Math CentralQuandaries & Queries


Question from John, a teacher:

I teach in a Faculty of Education. A colleague in the university asked me about fractions and lowest terms. I am quoting the person below, and would appreciate your insights into the question/thought.

"One I'm struggling with is why (for example) 6/18 is not considered as good an answer to a fraction question as 1/3. The traditional response is that 6/18 is not in lowest terms so the question has not been finished until the fraction is reduced, but what actually makes the lowest terms answer the better one? Is it convention? Is there a way to explain why simplest form answers in fractions are right and and anything else is considered incorrect without alluding to some need for this 'good habit' elsewhere in math or science? Is there a real-life reason?"

Thank you for any insights and if you have nothing to offer to this query, that is fine too. I appreciate your consideration.


Hi John,

The usual reason is that lowest-terms notation makes it easier to answer the question "are these fractions equal?" (And, of course, "is this the right answer?")

However, there are cases where this is not done, often where one might also want to answer the question "which of these is bigger?" In this case the use of a standard denominator is common.

"95%" rather than "19/20"
"48 minutes of arc" rather than "4/5 of a degree"
"18 thousandths of an inch" rather than "9/500 of an inch"
"sixteen millimeters" rather than "2/125 meter"
Cabinetmakers use 2/4 of an inch as a plank thickness because this is an exact dimension - half-inch may be nominal.

Good hunting!

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