Mi uzas pli akran tranĉilon, kiam mi volas tranĉi malmolan panon aŭ grandajn tomatojn.

Because tranĉilon is the direct object of uzas, so it takes the accusative ending -n. In Esperanto, adjectives must agree with the nouns they describe in number and case.

So:

• tranĉilo = a knife
• tranĉilon = a knife / knife as direct object
• akra = sharp
• akran = sharp, matching an accusative singular noun

The word pli does not change that. It just means more.

So:

• akra tranĉilo = a sharp knife
• akran tranĉilon = a sharp knife (as object)
• pli akran tranĉilon = a sharper knife (as object)

Pli makes a comparison: more.

So:

• akra = sharp
• pli akra = sharper / more sharp

In the sentence, pli akran tranĉilon means a sharper knife.

Esperanto usually forms the comparative with pli + adjective:

• pli granda = bigger
• pli bona = better
• pli akra = sharper

If you want to say what it is being compared to, you can add ol:

• pli akra ol tiu = sharper than that one

In your sentence, the thing being compared is not stated, but it is understood from context.

The ending -n marks the direct object in Esperanto.

In this sentence:

• Mi uzas = I use
• what do I use? tranĉilon

So tranĉilo becomes tranĉilon.

This is one of the most important uses of -n in Esperanto: marking the thing directly affected by the verb.

For the same reason: they are direct objects of tranĉi.

Inside the clause mi volas tranĉi malmolan panon aŭ grandajn tomatojn:

• tranĉi = to cut
• cut what? panon or tomatojn

So both nouns are direct objects and take the accusative ending.

You can see the agreement clearly:

• malmolan panon = hard bread
• grandajn tomatojn = large tomatoes

Both the nouns and their adjectives take the endings they need.

Because the noun is plural and also accusative.

• tomato = tomato
• tomatoj = tomatoes
• tomatojn = tomatoes as direct object

The adjective must match:

• granda tomato = a large tomato
• grandaj tomatoj = large tomatoes
• grandajn tomatojn = large tomatoes as direct object

So:

• -j = plural
• -n = accusative
• adjectives match the noun in both

That is just the speaker’s choice based on meaning.

Panon is singular because bread is often treated as a general substance or as one loaf/piece. English does this too: hard bread does not have to be plural.

Tomatojn is plural because the sentence is talking about large tomatoes in general, probably more than one.

You could change the number if the situation changes:

• malmolajn panojn = hard breads / hard loaves
• grandan tomaton = a large tomato

So the grammar is normal; the singular/plural choice depends on what the speaker means.

Yes. Malmola is formed from mola by adding the prefix mal-, which gives the opposite meaning.

• mola = soft
• malmola = hard

This is a very common feature of Esperanto. Instead of learning a completely separate word, you can often form an opposite with mal-:

• bona = good → malbona = bad
• granda = big → malgranda = small
• fermi = to close → malfermi = to open

In the sentence, malmolan panon means hard bread.

Kiam means when. It introduces a time clause.

So:

• Mi uzas pli akran tranĉilon = I use a sharper knife
• kiam mi volas tranĉi... = when I want to cut...

Together: I use a sharper knife when I want to cut...

This is a normal subordinate clause in Esperanto. The verb forms stay straightforward; Esperanto does not change tense because of sequence-of-tense rules the way English sometimes does.

Because kiam mi volas tranĉi... is a subordinate clause, and Esperanto commonly separates subordinate clauses with commas.

So the comma helps show the structure:

• main clause: Mi uzas pli akran tranĉilon
• subordinate clause: kiam mi volas tranĉi malmolan panon aŭ grandajn tomatojn

You will often see commas before words like kiam, se, ĉar, ke, and kvankam.

Because after voli (to want), Esperanto uses the infinitive.

So:

• mi volas tranĉi = I want to cut

Not:

• mi volas tranĉas

This is similar to English want to cut.

Some other examples:

• Mi volas iri. = I want to go.
• Ŝi volas manĝi. = She wants to eat.
• Ni volas lerni. = We want to learn.

Because the sentence is speaking in a general, nonspecific way.

• pli akran tranĉilon = a sharper knife
• malmolan panon = hard bread
• grandajn tomatojn = large tomatoes

Esperanto uses la only for something definite or already known in context.

If you meant specific things, you could say:

• Mi uzas la pli akran tranĉilon = I use the sharper knife / the sharper one
• la malmolan panon = the hard bread
• la grandajn tomatojn = the large tomatoes

Without la, the meaning is more general.

Yes. They both come from the root tranĉ-, which has to do with cutting.

• tranĉi = to cut
• tranĉilo = a cutting tool, a knife

The suffix -ilo means tool/instrument.

This is another very useful Esperanto pattern:

• skribi = to write → skribilo = a writing tool
• razi = to shave → razilo = a razor
• tranĉi = to cut → tranĉilo = a knife

So tranĉilo is literally a cutting tool.

Yes. Esperanto word order is flexible, and you can move the subordinate clause to the front.

For example:

• Kiam mi volas tranĉi malmolan panon aŭ grandajn tomatojn, mi uzas pli akran tranĉilon.

This means the same thing. The difference is mainly one of style or emphasis.

Starting with Kiam... puts the situation first; starting with Mi uzas... puts the action first.

Strictly speaking, aŭ means or: one or the other.

So the sentence means that a sharper knife is used when the speaker wants to cut:

• hard bread, or
• large tomatoes

In practice, it can simply present two possible situations. It does not have to mean the speaker is choosing only one right now; it can just mean in either case.

If you wanted to say both, you would use kaj:

• ... malmolan panon kaj grandajn tomatojn = hard bread and large tomatoes

Yes, at least implicitly. A comparative like pli akra normally means sharper than something.

But Esperanto, like English, often leaves the second part unstated when it is obvious from context.

So Mi uzas pli akran tranĉilon can mean something like:

• I use a sharper knife
• I use a sharper knife than usual
• I use a sharper knife than the other one

If you want to say the comparison explicitly, you can add ol:

• Mi uzas pli akran tranĉilon ol kutime. = I use a sharper knife than usual.
• Mi uzas pli akran tranĉilon ol ĉi tiu. = I use a sharper knife than this one.