Lutum e pavimento tollendum est.

It is a gerundive of obligation (also often called the passive periphrastic):

• tollendum = the gerundive of tollere
• est = is

Together, tollendum est means something like must be removed / has to be picked up.

So this is not just a plain passive like is removed. It specifically adds the idea of necessity or duty.

Because the gerundive has to agree with the noun it goes with.

Here the noun is lutum:

• lutum is neuter
• singular
• nominative here

So the gerundive must also be:

• neuter
• singular
• nominative

That gives tollendum.

If the noun were masculine singular, you would expect tollendus.
If feminine singular, tollenda.

Yes.

In English, we often say Someone must remove the mud, where someone feels like the real subject. But in Latin, with this construction, the thing that must be acted on is usually put as the grammatical subject.

So in Lutum e pavimento tollendum est, lutum is the subject:
The mud must be removed from the floor.

A beginner may wonder whether lutum is accusative, because in form it looks the same as nominative. But for a neuter second-declension noun like lutum, nominative singular and accusative singular are identical in form. Here it is nominative because of the construction.

Pavimento is ablative singular.

That is because it follows the preposition e (out of, from), and e/ex takes the ablative.

So:

• e = from / out of
• pavimento = from the floor

This is a very common Latin pattern: preposition + ablative.

E and ex are two forms of the same preposition.

Both mean out of / from. In many contexts, the difference is mainly a matter of sound and style:

• ex is especially common before vowels
• e is often used before consonants

Since pavimento begins with a consonant, e pavimento is perfectly normal.

You may also see ex pavimento in Latin; that would still be understandable.

Because e/ex often expresses removal out of or from something, and it fits naturally with a verb like tollere.

With tollere, e/ex is a very common way to say that something is lifted or taken from a place.

De can also mean from/down from, but it often suggests movement down from the top of something. So:

• e pavimento = from the floor
• de mensa = from the table can suggest taking something off its surface

In this sentence, e pavimento is the natural choice.

Latin often leaves that unstated if it is obvious or unimportant.

In a gerundive construction, the person who is obliged to do the action can be expressed in the dative. This is called the dative of agent.

For example:

• mihi lutum e pavimento tollendum est = I must remove the mud from the floor
• nobis ... tollendum est = we must remove...

In your sentence, no agent is given, so the meaning is more general: the mud has to be removed.

Latin can express necessity in more than one way.

For example:

• Lutum e pavimento tollendum est
• Oportet lutum e pavimento tollere

Both can mean roughly the mud must be removed from the floor.

But the first one, with the gerundive, is a very standard Latin way of expressing obligation. It is especially common in formal or straightforward statements of what needs to be done.

So this sentence is not unusual at all; it is a classic Latin structure.

Tollere has a range of meanings, including:

• to lift
• to take up
• to remove
• sometimes even to destroy in other contexts

Here, with lutum e pavimento, it means something like:

• pick up
• remove
• clean off

The context tells you which English wording sounds best.

Latin word order is more flexible than English word order, because the endings show how the words relate to one another.

So Lutum e pavimento tollendum est is a normal arrangement, but other orders are possible, for example:

• E pavimento lutum tollendum est
• Tollendum est lutum e pavimento

These would not radically change the basic meaning. The differences would mostly be matters of emphasis or style.

The given order is clear and natural.

Yes, in form it is passive, but it is better to think of it specifically as a necessity construction.

Compare:

• Lutum tollitur = the mud is being removed / is removed
• Lutum tollendum est = the mud must be removed

So the sentence is passive in grammar, but its main point is not just that something happens to the mud; it is that the mud needs to be removed.

Yes.

Latin singular nouns are often used where English might use either singular or a mass noun idea. Lutum can mean:

• mud
• dirt
• mire

So depending on context, the sense may be:

• The mud must be removed from the floor
• The dirt must be cleaned off the floor

Latin does not always force the same singular/plural distinction that English prefers.

A good step-by-step approach would be:

1. Spot est: there is a form of esse
2. Notice tollendum next to it: likely a gerundive + est construction
3. Find the noun it agrees with: lutum
4. Read e pavimento as a prepositional phrase in the ablative

So the structure is:

• lutum = the thing involved
• e pavimento = from the floor
• tollendum est = must be removed

That gives you the grammatical backbone of the whole sentence very quickly.