Is 9/1 an improper fraction?

Question

My son took a test in school. The teacher told them that they did not need to simplify improper fractions in their answers.

On one question, for example, the answer of 28/3 was marked as correct. But when's son correctly answered 9/1 to one question and 10/1 to another, the teacher marked both wrong. The teacher explained that 9/1 and 10/1 are not improper fractions.

The textbook provides an example of 9/9 as an improper fraction, but nothing where the denominator is 1. Frankly, I think this sort of nonsense makes students hate math and school. Lots of hard work, follow instructions, and the teacher flunks you anyway.

Answer 1

Techniccaly 9/1 is an improper fraction since the denominator is less than the numerator. But the teacher wants to avoid the students spending time on converting an improper fraction into a mixed number, yet the teacher expects the students to wrote 9/1 as 9 as it is "obvious". I think that the teacher should point this out very clear before the test takes place what is to be expected here. (Or maybe he did, we don't know) Anyway, to mark it wrong altogether is overkill and certainly a reason why a kid may not like math anymore. I would say, either simply an improper fraction into a mixed number at all times, or you don't.

Answer 2

The definition of "improper fraction" that your son would have probably been given is something like "an improper fraction is a number of the form $\frac{p}{q}$ where $p$ and $q$ are both whole numbers and $p\geq q$". I find it very doubtful that your son's teacher, or the textbook, would have included anything which excludes $q=1$, so unless the teacher said that this special case was to be excluded from the definition, $9/1$ is an improper fraction. If it's not an improper fraction, then what is it? It's certainly not a a proper fraction, nor is it a mixed fraction.

"Simplifying" an improper fraction in this context is writing it as a "mixed" fraction, which is a number with an integer part and a fractional part. In the case of $9/1$, the integer part is $9$ and the fractional part is $0$, so to write $\frac{9}{1}=9$ is indeed "simplifying an improper fraction", and I understand why your son would have left his answer like that.

The teacher is probably trying to make sure that students understand that $\frac{9}{1}$ is in fact "obviously" equal to $9$. That's a noble goal I guess, but according to the instructions as you've relayed them, $\frac{9}{1}$ is certainly a correct response.