A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not zero. In the case of 0.67, it can be written as 67/100, which is the ratio of the integers 67 and 100. Since both 67 and 100 are integers and the denominator is not zero, 0.67 is considered a rational number.
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Yes.
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It must be a generalised rational number. Otherwise, if you select a rational number to multiply, then you will only prove it for that number.
Yes. Any rational number divided by another rational number is also rational.