Why can't the denominator of a rational number be zero?
GeneralClass 12AllAnswered 27 Mar 2026
Answer
The denominator cannot be zero because division by zero is undefined in mathematics.
Explanation:
- If we try to calculate 5/0, we're asking "what number multiplied by 0 gives 5?"
- No such number exists because any number × 0 = 0, not 5
- Division by zero would break fundamental mathematical rules
- Therefore, q ≠ 0 is a mandatory condition for p/q to be a rational number
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