**In a chemistry class, students were learning about boiling point of various elements.Reuben has compiled a table that gives boiling points of each of various elements.

The lowest boiling point is of Element X: – 200 degrees Fahrenheit. The highest boiling point is of Element Y: 550 degrees Fahrenheit

Find the difference between the lowest and highest boiling point**

I know how to calculate the difference. -200 – 550 = -750.

I am not sure if the answer is written as a negative or positive. Isn’t difference in temperature always written as its absolute value? Will the answer be – 750 F or 750 F ?

Would greatly appreciate if you could explain what the correct answer is.

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    $\begingroup$ Use positive. $550-(-200) = 550+200 = 750$ $\endgroup$ – KM101 Nov 9 '18 at 8:33
  • $\begingroup$ @KM101 I agree but also "Find the difference between the lowest and highest" where "lowest" comes before "highest" can be confusing. $\endgroup$ – rb612 Nov 9 '18 at 8:33
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    $\begingroup$ @rb612 I guess I can see where the confusion can come from. Seems awkward to use negative as a difference though, so an absolute value/positive answer seems better. $\endgroup$ – KM101 Nov 9 '18 at 8:35

When you calculate $-200-550 = -750$, you have found that the boiling point of X is "$-750$ degrees higher" than the boiling point of Y. In other words, the sign tells you the direction of the difference, it tells you which of the two is higher.

If you were asked "How much higher is the boiling point of X than the boiling point of Y", then $-750$ degrees would be the right answer. However, when asked for the difference between two temperatures, that usually means just the distance between the two points on a thermometer scale, and distances are non-negative.

Some times, in order to get the correct answer, math exercises partially turn into language and culture exercises instead, where you have to know the glossary and what common phrases usually mean. This is one of those times. Combinatorics and probability is another field where this is a huge factor (you have to know that in a "hand of cards", there are no repeated cards and the order doesn't matter, for instance).


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