Unfortunately, the browser used by this site for posting questions is all but useless for mathematics since it rejects symbols.
All that we can see of your question is "Is a b a b for all ... " which cannot be answered sensibly. I could try to guess what you might have wanted to ask but I am not sure I'd guess correctly. And in that case, I may as well simply make up my own questions and answer them!
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A rational number is a number that can be written in the form a/b, where "a" and "b" are integers and b is not equal to zero. For example, whole numbers are rational numbers.
No, rational number are ones that can be written as a/b where a and b are integers. Irrational numbers are those real number that are NOT rational.
Rational numbers are numbers that can be expressed as a ratio of two integers, a/b, where b is not zero.
No. All integers are rational numbers with no fractional part-that is, they can be written as A/B such that B goes into A evenly.
All those numbers than can b represented as one integer over another integer r rational.