# How to explain “fractional terms”?

as I can see there are mainly two ways to introduce fractional terms. Two examples to demonstrate the two variants:

1. $\frac{a^2+3}{a}; \frac{3}{2c}$

2. $T(a) = \frac{a^2+3}{a}; T(c) = \frac{3}{2c}$.

In fact, the word "function" or "functional term" or "equation with variables" has not been learned at this point, but I think that variant two is able to demonstrate better that any term can be seen as a "number machine", in which you "throw" a number and get a certain result. I could imagine that the first variant leads to young learners being unsure what exactly to do with this experssion.

I made a quick research in some school books here (in Germany) and found those two variants. So even though this is really just a small difference, do you have any opinion or experience?

• What age group do you teach? I use fraction for just numerical and rational function for the functions of polynomials divided by polynomials. – Chris C Apr 28 '16 at 15:38
• It is (sometimes) helpful to distinguish "rational expressions" from "rational functions" for precisely the same reason that it is (sometimes) helpful to distinguish between "polynomials" and "polynomial functions". – mweiss Apr 28 '16 at 16:04
• Personally, I would not write $T(a) = \frac{a^2+3}{a}$ without first having the notion of "function". – Gerald Edgar Apr 28 '16 at 16:20
• "I could imagine that the first variant leads to young learners being unsure what exactly to do with this experssion." -- Well they shouldn't think that there's automatically something "to do" on any piece of math without a natural-language direction or question. – Daniel R. Collins Nov 2 '16 at 3:04
• I don't see how fractions are relevant to the question; the same question could be asked about $a+1$. – user797 Nov 2 '16 at 12:20