Integers are whole numbers. 1 3/4 is not a integer whereas 1 is.
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They are not the same!The set of integers is closed under multiplication but not under division.Multiplication is commutative, division is not.Multiplication is associative, division is not.
I am not at all sure that there are any rules that apply to integers in isolation. Any rules that exist are in the context of binary operations like addition or multiplication of integers.
add subtract divide multiplication
Those are the rules of multiplication (and division).
You need the rules of multiplication as well as of addition. But multiplication of integers can be viewed as repeated addition. Thus, if p/q and r/s are two rational numbers then their sum is(p*s + q*r)/(q*s)