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Question
If `p/q` is a rational number and m is a non-zero common divisor of p and q, then `p/q = (p ÷ m)/(q ÷ m)`.
Options
True
False
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Solution
This statement is True.
Explanation:
e.g. Let m = 1, 2, 3, ...
When m = 1, then `p/q = (p ÷ 1)/(q ÷ 1) = p/1 ÷ q/1 = p/1 xx 1/q = p/q`
When m = 2, then `p/q = (p ÷ 2)/(q ÷ 2) = p/2 ÷ q/2 = p/2 xx 2/q = p/q`
Hence, `p/q = (p ÷ m)/(q ÷ m)`.
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