# how to formulate/name a specific simple math operation in a formal way?

I wonder how to formulate/name a specific simple math operation. For instance, consider the following equation/indentity:

(Eq.1) y=a+b+c

where a is an effect, b is an effect and c is an effect and when all added they sum op to y. (note: in fact, an effect only comes to play when all terms are in first differences, but for simplicity I neglect that step)

My question: If I only want to consider the effects through b and c, the simple math operation would be to get "a" to the left. How can one say that in a formal/academic way?

How I would do it:

To examine the effects through "b and c", I neutralise the effects through "a" in Eq. (1) and consider the spread between "y-a"

OR

To examine the effects through "b and c", I cancel out the effects through "a" in Eq. (1) and consider the spread between "y-a"

Which of the two are preferable or does someone have a better option?

Ok, I think I see what you're saying. You want to know what we say to make this equation:

Y = A + B + C

become this one:

Y - A = B + C

In this case we say:

"subtract A from both sides of the equation."

Early in math education the teacher would explain how subtracting A from A cancels A out on the right side of the equation, but later on the teacher just assumes the student understands this and doesn't go into that much detail.

Similarly with this equation

Y = B * A

We would say "divide both sides by A" to get:

Y/A = B

• Thank you for your informative answer. So a formal way to say this would be: ''cancel out effects through ''a''? Since I think ''subtract A from both sided of the equation'' is not really formal right? Jan 15, 2017 at 15:31
• This is much too simple an example for me to consider how to explain it in a "formal way". In a formal proof I think you wouldn't bother to explain the trivial steps like this because you can assume the reader knows what you are doing -- they are other mathematicians. Jan 15, 2017 at 15:47
• It is a trade-off between giving a simple example and using too much jargon (I got critique on my previous post that I used too much jargon). But, on topic: it is not wrong to explain "subtract A from both sided of the equation'' by saying that you "cancel out" ''a'' in Eq. (1) ? Jan 15, 2017 at 16:25
• When you do the same thing to both "sides" of an identity, the identity persists. Phrases like "cancel out" are a teacher's shooting-from-the-hip short-hand terminology when referring to the visual representation of the equation. This kind of language is used even before the students understand the concept of "identity". As Andrew says, "early in math education". Jan 15, 2017 at 17:32
• The terms used in more advanced math courses are simplify and reduce. We simplify or reduce an equation by eliminating variables, but again you don't usually bother with trivial explanations. Instead you just cross things out or move things around and it's expected that others will follow along. It's more a Math thing than an English thing. Jan 15, 2017 at 17:58