Fun fact: Crêpe comes from Old French crespe, from Latin crispus - which is where we get "crisp" and "crispy" from. French uses the little ^ above the vowel to (normally) show where there was once a "s". You see this in château (castle) too. Might help someone, might not, thought I'd bring it up regardless.
A crepe, the crepe. What's the difference? I understand un/une and le/la/les and their literal translations, but a and the imply one. Which would be the more likely statement "i am eating a crepe" or "i am eating the crepe"? As if there is ever only one crepe, the crepe; you know, the crepe we are all familiar with.
Neither statement is more likely than the other - it depends on the intended meaning.
In this particular case the statement is "je mange la crêpe" - "I am eating the crêpe" - "I am eating the crêpe you made for me" - "the crêpe on my plate" - I am eating the crêpe rather than the sandwich. We are referring to a specific crêpe.
If we are not referring to a specific crêpe then it is "I am eating a crêpe" - "je mange une crêpe".
In this particular example the English and French articles are working in the same way. Unfortunately English and French articles don't always work the same way.
I tend to think that you will make progress in hearing all syllabes and sounds right when you have practiced saying them. My advise would be that you repeat together with the voice, many times, then you will EXPECT the word "la" and then you will hear it. Please try and come back to tell me.
"I eat" is simple present, which can be used to express a habit: at breakfast, I (usually) eat cereals.
"I am eating" is continuous present, which expresses the fact that the event is in progress at the time I speak: right now, I am eating cereals.
In French, there is no "continuous" tense as verbal form. So both "I eat" and "I am eating" generally translate to simple present "je mange".
However, if you want to express that the action is in progress now, you can use "je suis en train de manger" (I am in the process of eating).
"De la" is the feminine partitive article - that means it expresses an unspecified amount of a feminine non-countable noun.
"Crêpes" are countable. So if we were eating "a crêpe" or "crêpes" it would be "une crêpe" or "des crêpes".
However in this particular case we are eating "the crêpe" - the specific crêpe on our plate. So we use the definite article "la".
I understand your argument in terms of grammar, but a literal translation of the French definite article (and articles are used much less, and differently, in English) yields a sentence in English which I believe cannot be made sense of without context. What plate? Is it "the crepe" as opposed to some other food item? As opposed to some other crepe? Is there an argument over who will eat a specific crepe? I believe there should be more flexibility when interpreting a stand-alone sentence such as this. However, this is the second time this has happened to me so far, implying it is a "thing" on this site, and I intend to let the matter rest here.
You are right we can not fully understand this sentence without context. That is true of both the French sentence and the English translation.
The French sentence is referring to a particular crêpe. We have to read it as part of a larger conversation where the context is made clear. Maybe it is one crêpe rather than another, maybe it is the crêpe rather than some other specific food item previously mentioned etc. However the English translation is no more lacking in context than the French original. It is exactly the same.
In this particular case a literal translation of the definite article is the only option - it is not just a DL thing.
If we translated it as "I am eating a crêpe" - that might be a more satisfying stand alone sentence but it is clearly not what the French original means.