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Question
Give an example and verify the following statement.
Division is not associative for rational numbers
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Solution
Let a = `2/5`, b = `6/5`, c = `3/5` be three rational numbers.
a ÷ (b ÷ c) = `2/5 ÷ (6/5 ÷ 3/5)`
= `2/5 ÷ (6/5 xx 5/3)`
= `2/5 ÷ 2/1`
= `2/5 xx 1/2`
= `1/5` ....(1)
(a ÷ b) ÷ c = `(2/5 ÷6/5) ÷ 3/5`
= `(2/5 xx 5/6) ÷ 3/5`
= `1/3÷ 3/5`
= `1/3 xx 5/3`
= `5/9` ....(2)
From (1) and (2) `1/5 ≠ 5/9`
a ÷ (b ÷ c) ≠ (a ÷ b) ÷ c
∴ Division is not associative for rational numbers.
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