# Is this a misuse of the word “evaluate”?

I have found the following use of the word "evaluate" in several math books:

"To evaluate the continued fraction, start at the bottom and work your way up:"

$\huge \underbrace{2 + \frac{1}{1+\frac{1}{3}}}=2 + \frac{1}{\frac{4}{3}}=2+\frac{3}{4}= \underbrace{\frac{11}{4}}$ Why is this called an "evaluation" and not a simplification?

-
This may be of interest. – goblin Nov 28 '13 at 11:11
Because clearly fractions and decimals are the right way of representing numbers, not continued fractions. This is entirely a product of how we've been trained to think about numbers. – Dustan Levenstein Nov 28 '13 at 11:52
@DustanLevenstein Have we not also been trained to simplify an expression involving fractions, you write it as a single fraction in simplest form? – Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ Nov 28 '13 at 11:57
That doesn't contradict the use of the word "evaluate"; it simply means that "evaluate" and "simplify" are equally good words to use to describe this particular procedure. – Dustan Levenstein Nov 28 '13 at 12:03
I just checked the index of my Algebra textbook (Dummit & Foote) for the word "evaluate", and found the evaluation homomorphism from a polynomial ring. Indeed, you are right; I'm pretty sure that is not what we are discussing in this context. (NOTE: this is a joke.) – Dustan Levenstein Nov 28 '13 at 12:52

@badass: I agree with Peterson that $\frac{m}n$ is proper if $|m|<|n|$. It’s also true that use of the term proper fraction is largely limited to the early grades, before the question of negative fractions arises, and there’s no telling how any given fourth grade teacher, say, would answer the question ‘Is $-2/3$ a proper fraction?’ – Brian M. Scott Dec 12 '13 at 20:56