Quotient vs Ratio vs Fraction

Common usage observes distinctions that mathematics does not. The numeral 2 is a valid quotient, but not a fraction or ratio, although 2/1 and 2:1 are implied mathematically. Quotients may be in decimal form, which is not a proper fraction or ratio. Quotient is almost exclusively used in explicitly mathematical contexts.

In normal usage, fractions compare parts to wholes. "A small fraction of Green Party candidates support declaring Jupiter as an enemy planet" compares the in group (Jupiter is an enemy) from the whole (all Green Party candidates).

A ratio is normally used to distinguish between two groups, without requiring that the whole is addressed. "Ironically, Republicans favor mandatory tea drinking in a 2-to-1 ratio over tea party members" is not addressing the whole of all political party members, but specifically comparing the two groups.

A quotient is the result derived from dividing two numbers. For example, dividing 6 by 3 gives a quotient of 2.

A ratio is the quantity of one thing relative to the quantity of another. For example, Georgia Tech's guy-to-girl ratio is 2:1. This means that there are twice as many guys as there are girls at Georgia Tech. Another way to look at this is saying that for every girl at Georgia Tech, there are two guys.

A fraction is very similar to ratio but not quite. A fraction is a way to describe a quantity in parts of a whole, a whole, or more than a whole. But it is similar to a ratio since it describes quantities in parts, or relative to another quantity (what constitutes a "whole"). For example, after the pizza is cut up into eight pieces, eating one will remove 1/8 of the pizza. One piece is only one of eight pieces that make up the "whole" pizza.

So I guess the short answer is no, that you cannot use these words interchangeably. They each cater to different scenarios. Perhaps, the closest to being used interchangeably are ratio and fraction.