How to read parentheses equation [closed]

I have problems with reading mathematical equations in which there are parentheses; could anybody help me?

For example:

1. (x−a) (x+b) = 5
2. (x−a) + 2 (a+10) = z
3. 2 + (10−a) d = 7
4. y = a/b (7c+11)

How should I read this kind of equations?

• Are you sure you are in the right forum? Sep 15, 2012 at 8:42
• For the second one, I'd read it aloud as: "ex plus ay plus twenty equals zee" ;-). Sep 15, 2012 at 12:00

The primary way of communicating mathematics is not oral.

If absolutely necessary, you can usually get around major problems with tone of voice, pausing and speed of pronunciation. You can sometimes add in little linguistic clues, e.g. "x minus a, all multiplied by x plus b", or "two, plus d lots of ten minus a", but most of the work is done by making sure you pronounce those commas very carefully. If you don't, you might get questions back like "wait, was that x-minus-a ... multiplied by ... x-plus-b, or x ... minus... a lots of ... x-plus-b?".

You could also go for the more literal approach of pronouncing the brackets: I've heard mathematicians say things like "bracket x minus a close bracket times bracket x plus b close bracket", but this is pretty extreme. When (the going gets tough and) the formulas get long, just write it down, say something like "x minus a times x plus b", and point. That's what everyone else does.

• Also, don't forget that it's often obvious, either from the derivation or from the form, if your audience is sufficiently mathematically mature. If you're quoting a formula as "x plus a times x minus b", you probably don't mean x + ax - b (because this is not written very sensibly). But if you're proving a formula, and you have a sum of three numbers, and the first is x, the second is ax and the third is -b, then it'll probably be obvious from your explanation that x + ax - b is what you mean. Basically, assume your audience is mathematically literate, or write it down (or both). Sep 15, 2012 at 9:07

I have heard a few variants when it comes to reading aloud mathematical expressions involving parentheses. These include terms such as:

• (open) parenthesis, close parenthesis
• within parentheses
• (open) bracket, close bracket
• within brackets
• quantity, close quantity

I do believe that the term quantity is what is used by screen-readers which are MathML compatible. The use of this term is supported to an extent in this paper (PDF). An American educational organisation also prescribes it in addition to the others:

Expressions containing parentheses or brackets can be read in any of the following three ways:

quantity, close quantity

paren, close paren (or bracket, close bracket)

left paren, right paren (or left bracket, right bracket)

For "paren, close paren" or "left paren, right paren," it is also acceptable to use "parenthesis" instead of "paren." If you use the term "quantity," in complicated expressions, announce where enclosed portions end by saying "end quantity."

E.g., (2x - 6y) - 10 could be read

as "The quantity two x minus six y, close quantity, minus ten;"

as "paren, two x minus six y, close paren, minus ten;"

or as "left paren, two x minus six y, right paren, minus ten."

a (x - y) could be read as "a, parenthesis, x minus y, close parenthesis."

a × b2 could be read as "a times the square of b."

Use pauses to audibly group sections of an expression together.

z + (-a) could be read as "z plus [PAUSE] paren negative a close paren."

As mentioned by Billy, pauses, speed and intonation greatly assist in avoiding confusion.

Here's how I would read the examples aloud. Commas/pauses are important to seperate the different parts.

In my university experience so far, I haven't heard math teachers read aloud the start and close parenthesis, since you usually write it down while reading it.

1. (x−a) (x+b) = 5

• x minus a times the quantity of x plus b, equals 5.
2. (x−a) + 2 (a+10) = z

• x minus a plus, 2 times the quantity a plus 10, equals z.
3. 2 + (10−a) d = 7

• 2 plus quantity 10 minus a, times d, equals 7.
4. y = a/b (7c+11)

• y equals a divided by b times quantity seven c plus 11.
• this one might be clearer if the divide by b was at the end, instead of being in the middle. Written, you could have the b as the denominator of the whole right hand side, instead of needing to remember the order of operations rules.

If you have trouble with the Maths, remember BEDMAS — Brackets, Exponents, Division, Multiplication, Addition, Subtraction. Brackets and Exponents always go one and two. Division and Multiplication are left to right so sometimes it is BEMDAS; and Adding and Subtracting are Left to Right as well so you can have BEDMSA or BEMDSA etc.

So

1. do Brackets;
2. do Exponents;
3. do the multiply and divide, left to right;
4. do the add and subtract, left to right.

If by reading you mean reading out loud then you would say “Open brackets, x − a, close brackets. Open brackets, x + b, close brackets, equals, 5.”

It is assumed that the person listening will either write it down or make a mental picture of it, so you don’t have to say multiply the two sets together. That would be assumed. However, if you were reading to an inexperienced maths person you would say at the end “Remember you will need to multiply the two sets.”