In a map, if $1$ inch refers to $120 \mathrm{km}$, then find the distance between two cities $B$ and $C$ which are $4\frac{1}{6}$ inches and $3\frac{1}{3}$ inches from the city $A$ which is in between the cities $B$ and $C$.

Give an example and verify the following statement.

The collection of all non-zero rational numbers is closed under division.

Give an example and verify the following statement.

Subtraction is not commutative for rational numbers.

Give an example and verify the following statement.

Division is not associative for rational numbers.

Give an example and verify each of the following statements.

Distributive property of multiplication over subtraction is true for rational numbers. That is, $a(b-c)=ab-ac$.

Give an example and verify each of the following statements.

The mean of two rational numbers is rational and lies between them.