Pater placentam cultro secat et frusta inter convivas dividit.

Because placentam is the direct object of secat. It is the thing being cut.

The dictionary form is placenta. This is a first-declension noun, so its accusative singular ends in -am:

• nominative: placenta
• accusative: placentam

So Pater placentam secat means The father cuts the cake.

Latin often uses the ablative of means/instrument without a preposition to show the tool used to do something.

So:

• cultro = with a knife
• not literally by means of a knife, but that is the grammatical idea

The noun is culter, cultri (knife), and cultro is its ablative singular.

This is very common in Latin:

• gladio pugnat = he fights with a sword
• manu tenet = he holds it with his hand

Frusta is accusative plural, because it is the direct object of dividit: they are the things being divided.

Its singular is frustum, a neuter second-declension noun. Neuter nouns have a special pattern:

• nominative singular: frustum
• accusative singular: frustum
• nominative plural: frusta
• accusative plural: frusta

So frusta can be either nominative plural or accusative plural, and here it must be accusative plural because it is the object of dividit.

Because inter takes the accusative case.

So:

• inter convivas = among the guests / among the dinner companions

The dictionary form is conviva, and convivas is the accusative plural.

This is just a rule of the preposition:

• inter amicos = among friends
• inter pueros = among the boys

Because in Latin, declension and gender are not the same thing.

Even though many first-declension nouns are feminine, some are masculine, especially words for occupations or social roles. Conviva is one of those.

So:

• conviva = a first-declension noun
• but it is often masculine in meaning and agreement

This is not unusual in Latin. Another famous example is poeta (poet), which is also first declension but masculine.

Because the subject is understood from the structure and from the verb ending.

In this sentence, pater is the subject of both verbs:

• secat
• dividit

Latin often avoids repeating a subject when it is still the same person or thing. English can do this too:

• The father cuts the cake and divides the pieces among the guests.

We do not normally repeat the father before divides either.

Both are third-person singular present active indicative verbs.

• secat comes from secare = to cut
• dividit comes from dividere = to divide

Third-person singular means he/she/it does the action. Here, the subject is pater, so:

• secat = he cuts
• dividit = he divides

Because classical Latin does not have articles like English the and a/an.

So a noun like pater can mean:

• father
• the father
• sometimes even a father

The exact meaning depends on context. In a simple sentence like this, English usually translates it with the:

• The father cuts the cake...

Inter convivas emphasizes distribution among the group rather than simply giving something to them.

So the idea is not only that the pieces go to the guests, but that they are shared out among the diners.

Latin often chooses a prepositional phrase when it wants to make that relationship especially clear. With dividit, this works very naturally:

• frusta inter convivas dividit = he divides the pieces among the guests

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

This sentence is arranged quite naturally:

• Pater — subject first
• placentam — object of the first verb
• cultro — instrument
• secat — verb
• et
• frusta — object of the second verb
• inter convivas — prepositional phrase
• dividit — verb

A Latin author could rearrange some of these words without changing the basic meaning, because:

• placentam is still accusative
• cultro is still ablative
• convivas is still accusative after inter

So the endings, more than the position, tell you what each word is doing.

In form, frusta could be either nominative plural or accusative plural, because neuter plural nouns use the same ending for both.

But in this sentence, it must be the object because of the meaning and structure:

• pater is already the clear subject
• dividit needs something being divided
• frusta fits perfectly as that object

So here frusta means the pieces as the thing the father divides.

Yes. The sentence has two coordinated verbs joined by et:

• secat = cuts
• dividit = divides

They describe two connected actions done by the same subject:

1. he cuts the cake
2. he divides the pieces among the guests

So et links two parts of the sentence with the same subject, pater.