Quiero la mitad del pastel.

In Spanish, subject pronouns are often left out because the verb already shows who is doing the action.

• quiero = I want
• The -o ending tells you it is yo

So:

• Quiero la mitad del pastel. = I want half of the cake.
• Yo quiero la mitad del pastel. is also correct, but yo is usually only added for emphasis, contrast, or clarity.

For example:

• Yo quiero la mitad, no él. = I want half, not him.

Mitad is a feminine noun in Spanish, so it takes the feminine article la.

• la mitad = the half
• not el mitad

This is something you simply have to learn with the noun. Spanish nouns have grammatical gender, and it does not always match anything logical in English.

Other examples:

• la verdad = the truth
• la ciudad = the city

Even though mitad refers to a quantity, it is still just a normal noun grammatically.

Because mitad is being used as a noun, and in this sentence it refers to a specific half: half of the cake.

So Spanish says:

• la mitad del pastel

Literally, this is something like the half of the cake.

Spanish often uses the definite article in places where English does not, or where English structures things differently.

Compare:

• la mitad del pastel = half of the cake
• una mitad = one half / a half (less common in this kind of sentence)

In this sentence, la mitad is the natural choice.

Because de + el contracts to del in Spanish.

So:

• de + el pastel → del pastel

This contraction is normally required.

Examples:

• la puerta del coche = the car’s door
• el color del libro = the color of the book

One important exception: you do not contract if El is part of a proper name.

For example:

• de El Escorial → not del Escorial if you are treating El Escorial as the full place name

But in ordinary cases like el pastel, you must use del.

Both patterns exist, but they do not always mean exactly the same thing.

• la mitad del pastel = half of the cake
  This usually refers to half of a specific cake.
• medio pastel = half a cake
  This often sounds more like a quantity.

So the difference is similar to English:

• half of the cake
• half a cake

If there is one cake on the table and you want 50% of it, la mitad del pastel is very natural.

Yes, you could, but the nuance changes a little.

• Quiero la mitad del pastel. = I want half of the cake / half of this particular cake.
• Quiero medio pastel. = I want half a cake.

The second one can sound a bit more general or like a portion amount, not necessarily half of one specific cake already being discussed.

If the cake is clearly specific, la mitad del pastel is usually the clearer choice.

Yes — this is a very good question, especially for Spanish from Spain.

In Spain:

• tarta often refers to a whole cake, especially one for dessert or a celebration
• pastel can refer to a cake, but very often it also means a small cake or pastry

So depending on context, many people in Spain might naturally say:

• Quiero la mitad de la tarta.

That said, pastel is still a real and correct word, and learners will definitely see it. The exact preference can depend on region and on the type of dessert.

So the sentence is grammatically fine, but in everyday Spain Spanish, tarta may sometimes sound more natural for a whole cake.

Because the sentence is talking about a specific cake, not cake in general.

• del pastel = of the cake
• de pastel would be unusual here

Spanish usually uses the article when referring to a specific object.

Compare:

• la mitad del pastel = half of the cake
• la mitad de un pastel = half of a cake

So if you mean one particular cake, del pastel is the right form.

Not necessarily. Quiero literally means I want, and in some situations it can sound direct, but it is not automatically rude.

Context matters:

• With family or friends: Quiero la mitad del pastel. is fine.
• In a shop or restaurant, Spanish often allows more direct wording than English does.

Still, if you want to sound more polite or softer, you could say:

• Quisiera la mitad del pastel. = I would like half of the cake.
• Me gustaría la mitad del pastel. = I’d like half of the cake.

In Spain, directness is often more acceptable than in English, so quiero is not always as blunt as I want can sound in English.

In Spain Spanish, quiero is pronounced roughly like:

• KYEH-roh

A bit more accurately, it is approximately:

• /ˈkje.ɾo/

Notes:

• qui here sounds like ky, not like English kwee
• the e is a clear Spanish eh
• the r in quiero is the single Spanish r, a light tap, not a strong English r

So the whole sentence:

• Quiero la mitad del pastel.

is approximately:

• KYEH-roh la mee-TAHD del pah-STEL

That is only an approximation, but it helps as a starting point.

Because Spanish does not keep them separate in this combination. When de is followed by el, they combine into del.

So:

• de el pastel → incorrect in normal Spanish
• del pastel → correct

This is just like a built-in grammar rule. You should think of del as the normal form whenever you see de + el together.

Yes, but the original order is the most neutral and natural:

• Quiero la mitad del pastel.

Spanish word order is fairly flexible, but changing it often adds emphasis or sounds less neutral.

For example:

• La mitad del pastel quiero. sounds marked or poetic, not normal everyday speech.
• La mitad del pastel la quiero. can work if you are emphasizing that particular thing: It’s half of the cake that I want.

For a learner, the safest choice is to keep:

• Quiero la mitad del pastel.