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secondary 3 | E Maths
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Date Posted: 4 years ago
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(a) False.
Two negatives divided by each other simply become positive. As long as a is less negative than b (i.e. a > b), then a divided by b is less than 1.
-1/-5 = 1/5; -2/-100 = 1/50
(b) False. The fact that a is less negative than b means that the numerical magnitude of b is greater than a, so squaring each expression removes the negative signs and the one with the greater magnitude will eventually end up being bigger.
(-1)^2 = 1; (-100)^2 = 10000
(c) True, as per point in (a). If a > b, then a/b < 1 while b/a > 1, so b/a - a/b will be positive.
Two negatives divided by each other simply become positive. As long as a is less negative than b (i.e. a > b), then a divided by b is less than 1.
-1/-5 = 1/5; -2/-100 = 1/50
(b) False. The fact that a is less negative than b means that the numerical magnitude of b is greater than a, so squaring each expression removes the negative signs and the one with the greater magnitude will eventually end up being bigger.
(-1)^2 = 1; (-100)^2 = 10000
(c) True, as per point in (a). If a > b, then a/b < 1 while b/a > 1, so b/a - a/b will be positive.
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for part (b): apologies, (-3)^3 should be -27, but that doesnt change the concept that a^3 < b^3 (:
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