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I want to ask a question as a university student) I really love strict and complete mathematics. I don’t like to learn and cram something and I want to understand and axiomize. I want to ask a question: why, when multiplying and dividing the numerator and denominator of a fraction, the fraction itself does not change its value. and what does it mean to reduce, why can we reduce the numerator and denominator of a fraction? why can we multiply fractions, how are they multiplied, for example, why can we multiply 10 by 1/2 and what kind of number will it be? Of course, I understand everything perfectly and intuitively, and I’ve read a couple of books about number theory, but somehow I still want to figure it out and prove all these facts as strictly as possible, intuitively and clearly they are very clear to me

Bill Dubuque
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    Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. – Community Jun 20 '24 at 22:27

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