(i) Which rational number is its own additive inverse?

1. Zero is a rational number that is its own additive inverse.

2. Yes

Consider 

$\frac{a}{b}-\frac{c}{d}$ (with $a, b, c$ and $d$ as integers), where $b$ and $d$ are not equal to $0 .$

$\frac{a}{b}-\frac{c}{d}$ implies $\frac{a d}{b d}-\frac{b c}{b d}$ implies $\left(\frac{a d-b c}{b d}\right)$

Since $a d, b c a n d b d$ are integers since integers are closed under the operation of multiplication and $a d-b c$ is an integer since integers are closed under the operation of subtraction, then $\left(\frac{a d-b c}{b d}\right)$

since it is in the form of one integer divided by another and the denominator is not equal to 0

Since, b and d were not equal to 0

Thus, $\frac{a}{b}-\frac{c}{d}$ is a rational number.

3. Yes, rational numbers are commutative under addition. If $a$ and $b$ are rational numbers, then the commutative law under addition is $a+b=b+a$.

4. Yes, rational numbers are associative under addition. If $a, b$ and $c$ are rational numbers, then the associative law under addition is $a+(b+c)=(a+b)+c$.

5. No, subtraction is not commutative on rational numbers. In general, for any two rational numbers, $(a-b) \neq(b-a)$.

6. Rational numbers are not associative under subtraction. Therefore, $a-(b-c) \neq(a-b)-c .$

7. Negative of a negative rational number is a positive rational number.