razio no denti ga kirete ita node, yobi wo kai ni ikimasita.

Here, の links two nouns and shows a relationship between them.

So ラジオの電池 means:

• the radio's batteries
• the batteries of the radio
• more naturally in English, the batteries in the radio

It does not always mean strict ownership. It often just connects nouns in a way that English might express with of, in, for, or by putting one noun before another.

Because 切れる is an intransitive verb.

In this sentence, 切れる means something like:

• to run out
• to die
• to be used up

So the batteries are not a direct object being acted on by someone. Instead, they are the thing that undergoes the change of state. That is why they take が.

Compare:

• 電池が切れる = the battery dies / runs out
• ひもを切る = to cut a string
  Here 切る is transitive, so it takes を.

Even though 切れる and 切る look related, they behave differently.

This is a very common point of confusion.

While 切る often means to cut, 切れる has several meanings depending on context. With batteries, power, or expiration, 切れる often means:

• to run out
• to expire
• to stop working because supply is gone

So:

• 電池が切れる = the battery runs out / dies

In this sentence, 電池が切れていた means the batteries had already run out.

This is a set phrase you will see often:

• 電池が切れた = the battery died
• ガスが切れた = the gas ran out
• 期限が切れた = the deadline/validity expired

〜ている often describes a resulting state, not only an ongoing action.

With a verb like 切れる, the form 切れている means:

• is in the state of having run out
• has gone dead

So:

• 切れた = it ran out / died
• 切れていた = it had run out / it was dead

In this sentence, 切れていたので gives background for what happened next. It sets up the situation: the batteries were already dead, so the speaker went to buy spares.

That makes 切れていた very natural here.

ので means because or since.

So:

• 電池が切れていたので = because the batteries had run out

Compared with から, ので usually sounds:

• a little softer
• a little more explanatory
• a little less direct

For example:

• 電池が切れていたから、予備を買いに行きました。
• 電池が切れていたので、予備を買いに行きました。

Both are correct, but ので often sounds a bit more neutral or matter-of-fact.

予備 means spare or backup.

In this sentence, it refers to spare batteries, even though 電池 is not repeated.

So:

• 予備を買いに行きました = went to buy spares
• more naturally: went to buy spare batteries

Japanese often leaves out a noun when it is obvious from context. Since the sentence is already talking about batteries, 予備 naturally means spare batteries here.

You could also say more explicitly:

• 予備の電池を買いに行きました

But leaving it as 予備 is very natural if the context is clear.

Because 予備 is the thing being bought.

The verb 買う takes a direct object marked by を:

• 本を買う = buy a book
• 電池を買う = buy batteries
• 予備を買う = buy spares / backups

So in 予備を買いに行きました, the hidden full idea is:

• 予備の電池を買いに行きました

The を marks what the speaker went to buy.

This is a very useful grammar pattern:

verb stem + に + 行く

It means:

• to go in order to do something
• to go and do something

Here:

• 買う → verb stem 買い
• 買いに行く = to go to buy

So:

• 予備を買いに行きました = I went to buy spares

Other examples:

• 食べに行く = go to eat
• 見に行く = go to see/watch
• 迎えに行く = go to pick someone up

This is one of the most common ways to say go to do X in Japanese.

Because this pattern uses the verb stem, not the dictionary form.

For う-verbs, you change the final う sound to the i-stem:

• 買う → 買い
• 行く → 行き
• 読む → 読み

So:

• 買いに行く is correct
• 買うに行く is not correct

For る-verbs:

• 食べる → 食べ
• 見る → 見

So:

• 食べに行く
• 見に行く

Because the speaker is describing a completed action in the past:

• the batteries had run out
• then the speaker went to buy spares

So 行きました means went.

If it were present/future, it would be:

• 行きます = go / will go

But in this sentence, the speaker is talking about what they did, so past tense is appropriate.

The subject is omitted because it is understood from context.

Japanese often leaves out subjects when they are obvious. In a sentence like this, the natural interpretation is:

• I went to buy spares

So even though 私 is not written, it is understood.

This is extremely common in Japanese. A full version would be something like:

• 私は、ラジオの電池が切れていたので、予備を買いに行きました。

But in natural speech and writing, 私は is often unnecessary.

Japanese nouns usually do not show singular vs. plural clearly.

So 電池 can mean:

• a battery
• batteries

You figure it out from context.

With a radio, English often says the batteries, so that is a natural translation. But grammatically, Japanese itself does not force singular or plural here.

The same is true for many nouns in Japanese.

Yes, that would also be correct.

• 切れたので = because the batteries ran out
• 切れていたので = because the batteries had run out / were dead

The version with 切れていた gives a little more sense of an existing state in the background. It sounds like the speaker noticed the batteries were already dead, and because of that, went to buy spares.

So both work, but 切れていた gives slightly more background-state nuance.

Because Japanese often omits words that are already clear from context.

Once the sentence mentions 電池, the listener already knows what kind of spare is meant. So saying just 予備 is efficient and natural.

This kind of omission happens all the time in Japanese. English usually repeats words more often, but Japanese often avoids repetition when the meaning is obvious.