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Why do we need q ≠ 0 in the definition of a rational number p/q?
ABecause q = 0 makes the numerator infinity
BBecause division by zero is undefined — there is no number x such that 0 × x = any non-zero p
CBecause 0 is not a real number
DBecause q must be positive
Answer & Solution
Correct answer: B. Because division by zero is undefined — there is no number x such that 0 × x = any non-zero p
If q = 0, then p/0 has no meaningful value: there's no number that, multiplied by 0, gives a non-zero result. So 1/0, 5/0, etc. are 'undefined' — they're not rational, real, or even meaningful as numbers in standard arithmetic. The q ≠ 0 condition keeps the definition well-defined.
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