# How to pronounce "$a:b=c:d$" in English?

I just realized that I have never used something as simple as proportions in spoken English so far, but today I have to. So simple question for native speakers: How do you pronounce for example $$a:b=c:d$$ where the colon denotes a proportion rather than a division? (For example, in German we'd say "$a$ zu $b$ wie $c$ zu $d$" for proportions as opposed to "$a$ durch $b$ gleich $c$ durch $d$" for divisions).

• I've just enriched my German by approximately $800\%$. May 5, 2016 at 8:49
• @barakmanos 800%? With me writing just 4 different German words? ;) You must have known more than half a German word before, at least things like Kindergarten or Nullstellensatz May 5, 2016 at 8:52
• Well... $800\%$ assuming "Achtung" and "Baby" are both in German. May 5, 2016 at 8:55
• @barakmanos are you sure you didn't enrich it by '1 zu 800'? Feb 25, 2019 at 6:26

"$a$ is to $b$ as $c$ is to $d$."

Or,

"The ratio of $a$ to $b$ is equal to the ratio of $c$ to $d$."

On a rather pedantic note, this isn't an issue of "pronunciation" per se, but one of "verbalization." How do we speak or verbalize a mathematical construct (in this case, an equation between proportions).

In English, we pronounce $a:b :: c:d$ as "a is to b as b is to c", where the colon in particular is pronounced "is to".
The $::$ sign that I have used in place of the equality sign is the proportionality sign.
So if you wish to say $a:b = c:d$, then you will say "a is to b is equal to b is to c".

• Ah, so mathematical proportions are indeed pronounced (or verbalized, as I just learned) just like those pseudo-relations from intelligence tests "dog is to bark as cat is to ...?" May 5, 2016 at 8:49
• "a is to b is equals to b is to c" is wrong. At the very least it should be "a is to b is equal to b is to c", but even then I doubt many people would say it that way. May 5, 2016 at 8:52
• @HagenvonEitzen Indeed they are. We also use the same phrasing in geometry; e.g., for similar triangles, we might say "side $A$ is to side $A'$ as side $B$ is to side $B'$." Those "pseudo-relations" are called "analogies" in the parlance of the standardized tests in which they have traditionally appeared. May 5, 2016 at 8:55
• @joriki It was just a typo. Corrected it. Thanks. May 5, 2016 at 13:33
• My first thought was to verbalize the equality sign the same as I would the double colon; that is, the intent is the same. If I had to use some form of the word "equal", I would probably say "the ratio of $a$ to $b$ equals the ratio of $c$ to $d$". But I'd rather not do that. May 5, 2016 at 13:45