Division Pattern

Why is the answer to 5 ÷ 2/3 exactly one-half of the quotient for 5 ÷ 1/3? Is this relationship between quotients always true when you divide by 2/3 and 1/3?

What happens when the divisor is changed so the problem is 5 ÷ 3/4 and 5 ÷ 1/4?

Does the relationship between divisors and quotients remain constant for all whole numbers?

What happens when the dividend is a fraction? Does the relationship remain the same? Why or why not?