Я дав касирці готівку, тому вона швидко дала решту.

Because касирці is the dative singular form of касирка. After дати / давати the recipient usually goes in the dative case.

So the pattern is:

• дати комусь щось = give someone something
• комусь = dative
• щось = accusative

In this sentence:

• касирці = to the cashier
• готівку = cash

A lot of feminine nouns ending in -ка form the dative singular in -ці, for example:

• дівчинка → дівчинці
• касирка → касирці

There are two clues:

• The dictionary form is касирка, which is a feminine noun.
• The pronoun later is вона, meaning she.

So the sentence is talking about a female cashier.

If it were a male cashier, you would normally get something like:

• Я дав касиру готівку, тому він швидко дав решту.

Because готівку is the accusative singular form of готівка.

Here готівку is the direct object of дав: it is the thing that was given. For many feminine nouns ending in -а, the accusative singular changes to -у:

• готівка → готівку
• книга → книгу
• вода → воду

So:

• Я дав готівку = I gave cash

For the same reason as готівку.

Решту is the accusative singular form of решта, because it is the direct object of дала:

• вона дала решту = she gave the change

In shopping contexts, решта means change in the money sense. Literally, the word can also mean the rest or the remainder, but here it clearly means change.

Because Ukrainian past tense agrees with the subject in gender and number.

• дав = masculine singular
• дала = feminine singular
• дали = plural

So:

• Я дав = I gave if the speaker is male
• Я дала = I gave if the speaker is female
• вона дала = she gave

This is very different from English, where gave does not change for gender.

Not exactly. A woman would normally say:

• Я дала касирці готівку, тому вона швидко дала решту.

The first past-tense verb has to match the speaker’s gender:

• male speaker: я дав
• female speaker: я дала

The second verb stays дала because вона is feminine.

Here тому means so, therefore, or that’s why.

It introduces the result of the first clause:

• Я дав касирці готівку = I gave the cashier cash
• тому вона швидко дала решту = so she quickly gave change

A useful contrast:

• тому = so / therefore
• тому що = because

Compare:

• Я дав касирці готівку, тому вона дала решту. = I gave the cashier cash, so she gave change.
• Вона дала решту, тому що я дав касирці готівку. = She gave change because I gave the cashier cash.

Because the sentence has two clauses:

• Я дав касирці готівку
• вона швидко дала решту

They are connected by тому, and in Ukrainian this kind of clause link is normally separated by a comma.

It works a lot like English punctuation before so in a sentence such as:

• I paid in cash, so she quickly gave me change.

Yes. Ukrainian word order is fairly flexible because the case endings show each word’s role.

For example, these are all possible:

• Я дав касирці готівку, тому вона швидко дала решту.
• Я дав готівку касирці, тому вона швидко дала решту.
• Готівку я дав касирці, тому вона швидко дала решту.

The basic meaning stays the same, but the emphasis changes.

In the original sentence, касирці before готівку sounds natural and highlights the recipient a bit earlier.

Sometimes yes, but here keeping them is very helpful.

Ukrainian often drops subject pronouns when the verb form already makes the subject clear. But in the past tense, forms like дав do not show person clearly; they mainly show gender and number.

So дав by itself could mean:

• I gave
• he gave

depending on context.

That is why я is useful here. The same goes for вона: you could omit it in a very clear context, but keeping it makes the sentence easier to understand.

The verbs дав and дала are past-tense forms of дати, which is perfective.

That means the action is seen as completed:

• he gave the cash
• she gave the change

This fits the situation well, because both actions are single completed events.

The imperfective partner is давати:

• давав / давала

That would be used more for repeated action, process, or ongoing description, for example:

• Він завжди давав готівку. = He always used to give cash.

Because швидко is an adverb meaning quickly, and putting it before the verb is a very normal, neutral position in Ukrainian:

• вона швидко дала решту

You may also hear other orders, such as:

• вона дала решту швидко

But that can sound more marked or give slightly different emphasis. The version in the sentence is the most straightforward.

They are very common shopping words:

• готівка = cash
• решта = change

So this is the standard kind of store interaction:

• дати готівку = give cash / pay in cash
• дати решту = give change

Готівка is specifically cash, as opposed to paying by card.
Гроші is a broader word meaning money in general.

Because Ukrainian has no articles.

English needs words like a and the, but Ukrainian usually expresses that meaning through context, word order, and the situation itself.

So:

• касирці can mean to the cashier or to a cashier
• решту can mean the change

In this sentence, the context makes everything clear without articles.