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If a:b=1:2, which of the following would be correct?
a) The ratio of a and b is 1:2
b) The ratio of a to b is 1:2
c) The a to b ratio is 1:2.
d) The ratio of the two variables is 1:2
e) The ratio between the two variables is 1:2
f) The a:b ratio is 1:2.
g) The ratio of a and b is 0.5
h) The ratio of a to b is 0.5
i) The a to b ratio is 0.5.
j) The ratio of the two variables is 0.5
k) The ratio between the two variables is 0.5
l) The a:b ratio is 0.5.
It's this simple:
a) The ratio of a and b is 1:2 WRONG
b) The ratio of a to b is 1:2 OK
c) The a to b ratio is 1:2. OK
d) The ratio of the two variables is 1:2 WRONG
e) The ratio between the two variables is 1:2 OK
f) The a:b ratio is 1:2. OK
g) The ratio of a and b is 0.5 WRONG
h) The ratio of a to b is 0.5 OK
i) The a to b ratio is 0.5. OK
j) The ratio of the two variables is 0.5 WRONG
k) The ratio between the two variables is 0.5 OK
l) The a:b ratio is 0.5. OK
A ratio is a "thing"; indeed it exists "between" two values.
(You could certainly use alternates to "between" .. such as "in relation to" "with regard to" and so on ... but "between" is perfect.)
This applies to anything which exists in relation to "two values."
For example, consider difference.
Hence, "the difference between six and eight is two." Note that "the difference of six and eight..." is meaningless.
Exactly the same with, say distance.
"The distance from Nashville to Atlanta is 250 miles." Note that the phrase "The distance of Nashville and Atlanta..." is meaningless.
And: it's perfectly OK to use the pair as a naming adjective: so...
The big distance
The amazing distance
The small distance
The Nashville/Atlanta distance
The Nashville-Atlanta distance
The "Nashville, Atlanta" distance
The a/b ratio
The a,b ratio
The "a,b" ratio
.. all work.
No mystery here.
Here are some relevant definitions in Merriam-Webster's Eleventh Collegiate Dictionary (2003):
ratio n (1660) 1 a : the indicated quotient of two mathematical expressions b : the relationship in quantity, amount or size between two or more things: PROPORTION
The relevant definition of quotient from the same dictionary is this one:
quotient n (15c) 1 : the number resulting from the division of one number by another
And the relevant definition of proportion is this:
proportion n (14c) ... 3 : the relation of one part to another or to the whole with respect to magnitude, quantity or degree ; RATIO
It seems to me that all of the wordings you suggest that end in "1:2" are at best suitable to ratio definition 1b and that all of the wordings you suggest that end in "0.5" are at best suitable to ratio definition 1a.
In other words, if you mean ratio in the sense of "quotient," none of the options ending in "1:2" is appropriate, because all of them are expressing a proportion, not a quotient; and conversely, if you mean ratio in the sense of "proportion," none of the options ending in "0.5" is appropriate, because all of them are expressing a quotient.
Assuming that you have in mind the proportion a:b expressed as 1:2, I would agree with Joe Blow's answers for choices (a) through (f), except that I wouldn't approve of option (e) "The ratio between the two variables is 1:2," on the grounds that "the ratio between the two variables" may refer either to a:b or to b:a, and so the numerical equivalent may be either 1:2 or 2:1. In my view, there is no reason to be inexact in that way, when you have other options (including a number that you don't suggest) that express the proportion with greater precision.
If on the other hand you have in mind the quotient of a ÷ b, expressed as 0.5, I would argue that none of the suggested options is correct because each speaks of the relationship between a and b as if it were a proportion rather than as if it were an operation of division between a dividend (a) and a divisor (b). To express a and b as a ratio in the latter sense, you'd need to say something like this:
The ratio of a divided by b is 0.5.
Or this:
The ratio of a ÷ b is 0.5.
or this:
The ratio of a/b is 0.5.
Strictly speaking, 0.5 by itself isn't a proportion, because it is a single number—the after picture of a mathematical operation in which 1 was divided by 2 (for example). It becomes a legitimate proportion only if you actually or implicitly include the other half of the ratio, as in 0.5:1 or 0.5/1 or (for a change of pace) 0.5a:a.
