Cum mater in culina occupata esset, filia ipsa cubiculum purgavit nec ullam moram fecit.

Here cum introduces a circumstantial or background clause: it gives the situation in which the main action happened.

So cum mater in culina occupata esset means something like while/since mother was busy in the kitchen as background for what follows.

In Latin, this kind of cum clause very often takes the subjunctive, especially in narrative prose. That is why we get esset rather than erat.

A rough contrast:

• cum ... erat = more straightforward when ... was
• cum ... esset = since/while/when ... was, with a more descriptive background sense

Esset is the imperfect subjunctive of sum, esse.

It is used because:

• the clause is a cum clause requiring the subjunctive
• the action is ongoing in the background
• it is happening at the same time as the main action

The main verb purgavit is perfect, describing the completed action of the daughter. The imperfect subjunctive esset gives the ongoing situation during which that action took place.

Occupata agrees with mater.

Since mater is:

• feminine
• singular
• nominative

the adjective or participle describing her must also be:

• feminine
• singular
• nominative

So:

• mater occupata esset = mother was busy
• occupatam would be accusative feminine singular, which would not fit here

This is a very common Latin pattern:

• occupata = a perfect passive participle, literally occupied
• esset = was

Together they function like was busy or was occupied.

So although occupata is formally a participle, the whole phrase is basically acting like a normal predicate: it tells us the state the mother was in.

Because in with the ablative usually means in or on in the sense of location.

Here it answers where?

• in culina = in the kitchen

If motion into a place were meant, Latin would usually use in with the accusative instead.

So compare:

• in culina = in the kitchen (location)
• in culinam = into the kitchen (motion toward)

Ipsa adds emphasis.

So filia ipsa means something like:

• the daughter herself
• the daughter on her own
• the daughter personally

It highlights that she did it, perhaps without help, or unexpectedly, or in contrast with someone else.

Without ipsa, the sentence would simply state the fact. With ipsa, it gives that fact extra stress.

Because cubiculum is the direct object of purgavit.

The verb purgare means to clean or to clear, and the thing being cleaned is put in the accusative.

So:

• filia cubiculum purgavit = the daughter cleaned the room

Purgavit is the perfect indicative active of purgo, purgare.

In this sentence it expresses a completed past action:

• she cleaned
• she has cleaned in some contexts, but here plainly she cleaned

So the structure is:

• background: mother was busy
• main completed event: the daughter cleaned the room

Latin often likes idiomatic expressions with facere.

Here:

• moram facere = to cause delay, to delay, to hesitate
• nec ullam moram fecit = and she made no delay at all

This is a very natural Latin expression. English might prefer a simple verb, but Latin frequently uses this noun + facere pattern.

Because after a negative, Latin often uses ullus, -a, -um to mean any.

So:

• ullam moram = any delay
• nec ullam moram fecit = and she made no delay / and she did not delay at all

The form ullam is:

• feminine
• singular
• accusative

because it agrees with moram, which is feminine singular accusative as the object of fecit.

Nec means and not or more simply nor.

It links this clause to the previous one:

• filia ipsa cubiculum purgavit nec ullam moram fecit
• the daughter herself cleaned the room and made no delay

So nec is not just negating; it is also connecting.

If Latin had used non, it would simply negate the verb, but nec neatly continues the flow of the sentence.

Latin word order is more flexible than English word order because the endings show each word’s function.

This sentence is arranged quite naturally:

• Cum mater in culina occupata esset = background clause first
• filia ipsa = subject with emphasis
• cubiculum purgavit = object + verb
• nec ullam moram fecit = linked negative statement

A different order could still be grammatical, but the current arrangement is good literary Latin and puts the emphasis in sensible places.

For example, ipsa comes right next to filia, which makes the emphasis especially clear.

Yes. The exact English choice depends on context.

With this kind of cum clause, Latin often leaves some flexibility:

• when mother was busy in the kitchen
• while mother was busy in the kitchen
• since mother was busy in the kitchen

All can work, though while or since often captures the sense best:

• while if you want simple background time
• since if you want a slight hint that this situation explains why the daughter acted

So the grammar gives background context, and English can choose the most natural wording.