Quo diligentius serva pavimentum purgat, eo laetior mater fit.

It is the standard Latin way to express a correlative comparison: the more ... the more or the more ... the less.

So:

• quo diligentius = the more carefully
• eo laetior = the happier

The whole structure means that as one thing increases in degree, another changes correspondingly.

A very literal way to feel it is:

• by which greater degree ... by that greater degree

But in natural English, you normally translate it as the more ... the more.

That is a very common confusion.

Here, quo is not a question word meaning where? It is part of the idiom quo ... eo used with comparatives.

In this construction:

• quo introduces the first comparative idea
• eo introduces the matching result in the second part

So in this sentence, quo is not about place at all. It is about degree.

Both are ablative singular neuter forms.

In this construction, Latin uses the ablative adverbially with comparatives to express by that amount or to that degree.

So:

• quo diligentius = by which amount more carefully
• eo laetior = by that amount happier

You do not need to translate the case literally in normal English, but it helps explain why these particular forms appear.

Because they are different kinds of comparatives.

• diligentius is a comparative adverb
• laetior is a comparative adjective

diligentius

This modifies the verb purgat and tells how the cleaning is done:

• carefully
• more carefully

Adverbs often end in -ius in the comparative.

laetior

This describes mater, so it is an adjective:

• happy
• happier

Comparative adjectives often use -ior for masculine/feminine nominative singular.

So the sentence mixes:

• a comparative adverb: more carefully
• a comparative adjective: happier

That is perfectly normal.

Because serva is the subject of purgat.

The first part of the sentence is:

• serva pavimentum purgat = the slave-girl cleans the floor

Here:

• serva = subject, so nominative
• pavimentum = direct object, so accusative
• purgat = verb

Even though the sentence begins with quo diligentius, the subject of that clause is still serva.

Because it is the direct object of purgat.

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

So:

• serva pavimentum purgat = the slave-girl cleans the floor

That is very straightforward Latin object marking.

Because mater is the subject of the second clause, the one with fit.

The second part is:

• eo laetior mater fit = the happier the mother becomes

Here:

• mater = subject, nominative
• laetior = predicate adjective describing mater
• fit = becomes

So the sentence has two different subjects:

• serva for purgat
• mater for fit

Because fit means becomes, while est means is.

That difference matters.

• mater laetior est = the mother is happier
• mater laetior fit = the mother becomes happier

In this sentence, the idea is that the mother's mood changes as the servant cleans more carefully. So fit is the better verb.

fit is the present tense of fio, a verb often meaning become, come to be, or sometimes be made depending on context.

Yes.

Laetior is a comparative adjective describing mater, so it agrees with mater in:

• gender: feminine
• number: singular
• case: nominative

For a third-declension comparative adjective like laetior, the nominative singular masculine and feminine are the same form: laetior.

So even though mater is feminine, laetior is exactly the form you would expect.

Latin word order is much freer than English word order.

English strongly prefers something like:

• The more carefully the slave-girl cleans the floor, the happier the mother becomes.

Latin can arrange the words more flexibly because the endings show their grammatical roles.

In this sentence, Latin puts the correlatives first:

• Quo diligentius ... eo laetior ...

That highlights the comparison immediately. Then the subjects and verbs appear in their own clauses.

So the order is not random; it helps foreground the pattern:

• first degree: quo diligentius
• matching result: eo laetior

Yes, Latin can use quanto ... tanto with a very similar meaning.

Both patterns can express the more ... the more.

However, quo ... eo is a very common classical construction with comparatives, and it is exactly the one used here.

So as a learner, it is best to recognize quo ... eo immediately as a comparison of degree.

Yes, in the sense that Latin builds more into the word itself.

Compare:

• diligenter = carefully
• diligentius = more carefully

and:

• laeta / laetus = happy
• laetior = happier

English often uses a separate word like more, but Latin usually forms the comparative directly by changing the ending.

So you should read:

• diligentius as one word meaning more carefully
• laetior as one word meaning happier

It is expressing a correlation of degree, which often implies cause or connection, but the grammar itself mainly says:

• as one thing increases, another also increases

So the sentence means something like:

• the more carefully the slave-girl cleans, the happier the mother becomes

That often feels causal in context, but grammatically the construction is about proportional change rather than a separate explicit because clause.