Worksheet on Properties of Addition of Rational Numbers

Practice the questions given in the worksheet on properties of addition of rational numbers. The questions are based on closure property, commutative property, associative property, existence of additive identity property and existence of additive inverse property of addition of rational numbers.

1. Verify the following:

(i) -12/5 + 2/7 = 2/7 + -12/7

(ii) -5/8 + -9/13 = -9/13 + -5 /8

(iii) 3 + -7/12 = -7/12 + 3

(iv) 2/-7 + 12/-35 = 12/-35 + 2/-7

2. Fill in the blanks:

(i) (-3/17) + (-12/5) = (-12/5) + (_____ )

(ii) -9 + (-21/8) = (_____ ) + (-9)

(iii) (-8/13 + 3/7) + (-13/4) = (_____ ) + [3/7 + (-13/4)]

(iv) -12 + (7/12 + -9/11) = (-12 + 7/12) + (_____ )

(v) 19/-5 + (-3/11 + -7/8) = {19/-5 + (_____ )} + -7/8

(vi) -16/7 + _____ = _____ + -16/7 = -16/7

3. Find the additive inverse of each of the following:

(i) 1/3

(ii) 23/9

(iii) -18

(iv) -17/8

(v) 15/-4

(vi) -16/-5

(vii) -3/11

(viii) 0

(ix) 19/-6

(x) -8/ -7

4. (i) Which rational number is its own additive inverse?

(ii) Is addition commutative on rational numbers?

(iii) Is addition associative on rational numbers?

(iv) Is subtraction commutative on rational numbers?

(v) Is subtraction associative on rational numbers?

Answers for the worksheet on properties of addition of rational numbers are given below to check the exact answers of the above questions on rational numbers.

Answers:

2. (i) -3/17

(ii) -21/8

(iii) -8/13

(iv) -9/11

(v) -3/11

(vi) 0, 0

3. (i) -1/3

(ii) -23/9

(iii) 18

(iv) 17/8

(v) 15/4

(vi) -16/5

(vii) 3/11

(viii) 0

(ix) 19/6

(x) -8/7

4. (i) 0

(ii) Yes

(iii) Yes

(iv) No

(v) No

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