Avia in horto cantans a puella libenter auditur.

Because auditur is passive: is heard.

In a passive sentence, the person or thing receiving the action becomes the grammatical subject, so it goes in the nominative case.

• avia = the grandmother → nominative singular
• auditur = is heard

So Latin is structured like:

• The grandmother ... is heard by the girl.

Even though the grandmother is the one being heard, she is still the subject of the passive verb.

Because with a passive verb, the person doing the action is often expressed with a/ab + ablative. This is called the personal agent.

So:

• a puella = by the girl

Here:

• puella is ablative singular
• a means by

This shows clearly that the girl is the one doing the hearing.

Compare:

• puella audit = the girl hears
• avia a puella auditur = the grandmother is heard by the girl

cantans is a present active participle from cantare (to sing). It means singing.

It agrees with avia:

• avia = feminine singular nominative
• cantans = nominative singular participle, matching avia

So avia ... cantans means:

• the grandmother singing
• or the grandmother who is singing

You can think of it as a shorter way of saying:

• avia quae in horto cantat
• the grandmother who is singing in the garden

Often, yes. Here it does.

cantans is very naturally translated as:

• singing

So:

• Avia in horto cantans = The grandmother singing in the garden

But grammatically, Latin participles are more adjective-like than English -ing forms. They agree with the noun they describe in gender, number, and case.

So cantans is not just a loose verb form: it is specifically describing avia.

Because in can take either the ablative or the accusative, depending on the meaning.

• in + ablative = in/on a place, showing location
• in + accusative = into/onto a place, showing motion toward

Here the meaning is in the garden, not into the garden, so Latin uses the ablative:

• horto = ablative singular
• in horto = in the garden

If it meant into the garden, it would be:

• in hortum

libenter is an adverb meaning:

• gladly
• willingly
• with pleasure

It modifies the action of auditur. So the idea is that the girl hears the grandmother gladly or with pleasure.

A natural translation might be:

• The girl gladly hears the grandmother
• or, keeping the passive structure, The grandmother is gladly heard by the girl

Because its subject, avia, is singular.

• avia = one grandmother
• auditur = is heard (3rd person singular present passive)

If the subject were plural, the verb would also be plural. For example:

• aviae ... audiuntur = the grandmothers ... are heard

Latin verbs agree with their subject in person and number.

auditur is present tense, passive voice, indicative mood.

So it means:

• is heard

It is not future and not perfect.

Breakdown:

• audi- = hear
• -tur = passive ending for he/she/it

So:

• audit = he/she hears
• auditur = he/she is heard

In some contexts, a/ab can mean from, but here the passive verb makes by the girl the correct interpretation.

Because auditur is passive, a puella is understood as the agent:

• is heard by the girl

So in this sentence, a learner should read a puella as by the girl, not from the girl.

A useful way to divide it is:

• Avia = the grandmother
• in horto cantans = singing in the garden
• a puella = by the girl
• libenter auditur = is gladly heard

So the structure is:

• [Subject] Avia
• [Participle phrase describing the subject] in horto cantans
• [Agent with passive verb] a puella
• [Main verb + adverb] libenter auditur

In smoother English, this is something like:

• The grandmother, singing in the garden, is gladly heard by the girl.

For English, yes. For Latin, not especially.

Latin word order is much more flexible because the endings show the grammatical relationships. The sentence could be rearranged in different ways without changing the basic meaning.

For example, the same idea could appear as:

• Avia a puella libenter auditur, in horto cantans.
• In horto cantans avia a puella libenter auditur.

The original order helps group related words nicely:

• avia ... cantans go together
• a puella clearly marks the agent
• libenter auditur closes the sentence with the action

So the word order is stylistic rather than required in the way English word order usually is.