Cum pater abest, avia pueris adest et cenam parat.

Here cum is a conjunction meaning when or while.

So Cum pater abest means When the father is away or While the father is absent.

In this sentence, cum introduces a time clause. It is not the preposition cum meaning with.

Pater is the subject of abest, so it is in the nominative.

• pater = father
• abest = is away / is absent

So pater abest literally means the father is absent.

Abest is the 3rd person singular present form of absum, which means to be away, to be absent, or to be missing.

It is built from:

• ab- = away from
• sum / est = am / is

So:

• abest = he/she/it is away

In this sentence, it refers to pater, so it means the father is away.

Avia is the subject of the main clause.

The sentence has:

• a subordinate clause: Cum pater abest
• a main clause: avia pueris adest et cenam parat

In the main clause, avia does both actions:

• adest
• parat

So avia is nominative because it is the subject of both verbs.

Because adest does not take a direct object. Instead, adsum commonly takes the dative.

• adest alicui = is present for someone, is there for someone, sometimes helps someone

So:

• pueris = dative plural
• meaning for the boys / to the children

This is a very common thing to notice with compounds of sum: they may govern cases differently from what an English speaker expects.

Adest is from adsum, literally to be at or to be present.

Depending on context, it can mean:

• is present
• is there
• is at hand
• helps / supports

In this sentence, avia pueris adest suggests that the grandmother is there for the children or helps the children while the father is away.

It is closely related in form to abest:

• abest = is away
• adest = is here / is present

That contrast is probably deliberate.

Because cenam is the direct object of parat.

• parat = prepares
• cenam = dinner in the accusative singular

So cenam parat means she prepares dinner.

This is a straightforward verb + direct object pattern.

Latin has no articles like English the or a/an.

So words like:

• pater can mean father, a father, or the father
• avia can mean grandmother, a grandmother, or the grandmother
• cenam can mean dinner or the dinner, depending on context

You understand the exact sense from the context, not from an article.

Latin word order is much more flexible than English word order because the endings show the grammatical roles.

English usually depends heavily on position:

• The grandmother prepares dinner

Latin can move words around more freely because:

• avia is nominative, so it is the subject
• cenam is accusative, so it is the object
• pueris is dative, so it is the indirect/dative complement

The sentence puts Cum pater abest first to set the scene: when the father is away...

Then the main clause follows.

Because one subject can govern multiple verbs without being repeated.

Here avia is the subject of both:

• adest
• parat

So Latin, like English, can say:

• The grandmother is there for the children and prepares dinner

There is no need to repeat avia before parat.

No. Here abest is indicative, not subjunctive.

That is normal for a simple time clause meaning when or while in a factual sense.

So this is just a straightforward statement of circumstance:

• When the father is away, the grandmother is there for the children and prepares dinner.

A learner may later meet cum with the subjunctive, but that is a different construction.

Yes. They are excellent examples.

Both are forms built on sum, esse (to be), but the prefix changes the meaning:

• ab-
  • est → abest = is away
• ad-
  • est → adest = is present / is there

This is very common in Latin. Learning prefixes helps a lot with vocabulary, because related forms often stay easy to recognize once you know the base verb.