# Name the property used in each of the following.

Question:

Name the property used in each of the following.

(i) (-7/4) × (-3/4) = (-3/5) × (-7/11)

(ii) (-2/3) × [(3/4) + (-½)] = [(-2/3) × (3/4)] + [(-2/3) × (½)]

(iii) (1/3) + [(4/9) + (-4/3)] = [(1/3) + (4/9)] + [-4/3]

(iv) (-2/7) + 0 = 0 + (-2/7) = (-2/7)

(v) (3/8) × 1 = 1 × (3/8) = (3/8)

Solution:

(i) (-7/4) × (-3/4) = (-3/5) × (-7/11)

The above rational number is in the form of Commutative property over multiplication.

(ii) (-2/3) × [(3/4) + (-½)] = [(-2/3) × (3/4)] + [(-2/3) × (½)]

The above rational number is in the form of Distributive property over addition.

(iii) (1/3) + [(4/9) + (-4/3)] = [(1/3) + (4/9)] + [-4/3]

The above rational number is in the form of Associative property over addition.

(iv) (-2/7) + 0 = 0 + (-2/7) = (-2/7)

The above rational number is in the form of Additive identity of rational number.

(v) (3/8) × 1 = 1 × (3/8) = (3/8)

The above rational number is in the form of Multiplicative identity of rational number.