# How to express the ratio a=b/c?

How to express the ratio `a=b/c` into words?
(e.g., in the context of an election: `turnout = number of expressed votes / number of person listed on electoral register`)

I would suggest "`a` is the ratio of `b` divided by `c`". However, it seems pretty bulky to me.

• I could also say "The `turnout` is `the number of expressed votes` divided by `number of person listed on electoral register`". I would however like to keep explicit the notion of ratio (i.e. a number without unit). – ebosi Jan 4 '17 at 16:42
• What do you mean by "expressed votes"? I don't think that's a commonly used term in this context. I think you mean "votes cast". – Jay Jan 4 '17 at 17:21
• Does this differ between regions? In Australia I'd be much more inclined to say 'divided by' than 'over'. – The6P4C Jan 5 '17 at 3:31
• In practice, ratios are often expressed as some standard multiple of b/c, for example "percentage turnout" (which is 100 times b/c) or "deaths per 100,000 population". The reading-aloud tag (added in an edit) implies that the formula is already written in some text with the symbols "=" and "/" and you want to recite the text orally; was that the intended question, or do you intend to write the text rather than just read it? – David K Jan 5 '17 at 13:16

Ratios are most often notated as a:b, rather than a/b, which is said "a to b". For example, if I have ten bananas and four apples then I could say the ratio of bananas to apples is 5 to 2 (or 10 to 4). So in your situation you could say:

Voter turnout is the ratio of votes cast to registered voters.

To emphasize that a is a sub-set of b we often use the phrase "out of" or "in" (these might sound opposite, but they actually mean the same thing), especially when giving the actual number. A very common type of statement would be something like

One out of/in ten* registered voters actually cast a vote in the recent election. This ratio is a little higher than the previous election, although in general voter turnout has been declining for the past several decades.

This language for ratios of part-to-whole works well for the non-mathematically-inclined who might be thrown off by mathier terms like "divided by" or "fraction" or "quotient". (I know people who have a hard time with the idea of "one divided by three" but no problem at all with "one in three"). Unfortunately, it is a little awkward for a purely explanatory sentence, with no numbers. You could perhaps say:

The voter turnout ratio is the number of voters who actually voted out of the total number of registered voters.

However, I might stick with the "to" language, just changing your terminology a bit to make the relationship clear:

Voter turnout is the ratio of registered voters who actually cast votes to total registered voters.

*All numbers there are fictional.

The most common way to express fractions (or ratios) is with "over".

3/4 is three over four

7/15 is seven over fifteen.

A = B/C A is equal to B over C

However your "bulky" way is better for anything other than casual conversation, such as a school report.

The common way to say this is, "Turnout is the number of votes cast divided by the number of registered voters", or "... the number of people who voted divided by the number of registered voters".

You can say "over" instead of "divided by", e.g. "votes cast over registered voters".

Or if you want to express it as a percentage, you might say "the percentage of registered voters who cast a vote".

For casual writing you don't usually use the word "ratio", just say "X divided by Y". You can say "the ratio of X divided by Y" or "the ratio of X over Y", but I think that's unnecessary extra words. I think generally, a "ratio" means a number between 0 and 1 while a percentage indicated a number between 0 and 100, i.e. a ratio might be ".47" while a percentage would be "47%". But that might be a little technical, the average person might not understand it that way.

You can also say it like this:

turnout ratio is total votes expressed over total registered persons.