Eu preciso de uma borracha para a prova.

Because precisar is commonly used as precisar de when it means to need something.

• Eu preciso de uma borracha. = I need an eraser.
• Ela precisa de ajuda. = She needs help.

In everyday Brazilian Portuguese, many people also say preciso uma borracha without de, but preciso de is the more standard and traditionally taught form.

Yes. In Portuguese, subject pronouns are often omitted when the verb already makes the subject clear.

So both of these are natural:

• Eu preciso de uma borracha para a prova.
• Preciso de uma borracha para a prova.

Since preciso already shows I need, eu is optional unless you want emphasis or contrast.

Uma means a/an, so uma borracha means an eraser.

You can sometimes omit the article in Portuguese, but with a countable singular noun like this, uma is the most natural choice when you mean one unspecified item.

• Preciso de uma borracha. = I need an eraser.

If you said just Preciso de borracha, it would sound more like I need rubber or I need eraser material, not usually one eraser.

Because nouns in Portuguese have grammatical gender, and borracha is a feminine noun. That is why it takes the feminine article uma.

• uma borracha
• not um borracha

This gender is grammatical, not logical. You simply learn the noun together with its article.

In this sentence, borracha means eraser.

The word borracha can also mean rubber as a material, depending on context. In a school-related sentence like para a prova, the meaning eraser is the natural one.

Para a prova means for the test or for the exam.

• para = for
• a prova = the test / the exam

So the full idea is: I need an eraser for the test.

It implies a specific test, not just tests in general.

The article a means the, so a prova means the test or the exam.

Portuguese uses definite articles more often than English does. Here it sounds natural because the speaker is probably referring to a specific test that both speaker and listener understand.

• para a prova = for the test
• para uma prova = for a test (any test / an unspecified test)

No. Prova can mean different things depending on context, including:

• test / exam
• proof / evidence
• sometimes tasting / sample in certain contexts

In para a prova, the school context makes test/exam the correct meaning.

Yes, in informal Brazilian Portuguese, para a is very often reduced to pra.

So these are both common:

• para a prova — more neutral / standard
• pra prova — informal and very common in speech

In careful writing, para a prova is safer. In conversation, pra prova sounds very natural.

Good question. Portuguese has many required contractions, such as:

• de + o = do
• de + a = da
• em + o = no
• em + a = na

But para + a does not have one standard mandatory contraction in formal Portuguese. Instead:

• para a stays para a in standard writing
• in speech and informal writing, it often becomes pra

So para a prova is correct, and pra prova is the informal spoken version.

The given order is the most neutral and natural:

• Eu preciso de uma borracha para a prova.

But Portuguese allows some flexibility. For example:

• Para a prova, eu preciso de uma borracha.

This puts more emphasis on for the test.

So the original sentence is standard, but other word orders are possible depending on emphasis.

Yes, grammatically you can say:

• Eu necessito de uma borracha para a prova.

But necessito sounds more formal or less common in everyday speech. Preciso is much more natural in normal conversation.

So for most situations, preciso is the better choice.

A very natural spoken version would often be:

• Preciso de uma borracha pra prova.

This version:

• drops eu because it is understood
• changes para a to pra

The full sentence Eu preciso de uma borracha para a prova is absolutely correct, but the shorter version is often what you would hear in conversation.