Pater placentam inter convivas aeque dividit.

Because pater is in the nominative singular, the case normally used for the subject of a Latin sentence.

• pater = father
• It is the person doing the action of dividit (divides)

So pater is the one who is dividing the cake.

Because placentam is in the accusative singular, which is the case used for the direct object.

• Dictionary form: placenta
• Accusative singular: placentam

It is the thing being divided, so it takes the accusative:

• pater = subject
• placentam = direct object

Because the preposition inter takes the accusative case.

So:

• inter = among, between
• convivas = accusative plural of conviva

Even though convivas is not the direct object of the verb, it is still accusative because it is governed by inter.

Convivas is accusative plural. Its basic dictionary form is conviva.

So the forms here are:

• singular: conviva = guest, dinner guest
• plural accusative: convivas = guests

Because it follows inter, Latin uses the accusative plural.

Aeque is an adverb. It describes how the father divides the cake.

Here it means something like:

• equally
• evenly

So it modifies the verb dividit, not a noun.

Because the sentence needs a word that modifies the action of dividing, not a noun.

• An adjective modifies a noun.
• An adverb modifies a verb, adjective, or another adverb.

Since the idea is he divides equally, Latin uses the adverb aeque.

Dividit is the verb, from dividere (to divide).

Its form tells us several things at once:

• 3rd person singular = he/she/it
• present tense = is dividing / divides
• active voice
• indicative mood

Because the subject is pater, we understand dividit as the father divides.

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

So:

• pater can mean father or the father
• placentam can mean a cake or the cake
• convivas can mean guests or the guests

The exact sense depends on context.

Latin word order is much more flexible than English word order because the endings show each word’s job in the sentence.

So this sentence could be rearranged in different ways without changing the basic meaning, for example:

• Pater placentam inter convivas aeque dividit.
• Pater aeque placentam inter convivas dividit.
• Placentam pater inter convivas aeque dividit.

The endings still show:

• pater = subject
• placentam = object
• convivas = object of inter

However, changing the order can slightly change emphasis.

Inter means among or between. In this sentence it shows among whom the cake is divided.

So inter convivas means:

• among the guests
• literally, in the midst of the guests

It is a very natural way in Latin to express distribution among a group.

No. In Latin, placenta means a kind of cake or flat cake.

Although English borrowed the same form for the anatomical word placenta, in this Latin sentence placentam clearly means cake, not the modern medical term.

Because pater is the subject, so it must be nominative, not accusative.

Compare:

• pater = nominative singular, father as subject
• patrem = accusative singular, father as direct object

If the sentence had patrem, it would mean that father was receiving the action, which is not the case here.

Yes. The Latin present tense often covers both ideas that English separates:

• divides
• is dividing

Which English translation sounds best depends on context. Latin dividit itself does not force one or the other.

Mostly for normal Latin style and flow. Latin often places prepositional phrases near the words they relate to, but it is not as rigid as English.

Here the order feels natural:

• subject first: pater
• object next: placentam
• phrase showing the group involved: inter convivas
• adverb and verb: aeque dividit

But Latin could move these parts around for emphasis without changing the basic grammar.