# Three times the second integer less 4

I am learning word problems for Quantitative reasoning GRE exams. English is not my first language and I wonder if the following expression is ambiguous in English: "Three times the second integer less 4" I interpreted that as 3(x-4), but the solution was 3x-4. Are there any conventions in English language? How do I know that "less 4" refers to the whole expression "three times the second integer" rather than to the expression "the second integer"? I have not had this problem in non-mathematical literature since the relations were possible to be derived from the context, but here it does not seem to be the case.

• Spoken English (i.e. - the real language) doesn't support brackets, but the intended sense could be indicated by stress/cadence. I writing, the ambiguity could be avoided by using brackets - but I think whoever decided to put this in a test thinking there was a single unambiguously "correct" answer is in the wrong job. – FumbleFingers Jun 30 '13 at 20:59

The convention is to write 3x-4 or 3(x-4). Mathematical notation was invented to reduce this kind of ambiguity.

However, the word quantity is often used to indicate parentheses. I would generally expect 3(x-4) to be pronounced as:

three times the quantity, 'x' minus four
three times the quantity of the second integer minus four

If the word quantity wasn't present, the phrase is ambiguous, but I would assume the phrase should be interpreted as a sequence of symbols precisely as stated, as though no parentheses are present, 3·x-4. In which case, the conventional order of operations takes precedence and multiplication should be performed first.

• I often hear this same convention used, sometimes without the "the": Three times quantity x minus four. – J.R. Jun 30 '13 at 22:44
• @J.R. I've also heard x minus four quantity times three. Ultimately, this doesn't help reduce ambiguity that much. – p.s.w.g Jul 1 '13 at 0:21

In the absence of any other indication, I would take it in the sequence given:
(1) "Three times the second integer", then
(2) "less 4".
That would also be the mathematical sequence in the absence of brackets.

While I agree that there is an ambiguity, there is nothing to suggest doing the calculation in anything other than the specified sequence.