I am mathematician for whom English is the second language.
In general I feel like I do not have major problems keeping up with math vocabulary, whether I am reading an article or giving a lecture.
That being said, there is one question which have been bothering me for quite a long time.
I am not exactly clear on the nuances of the meaning the three words from the title.
To be more specific, the essences of my concerns can be articulated as
Can I use words "quotient", "ratio", and "fraction" interchangeably?
I am mostly concerned about using them within math academia environment, although more general rules would also be interesting to see.
In particular, which of the words from the list would be appropriate to use when talking about dividing one function by another one?
Ultimately, even laconic yes/no answer will be greatly appreciated.
However, I am also somewhat curious to see detailed explanation of how each of these words is different from the others.
PS As mentioned in the comment section by @BrianDonovan, my list of three words can probably be extended with the word "proportion".
EDIT:
Following advices of @Rathony, I include the outline of Wikipedia definitions of each of these words:
- In mathematics, a ratio is a relationship between two numbers indicating how many times the first number contains the second
- A fraction (⋯) represents a part of a whole or, more generally, any number of equal parts.
(⋯)
The word fraction is also used to describe mathematical expressions that are not rational numbers, for example algebraic fractions (quotients of algebraic expressions), and expressions that contain irrational numbers (⋯)- (⋯) a quotient (⋯) is the result of division.
Let me point out once again that I am particularly interested in the differences in use of these words in math academic environment, e.g. about the case when both enumerator and denominator of a fraction are general functions or algebraic expressions of some sort.
Best Answer
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.