# Is there any specific convention to how mathematical equations are “read out”?

Often, mathematical information and formulas are shared through text, maybe on books or on websites. If you see the equation:

$$x + 3 = 4y$$

we can easily read it out as "x plus three equals four y". But for some other equations such as:

$$\frac{x+3}{x-7}=y$$

it doesn't seem too obvious on what it should be read out as. I would read it as "x plus three the whole divided by x minus seven equals y", however someone else may read it out differently.

My question is therefore: If in a situation where oral communication of mathematical equations is necessary, does there exist a convention to read out mathematical equations such that one particular equation is read out in only one way, and that it is possible to deduce the equation from the spoken name alone?

• In French, I would read it as "x plus trois sur x moins sept égal y", which would translate as "x plus three over x minus seven equals y". I don't know if "over" really is commonly used in English though. I don't think there is any universal convention though. What I said could also be interpreted as $x+\frac{3}{x} -7 = y$. If I notice that the person I am talking to has gotten it wrong, I would just say it again, insisting on the expression I really meant. – Suzet Jul 12 '18 at 1:55
• "over" is indeed used by some people I know. And here is the point, even in English, the same equation is being read out in two different ways. – Pritt Balagopal Jul 12 '18 at 1:57
• The different groupings / implied parantheses are often expressed via pauses and prosody. – Hagen von Eitzen Jul 12 '18 at 2:02
• "The quotient of [the quantity] $x+3$ and [the quantity] $x-7$ is $y$." To avoid a pile-up of symbols at the end, one could say "$y$ is the quotient of $x+3$ and $x-7$." – Blue Jul 12 '18 at 2:26
• @HagenvonEitzen: On the first day of a stint as a Pre-Calculus substitute teacher, I instructed my students to express groupings using "air parentheses", indicated by raising one's slightly-bent arms over one's head. So, here: "[raise arms] x plus three [lower arms] over [raise arms] ex minus seven [lower arms] is y." The students looked at me like I was crazy, but took to the practice. So earnest were they in this —even prompting each other when someone would forget— that, at the end of my six-week stay, I didn't have the heart to tell them that I'd only been kidding that first day. :D – Blue Jul 12 '18 at 2:33

I would like to elaborate on Hagen von Eitzen's insightful comment:

The different groupings / implied parantheses are often expressed via pauses and prosody.

I think this is exactly right and plays an extremely important role in disambiguating oral mathematics. There is a huge difference between:

"X plus 3, over X minus 7, equals Y"

and

"X, plus 3 over X, minus 7 equals Y"

and

"X plus 3, over X, minus 7 equals Y"

If the cadences and pauses in the sentences are read aloud consistently, I think it is unlikely that anyone would transcribe one of those in place of another.

However, in some cases (particularly for extremely complicated expressions with groupings nested inside other groupings) one may call attention to the grouping using verbal annotations like "the quantity" or "all". For example, the quadratic formula is often read aloud as

• "X equals negative b, plus or minus the square root of the quantity b-squared minus 4ac, all over 2a".

I would read $$\frac{x+3}{x-7}=y$$ as:

Quantity $x$ plus $3$ over quantity $x$ minus $7$ equals $y$.