Which is simpler, a mixed fraction, or an improper fraction?

Question

My son's homework sheet says to solve problems like:

(5) / (15/4)

and to write the "quotient" in its "simplest" form.

The crux of my question is, which form is generally considered the "simplest" from the two forms shown below?

4/3 or 1+1/3

Answer 1

Depends on what level of math you're at. In elementary school, they generally prefer mixed fractions, i.e. the latter. The more advanced math you get to, the less often we used mixed fractions, to the point where at college they are pretty much never used.

So, the short answer is...ask the teacher.

Answer 2

Once you get past grade school there are no mixed fractions. "Improper" fractions are the only kind of notation ever used for rational numbers. In other words 3/2 is always 3/2 and never would anyone ever write 1 & 1/2.

But in grade school, who knows. Best ask the teacher, it all depends on what curriculum they're using. This is unfortunately not a math question, since a mathematician would always use the "improper" fraction, but that might not be the right answer in grade school.

Answer 3

Considering that you can't really divide fractions without considering improper ones, and that the improper fraction $15/4$ is even part of the problem statement, it's likely that an improper fraction is expected.

The word "simplest" here most likely isn't meant to distinguish $4/3$ from $1 + 1/3$; it's probably meant to distinguish it from things like $8/6$.

The word "quotient" probably refers to the fact that you're dividing $5$ by $15/4$.