Learn Hardcore Japanese: watasi no ie no reizouko ni ha tiisai reitouko ga tuite imasu. - My refrigerator at home has a small freezer.

冷蔵庫（れいぞうこ）
- Literally: cold-store box
- Meaning: refrigerator, the part that keeps things cool but not frozen.
冷凍庫（れいとうこ）
- Literally: cold-freeze box
- Meaning: freezer, the part that freezes things.

In modern fridges, 冷凍庫 is usually one compartment of the 冷蔵庫, which is exactly what the sentence is describing.

What does に do in 冷蔵庫には? Is it a location marker?

Yes. Here に marks a location or place where something exists:

冷蔵庫に = in/on the refrigerator

So the core pattern is:

場所 + に + 〜があります／います
(At place X, there is Y.)

In this sentence:

冷蔵庫に = in the refrigerator
小さい冷凍庫が = a small freezer
付いています = is attached / comes with

So literally: As for the refrigerator, a small freezer is attached in it.
More natural English: The refrigerator in my house has a small freezer.

Why is there both に and は in 冷蔵庫には?

This is particle stacking: に (location) + は (topic).

に: shows where something exists → in the refrigerator
は: makes that phrase the topic → as for the refrigerator / speaking of the refrigerator

So 冷蔵庫には roughly means:

As for the refrigerator (in terms of what it has / in it), ...

Using には emphasizes the refrigerator as the thing you’re talking about, rather than the freezer itself.

Why does 冷凍庫 take が instead of は?

Because 冷凍庫 is the subject of the verb 付いています in this sentence.

冷凍庫が付いています = a freezer is attached / there is a freezer attached

Meanwhile, 冷蔵庫 is the location (with に) and also the topic (with は). The topic is often not marked with が, but は, while the actual subject of the action takes が.

So structurally:

Topic / location: 冷蔵庫には (As for the refrigerator / in the refrigerator)
Subject: 小さい冷凍庫が (a small freezer)
Verb: 付いています (is attached)

Why is it 付いています and not just 付いている?

付いています is simply the polite form:

Plain: 付いている
Polite: 付いています

Polite ます-form is used in neutral/formal conversation, textbooks, and when speaking to people you’re not very close to. The grammar meaning (a state of being attached) is the same; only the politeness level changes.

What exactly does 付いています mean here? Is it “is attaching” (ongoing action) or “is attached / comes with” (state)?

Here it describes a resulting state, not an ongoing action.

付く can mean to stick, to be attached, to be added, to be included.
The 〜ている form often expresses:
- an ongoing action (I am doing X)
- or a resulting state (X is in the state of having become ~)

In this case, 冷凍庫が付いています means:

There is a freezer attached (to it).
Or The fridge comes with a freezer.

No one is actively attaching the freezer right now; it’s already there as a feature.

What’s the difference between 冷凍庫が付いています and 冷凍庫があります?

Subtle nuance:

冷凍庫があります
- Literally: There is a freezer.
- Just states existence: a freezer exists (there).
冷凍庫が付いています
- Literally: A freezer is attached.
- Emphasizes that the freezer is a built-in part / extra feature of something (here, the fridge).

So:

私の家の冷蔵庫には小さい冷凍庫があります。
= My fridge has a small freezer. (Quite fine, just existence.)
私の家の冷蔵庫には小さい冷凍庫が付いています。
= My fridge has a small freezer attached / comes with a small freezer.
(Highlights it as a “feature that comes with” the fridge.)

Why use 小さい and not 小さな before 冷凍庫?

Both are possible, but there’s a nuance:

小さい冷凍庫
- 小さい is a regular い-adjective.
- Neutral, most basic way: a small freezer.
小さな冷凍庫
- 小さな is the adverbial / prenominal form of 小さい.
- Slightly more literary / stylistic. You might see it more in writing, descriptions, or set phrases.

In everyday conversation, 小さい冷凍庫 sounds more ordinary.
You could say either; the meaning is essentially the same: a small freezer.

Can the word order be changed? For example, can I say 小さい冷凍庫が私の家の冷蔵庫には付いています?

Grammatically yes, but the naturalness and emphasis change.

Original:

私の家の冷蔵庫には小さい冷凍庫が付いています。
→ Sets the refrigerator as the main topic; then tells you what it has.

Your version:

小さい冷凍庫が私の家の冷蔵庫には付いています。
→ Puts 小さい冷凍庫 at the front; it sounds like you’re emphasizing the small freezer:
It’s a small freezer that is attached to the fridge at my house (as opposed to somewhere else).

It’s not wrong, just more marked. The original order is more neutral and natural for simply stating the fact.

Could I drop 私 and just say 家の冷蔵庫には小さい冷凍庫が付いています?

Yes, that’s very natural in many situations.

If it’s clear from context that you’re talking about your own house, Japanese often omits 私.
家の冷蔵庫 would be understood as the fridge at (my/our) house in many contexts.

You’d only keep 私の if:

you need to contrast with someone else’s house, or
the context is unclear and you want to be explicit.

What’s the difference between 家 and うち here? Could I say うちの冷蔵庫には…?

Yes, you can.

家（いえ）
- More neutral, often refers to the building or house itself, slightly more formal.
うち
- Very common in conversation to mean my home / my place / our family.
- うちの冷蔵庫 sounds very natural and casual: our fridge, the fridge at my place.

So you could say:

うちの冷蔵庫には小さい冷凍庫が付いています。
→ Very natural in everyday speech.

Is 冷蔵庫には describing “in the fridge” or “on the fridge”? Where exactly is the freezer supposed to be?

Grammatically, に just indicates the location or target of attachment.

In real-world context:

A 冷凍庫 that “comes with a refrigerator” is usually:
- a compartment inside the fridge unit, or
- structurally built into the fridge.

So 冷蔵庫に冷凍庫が付いています means the freezer is attached as part of the fridge. English often simplifies this to:

The fridge has a small freezer.

Why is 付いて in hiragana? Can it also be written in kanji 付いて?

Both are possible:

付いています (mixed kanji + hiragana)
ついています (all hiragana)

Using kanji 付く is correct in meaning here, but:

In everyday Japanese, many common verbs are often written with kana (hiragana), especially in casual writing.
Textbooks also often use kana to reduce kanji load for learners.

So 付いています or ついています are both acceptable. The meaning and grammar are the same.

What is the basic dictionary form of 付いています, and how is the whole verb phrase formed?

The verb phrase is built like this:

Dictionary (plain) form: 付く
- Meaning: to stick, to be attached, to be added, etc.
て-form (for state/continuation): 付いて
〜ている form: 付いている
- Expresses a continuing state: is attached / has been attached
Polite 〜ている → 〜ています: 付いています

So:

付く → 付いている → 付いています
= is attached / comes attached (polite form)