Because
1. Positive integers are greater than negative integers, and
2. Division by a positive number preserves the order.
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Rational numbers can be negative or positive.
No, not all negative numbers are rational. There are many negative numbers that are irrational, just like the positive numbers.
Yes. It can also be negative in the numerator. Both positive and negative numbers (as well as zero) can be rational numbers. Both positive and negative numbers can be irrational numbers. Both positive and negative numbers (as well as zero) can be integers.
Any rational positive number is still rational when you make the same number negative.
It the two rational numbers have different signs, then the answer will be negative, otherwise it will be positive.