/5**

**(vi) -4 and 4/-7**

**Answer :**Commutativity of the addition of rational numbers means that if a/b and c/d are two rational numbers, then a / b + c / d = / d + a / b .(i)

We have -11/5 and 4/7.

Hence verified.(ii)

We have 4/9 and 7/-12.

Hence verified. (iii)

Hence verified. (iv)

Hence verified. (v)

We have 4 and -3/5.

Hence verified. (vi)

We have -4 and 4/-7

Hence verified.

**Question 2: Verify associativity of addition of rational numbers i.e., ( x + y) + z = x + (y + z), when:**

**Answer :** We have to verify that (x+y)+z = x+(y+z).

(i)

Hence verified. (ii)

Hence verified. (iii)

Hence verified. (iv)

Hence verified.

**Question 3: Write the additive inverse of each of the following rational numbers:**

**Answer: **

(i)Additive inverse is the negative of the given number.So, additive inverse of âˆ’2/17 is 2/17.

(ii) Additive inverse is the negative of the given number.So, additive inverse of 3/-11 is 3/11.** **

(iii) Additive inverse is the negative of the given number.So, additive inverse of** **-17/5 is 17/5.

(iv) Additive inverse is the negative of the given number.So, additive inverse of -11/-25 is -11/25.

**Question 4: Write the negative (additive inverse) of each of the following:**

**(i) -2/5-25 (ii) 7/-97-9 (iii) -16/13 (iv) -5/1 (v) 0 (vi) 1 (vii) âˆ’1 **

**Answer :** (i) Negative of âˆ’2/5 is 2/5.

(ii) Negative of 7/âˆ’9 is 7/9.

(iii) Negative of âˆ’16/13 is 16/13.

(iv) Negative of âˆ’5/1 is 5/1.

(v) Negative value of 0 is 0.

(vi) Negative of 1 is âˆ’1.

(vi) Negative of âˆ’1 is 1.

**Question 5: Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number:**

** **

**Answer :**

(i) We have:

= 24/15= 8/5

(ii) We have:

= -51/63= -17/21

(iii) We have:

= 37/15

(iv) We have:

= -86/63

**Question 6: Re-arrange suitably and find the sum in each of the following:**

**Answer : (i)**

= -47/4

(ii)

= -77/18

(iii)

= 23/15

(iv)

= -25/104

(v)

= 3/5

(vi)

= 801/336

= 267/112