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(5/7×3/4)+(5/7×-1/6) answer in distributive property |
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Answer» (i) -2/3 x 3/5 + 5/2 - 3/5 x 1/6 = -2/3 x 3/5 - 3/5 x 1/6 + 5/2 [by commutativity] = (-2/3 x 3/5) - (3/5 x 1/6) + 5/2 = 3/5 [-2/3 - 1/6] + 5/2 [by DISTRIBUTIVITY] = -3/5 [2/3 + 1/6] + 5/2 = -3/5 [(4 + 1)/6] + 5/2 = -3/5 x 5/6 + 5/2 = -3/6 + 5/2 = -1/2 + 5/2 = (-1 + 5)/2 = 4/2 = 2 (ii) 2/5 x (-3/7) - 1/6 x 3/2 + 1/14 x 2/5 = 2/5 x (-3/7) + 1/14 x 2/5 - 1/6 x 3/2 [by commutativity] = [2/5 x (-3/7)] + [1/14 x 2/5] - 1/6 x 3/2 = 2/5 [-3/7 + 1/14] - 3/12 [by distributivity] = 2/5 [(-6 + 1)/14] - 1/4 = 2/5 x (-5/14) - 1/4 = -2/14 - 1/4 = (-4 - 7)/28 = -11/28Step-by-step explanation:(i) -2/3 x 3/5 + 5/2 - 3/5 x 1/6 = -2/3 x 3/5 - 3/5 x 1/6 + 5/2 [by commutativity] = (-2/3 x 3/5) - (3/5 x 1/6) + 5/2 = 3/5 [-2/3 - 1/6] + 5/2 [by distributivity] = -3/5 [2/3 + 1/6] + 5/2 = -3/5 [(4 + 1)/6] + 5/2 = -3/5 x 5/6 + 5/2 = -3/6 + 5/2 = -1/2 + 5/2 = (-1 + 5)/2 = 4/2 = 2 (ii) 2/5 x (-3/7) - 1/6 x 3/2 + 1/14 x 2/5 = 2/5 x (-3/7) + 1/14 x 2/5 - 1/6 x 3/2 [by commutativity] = [2/5 x (-3/7)] + [1/14 x 2/5] - 1/6 x 3/2 = 2/5 [-3/7 + 1/14] - 3/12 [by distributivity] = 2/5 [(-6 + 1)/14] - 1/4 = 2/5 x (-5/14) - 1/4 = -2/14 - 1/4 = (-4 - 7)/28 = -11/28 |
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