Ich teile eine Grapefruit mit meiner Schwester.

Because ich takes the first-person singular form of the verb.

The verb is teilen = to share / to divide.
Its present-tense forms are:

• ich teile = I share
• du teilst = you share
• er/sie/es teilt = he/she/it shares
• wir teilen = we share
• ihr teilt = you all share
• sie/Sie teilen = they / you (formal) share

So with ich, the correct form is teile.

Here, teilen means to share.

So Ich teile eine Grapefruit mit meiner Schwester means that the speaker and the sister are sharing one grapefruit.

But teilen can also mean to divide / split in other contexts, for example:

• Ich teile den Kuchen in zwei Stücke. = I divide the cake into two pieces.
• Wir teilen uns eine Pizza. = We share a pizza.

So the core idea is dividing something so that more than one person has part of it.

Because Grapefruit is a feminine noun in German: die Grapefruit.

Since it is the direct object of the sentence, it is in the accusative case.
The feminine indefinite article in both nominative and accusative is eine.

So:

• die Grapefruit = the grapefruit
• eine Grapefruit = a grapefruit

That is why the sentence has eine Grapefruit.

Because the preposition mit always takes the dative case.

The noun is die Schwester.
In the dative singular, meine Schwester becomes meiner Schwester.

So:

• meine Schwester = my sister
• mit meiner Schwester = with my sister

This is a very common pattern in German:

• mit meinem Bruder = with my brother
• mit meiner Mutter = with my mother
• mit meinen Freunden = with my friends

So the important rule is:

mit + dative

Because it matches Schwester, which is a feminine singular noun, and it follows mit, which requires the dative.

Here is the pattern for mein- with a feminine singular noun:

• meine Schwester = nominative / accusative
• meiner Schwester = dative / genitive

So meiner tells you:

• feminine
• singular
• dative here

This kind of adjective-like ending is very common with possessive words such as:

• mein
• dein
• sein
• ihr
• unser

Because German sentence structure often puts the verb in second position and other information after it.

In this sentence:

• Ich = subject
• teile = verb
• eine Grapefruit = direct object
• mit meiner Schwester = prepositional phrase

So the sentence follows a very normal pattern:

Subject + verb + object + extra information

That said, German word order is flexible. You could also say:

• Ich teile mit meiner Schwester eine Grapefruit.

That is grammatically possible, but Ich teile eine Grapefruit mit meiner Schwester sounds more natural in many everyday situations.

Yes, in a literal sense teilen can mean divide, but in this sentence the natural meaning is share.

A native speaker would normally understand:

• Ich teile eine Grapefruit mit meiner Schwester.
  = I am sharing a grapefruit with my sister.

If you wanted to emphasize the act of physically cutting or splitting it, you might say something like:

• Ich halbiere die Grapefruit. = I cut the grapefruit in half.
• Ich teile die Grapefruit in zwei Hälften. = I divide the grapefruit into two halves.

So in this sentence, share is the best interpretation.

No, that would not be correct here.

You may see the reflexive form sich etwas teilen, for example:

• Wir teilen uns eine Grapefruit. = We share a grapefruit.

That structure is very common when several people share something together.

So these are both natural:

• Ich teile eine Grapefruit mit meiner Schwester.
• Meine Schwester und ich teilen uns eine Grapefruit.

But Ich teile mir eine Grapefruit mit meiner Schwester is not the normal structure.

Both can express basically the same situation, but the focus is a little different.

Ich teile eine Grapefruit mit meiner Schwester

• focuses on I as the subject
• literally: I share a grapefruit with my sister

Meine Schwester und ich teilen uns eine Grapefruit

• focuses on both people together
• very natural for we are sharing a grapefruit

So the difference is mostly about perspective and style, not basic meaning.

Yes, die Grapefruit is the normal German word, and it looks almost the same as the English word.

A few useful details:

• article: die
• plural: die Grapefruits
• pronunciation is somewhat Germanized, but many learners will recognize the word immediately

So this is one of those vocabulary items that is easy to remember for English speakers.

A rough learner-friendly guide is:

ikh TY-luh EYE-nuh GRAYP-froot mit MY-nuh SHVES-tuh

A few important pronunciation points:

• ich: the ch is the soft German sound, not like English k or ch in chair
• teile: the ei sounds like English eye
• eine: also has ei = eye
• meiner: again ei = eye
• Schwester: sch sounds like English sh

If you want to sound more natural, pay special attention to ich and Schwester, since those sounds are often new for English speakers.

Yes. The structure stays the same:

Ich teile + accusative thing + mit + dative person

Examples:

• Ich teile eine Grapefruit mit meinem Bruder. = I share a grapefruit with my brother.
• Ich teile eine Grapefruit mit meiner Mutter. = I share a grapefruit with my mother.
• Ich teile eine Grapefruit mit meinen Freunden. = I share a grapefruit with my friends.

So this sentence is a very useful model for making your own German sentences.