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I saw this phrase/sentence in a worksheet,

"subtract 4 from 3 times X"

The question asks the students to write the statement using numbers and symbols.

I think the correct answer is 3X - 4, but how can I explain to the students it's not (3 - 4)X? Thank you!

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  • $\begingroup$ The question was put on hold as it does not make an educational or pedagogical angle explicit. Could you maybe include the context in which this question arose via an edit? With this context the question might be reopened. $\endgroup$ – quid Aug 11 '17 at 12:16
  • $\begingroup$ @quid I edited the question. Can the question be reopened? $\endgroup$ – EmmaXL Aug 15 '17 at 8:29
  • $\begingroup$ Thank you for the edit; I reopened it. $\endgroup$ – quid Aug 15 '17 at 10:01
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I think this is a fine education question, particularly because teachers and students should be communicating clearly and correctly to each other.

I suspect "subtract 4 from 3 times X" is ambiguous enough for most readers that we might choose to avoid the operation words (subtract, times, etc.) and use noun phrases. If the arithmetic expression you're after is $3X - 4$, then a clearer option might be "The difference of $3X$ and $4$". Here, you're more clearly separating the the objects (the terms) being subtracted by using the word "and". Similarly, if you want to describe $3(X-4)$, then you could say "the product of $3$ and the difference of $X$ and $4$" -- Kind of awful to have to say, but not ambiguous. The factors (parts of the product) are each clear objects themselves: $3$ and $X-4$

Answering this from a teacher's perspective, I would avoid saying anything like this out loud (if at all possible) without also showing the relevant mathematical expression, unless it was something extremely simple (such as "5 plus 2"). After teaching a section on this topic (translating Math to-and-from English), my students always come away thankful that we can actually use symbols instead of having to be so wordy. However, whenever we happen to read a mathematical expression out in words, I am always taking the time to (try to) make the phrase unambiguous, or I'm pointing to the particular symbols.

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Seems more of a grammar question than a math education question. There is only one way to parse the sentence. "Subtract" is a transitive verb which requires two objects. These are "4" and "3 times X". Thus it reads as $3*X - 4$.

The alternative reading doesn't make sense since "subtract 4 from 3" isn't a noun phrase which can be used as an object for "times", especially since "times" isn't even a verb (it is a preposition).

Note that I am using parts of speech rather than precedence rules to parse the sentence. Natural languages don't have well-defined rules of precedence. A phrase like "3 times X minus 4" is simply ambiguous and could be interpreted in different ways depending on how the speaker stresses the words and times their pauses. "3 times [pause] x minus 4" would seem to mean $3*(X-4)$ but "3 times X [pause] minus 4" would seem to mean $3*X - 4$.

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