kuukou made katamiti no kippu wo kaimasita.

まで marks an end point or destination, so 空港まで means to the airport or more literally as far as the airport.

In this sentence, it shows where the ticket is for.

• 空港まで = to the airport
• 駅まで = to the station
• 東京まで = to Tokyo

A learner might expect に, but まで is very natural when talking about the destination covered by a ticket or route.

Because 片道 and 切符 are both nouns, and の is commonly used to connect one noun to another.

So:

• 片道 = one-way
• 切符 = ticket
• 片道の切符 = a one-way ticket

This is a very common pattern in Japanese:

• 日本の車 = a Japanese car
• 学生の本 = a student’s book
• 片道の切符 = a one-way ticket

Here, の works a bit like of or like a linking marker between nouns.

Sometimes Japanese compounds can appear without の, but in this case 片道の切符 is a very natural learner-friendly structure.

You may also hear expressions like:

• 片道切符
• 往復切符

These are more compound-like and compact. But 片道の切符 is perfectly correct and easy to understand.

So for a learner:

• 片道の切符 = clear and natural
• 片道切符 = also possible, more like a set compound

片道 means one way, as opposed to round trip.

So:

• 片道 = one-way
• 往復 = round trip

Examples:

• 片道の切符 = a one-way ticket
• 往復の切符 = a round-trip ticket

It does not mean simply one road or one path in this sentence. It specifically describes the type of ticket.

を marks the direct object of the verb.

The verb here is 買いました = bought, so the thing being bought is marked by を.

• 切符を買いました = bought a ticket
• 本を買いました = bought a book
• 水を飲みました = drank water

So 切符を tells you that ticket is the object of buying.

Because Japanese is basically an SOV language: subject – object – verb. The verb usually comes at the end.

This sentence is structured like:

• 空港まで = to the airport
• 片道の切符を = a one-way ticket
• 買いました = bought

So Japanese puts the action last.

This is one of the biggest differences from English, which is usually SVO:

• English: I bought a one-way ticket to the airport.
• Japanese: I to-the-airport a-one-way-ticket bought.

That English-like word order sounds strange in English, but it is normal in Japanese.

Japanese often leaves out the subject when it is obvious from context.

So even though English needs I bought..., Japanese can simply say:

• 空港まで片道の切符を買いました。

The subject is understood, often as I, depending on the situation.

This omission is very common in Japanese. If the speaker needed to be explicit, they could say:

• 私は空港まで片道の切符を買いました。

But very often 私は is unnecessary.

買いました is the polite past form of 買う.

• 買う = to buy
• 買います = buy / will buy (polite, non-past)
• 買いました = bought (polite, past)

Since the sentence talks about a completed action, the past form is used.

So:

• 切符を買います = I buy / I will buy a ticket
• 切符を買いました = I bought a ticket

Grammatically, 空港まで is separate from 片道の切符 and gives the destination related to the ticket purchase.

So the sentence is naturally understood as:

• [空港まで] [片道の切符] を 買いました
• I bought [a one-way ticket] [to the airport].

Japanese often leaves this kind of relationship a little looser than English does.

If you want to attach the destination more directly to ticket, you can also say:

• 空港までの片道切符を買いました。

That makes to the airport more explicitly modify ticket.

So:

• 空港まで片道の切符を買いました。 = natural and understandable
• 空港までの片道切符を買いました。 = more tightly connected phrasing

Both can mean ticket, but they are used a little differently.

• 切符 is very common for transportation tickets such as train or bus tickets.
• チケット is a loanword and is common for things like concert tickets, movie tickets, and sometimes transportation tickets too.

In this sentence, 切符 is a very natural choice because it sounds like a travel/transport ticket.

Examples:

• 電車の切符 = train ticket
• コンサートのチケット = concert ticket

A natural reading is:

くうこう まで かたみち の きっぷ を かいました。

Word by word:

• 空港 → くうこう
• まで
• 片道 → かたみち
• の
• 切符 → きっぷ
• を
• 買いました → かいました

A small pronunciation note: を is usually pronounced お in modern Japanese, even though it is written を.

Usually, まで is better here.

• へ emphasizes direction: toward
• まで emphasizes the end point: as far as / up to

With tickets, routes, and fares, Japanese often uses まで because the important idea is the destination limit.

So:

• 空港まで = to the airport / as far as the airport

Using へ here would sound less natural in the context of what destination the ticket covers.