haha ha ringo wo hanbun ni kitte, kodomo ni agemasita.

母は marks mother as the topic of the sentence: as for Mother, she cut the apple in half and gave it to the child.

Using が would put more focus on mother as the specific person who did the action. In a neutral sentence like this, は is very natural because it introduces what the sentence is about.

So:

• 母は = As for Mother, ...
• 母が = Mother (rather than someone else) ... or stronger focus on who did it

Japanese often leaves out subjects and pronouns when they are clear from context.

In English, you usually need she:
She cut the apple in half and gave it to the child.

In Japanese, once 母は is stated, there is no need to keep repeating she. The subject is understood through context.

This is one of the biggest differences from English: Japanese frequently omits words that English would require.

を marks the direct object of the verb—the thing being acted on.

Here, the apple is the thing Mother cut:

• りんごを切る = to cut an apple

So りんごを tells you that apple is what the action is being done to.

半分 means half.
半分に切る means to cut into halves / to cut in half.

The particle に often marks the resulting state of a change. Here, the apple changes into the state of being two halves.

So:

• 半分に切る = cut it so that it becomes half / two halves
• compare with:
  • 小さく切る = cut into small pieces
  • 二つに分ける = divide into two

In this sentence, 半分に tells you the result of the cutting.

Yes. 半分に切る is very common, but there are other natural ways to say something similar.

Examples:

• りんごを半分に切る = cut the apple in half
• りんごを二つに切る = cut the apple into two pieces
• りんごを半分ずつに分ける = divide the apple into halves

The sentence you have is a standard and natural way to say it.

切って is the て-form of 切る.

The て-form has many uses. In this sentence, it connects two actions in sequence:

1. cut the apple in half
2. give it to the child

So:

• 切って、子供にあげました
• cut it, and gave it to the child

A useful way to think about it here is: did X, then did Y.

Not always. The て-form can connect actions in several ways, depending on context:

• sequence: did X and then did Y
• manner: do Y by doing X
• cause/reason in some cases
• linking descriptions

In this sentence, the most natural interpretation is sequence:

• Mother cut the apple in half, then gave it to the child.

Here, に marks the recipient—the person who receives something.

With あげる (to give), the pattern is:

• A は B に C を あげる
• A gives C to B

So in this sentence:

• 子供に = to the child

This is very common with giving verbs:

• 友だちに本をあげた = I gave a book to my friend.

This is a very common question, because Japanese giving verbs depend on perspective.

• あげる = give (from the giver outward)
• くれる = give to me / to someone close to me, from the speaker’s point of view
• もらう = receive

In your sentence, Mother gives the apple to the child. The sentence is simply describing Mother’s action toward the child, so あげました is the natural choice.

If the child were me (or someone in my in-group), then くれました might be used:

• 母は私にりんごをくれました = Mother gave me an apple.

So あげる and くれる do not both just mean give in exactly the same way; they depend on viewpoint.

The child is involved, but not as the direct object of あげる in this pattern.

In Japanese:

• the thing given is marked by を
• the recipient is marked by に

So:

• りんごを = the thing given
• 子供に = the person receiving it

Even though English says gave the child the apple, Japanese usually marks those roles with particles rather than word order.

Good observation. Logically, the thing being given is also the apple, but Japanese often omits repeated information when it is obvious.

The full idea is something like:

• Mother cut the apple in half, and gave it to the child.

English uses it. Japanese often just leaves it out. Since the listener already knows the apple is what was cut and then given, repeating it is unnecessary.

A more explicit version could be:

• 母はりんごを半分に切って、それを子供にあげました。

But your original sentence is more natural and less repetitive.

Japanese word order is more flexible than English, but not completely free.

The basic order here is:

• 母は = topic
• りんごを = object
• 半分に = result/state
• 切って = first action
• 子供に = recipient
• あげました = main/final verb

You could move some parts around for emphasis, but the verb usually stays at the end of its clause. For example:

• 母は子供にりんごを半分に切ってあげました
  This can mean something slightly different, though, because 〜てあげる may sound like did the favor of cutting it for the child.

So even when word order is flexible, changing it can change nuance.

The comma mainly helps readability and shows a pause between the two actions.

Japanese commas are often more optional and stylistic than English commas. The sentence could also be written without it:

• 母はりんごを半分に切って子供にあげました。

That is still perfectly natural.

So the comma does not change the basic grammar; it just makes the structure easier to see.

あげました is:

• past tense
• polite style (ます-form)

Dictionary form:

• あげる

Polite non-past:

• あげます

Polite past:

• あげました

So the sentence is politely stating a completed action in the past.

A plain-style version would be:

• 母はりんごを半分に切って、子供にあげた。

A natural reading is:

• 母（はは）は りんごを はんぶんに きって、こどもに あげました。

Word readings:

• 母 = はは
• りんご = りんご
• 半分 = はんぶん
• 切って = きって
• 子供 = こども
• あげました = あげました

One useful note: 母 can be read differently depending on context.

• はは = my mother, when talking about her to others
• お母さん（おかあさん） = mother / someone else’s mother / how you address your own mother

In a sentence like this, はは is the expected reading.

It strongly suggests that Mother cut the apple in half and then gave it to the child, but it does not explicitly say what happened to the other half.

So the sentence tells you:

1. the apple was cut in half
2. the child received the apple, or at least the cut apple

In real-life context, people may assume she gave one half to the child, or shared it, but the sentence itself does not spell that out exactly.

If you wanted to be more precise, you could say something like:

• 母はりんごを半分に切って、その半分を子供にあげました。
  = Mother cut the apple in half and gave one half to the child.

By itself, 子供 can mean child or children, depending on context.

In this sentence, English might translate it as the child, but Japanese does not always mark singular/plural clearly.

If you needed to make it explicit, you could say:

• 一人の子供 = one child
• 子供たち = children

So the original sentence is naturally understood as the child if the meaning already given says that, but the Japanese word itself is not strictly singular.