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Question

Verify that a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c) for each of the following values of a, b and c.

(a) a = 12, b = −4, c = 2

(b) a = (− 10), b = 1, c = 1

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Solution

(a) a = 12, b = −4, c = 2

a ÷ (b + c) = 12 ÷ (− 4 + 2) = 12 ÷ (−2) = −6

(a ÷ b) + (a ÷ c) = [12 ÷ (−4)] + [12 ÷ 2] = −3 + 6 = 3

Hence, a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c)

(b) a = −10, b = 1, c = 1

a ÷ (b + c) = (−10) ÷ (1 + 1) = (−10) ÷ 2 = −5

(a ÷ b) + (a ÷ c) = [(−10) ÷ 1] + [(−10) ÷ 1] = − 10 − 10 = −20

Hence, a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c)


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