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The question asked is very vague. There are many things that can be done with rational numbers, some basic operations are addition, subtraction, multiplication and division.
When working with rational numbers, the order of precedence of operations can be remembered by the mnemonic BODMAS. First, operations with brackets should be done first, then deal with exponents, multiplication and division is done before addition and subtraction. If there are multiplication/division or addition/subtraction operations to be performed, move from left to right.
The associative and commutative property is unique to addition and multiplication:
(a+b) + c = a + (b +c) and (a*b)*c = a*(b*c)
a + b = b + a and a*b = b*a
The distributive property gives the relation a*(b+c) = a*b + a*c
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