Я ріжу огірок ножем.

• Я = the subject, I
• ріжу = the verb, I am cutting / I cut
• огірок = the direct object, cucumber
• ножем = the instrument, with a knife

So the structure is basically subject + verb + object + instrument.

Yes. Ukrainian often drops subject pronouns when they are clear from the verb ending.

• Я ріжу огірок ножем = neutral or slightly emphasized I
• Ріжу огірок ножем = still means I am cutting a cucumber with a knife

The ending -у in ріжу already shows first person singular, so я is not required.

Because Ukrainian present tense often covers both ideas:

• I cut
• I am cutting

In this sentence, without extra context, I am cutting is the most natural English translation, because it sounds like an action happening right now.

Also, ріжу comes from an imperfective verb, so it describes an ongoing, repeated, or general action rather than a completed one.

This is a normal verb stem change in Ukrainian.

The infinitive is різати, but in the present tense the stem changes:

• я ріжу
• ти ріжеш
• він / вона ріже
• ми ріжемо
• ви ріжете
• вони ріжуть

So the з in різ- changes to ж in these forms. This is something you mainly learn as part of the verb’s conjugation pattern.

It is in the accusative case, but for many masculine inanimate nouns, the accusative singular looks exactly the same as the nominative singular.

So:

• nominative: огірок
• accusative: огірок

That is why the direct object does not visibly change here.

Compare that with an animate masculine noun, where you often do see a different accusative form:

• nominative: брат
• accusative: брата

Because it is in the instrumental case.

Ukrainian uses the instrumental to show the tool or means used to do something. So:

• ніж = knife
• ножем = with a knife / by means of a knife

In this sentence, ножем tells you what tool is being used for the cutting.

Because Ukrainian often does not need a preposition here. The instrumental case by itself can express with when you mean the instrument used.

So English says:

• with a knife

But Ukrainian can simply say:

• ножем

This is very common:

• писати олівцем = to write with a pencil
• їсти ложкою = to eat with a spoon

Because ніж has a stem change in its other forms.

Its nominative singular is ніж, but in many other cases the stem becomes нож-:

• ніж
• ножа
• ножем

This kind of vowel alternation is fairly common in Ukrainian nouns, so it is something you usually learn together with the noun’s case forms.

Yes. Ukrainian word order is more flexible than English word order because cases show the grammatical roles.

The sentence Я ріжу огірок ножем is a neutral order. But you could also say:

• Огірок я ріжу ножем — puts more focus on the cucumber
• Ножем я ріжу огірок — puts more focus on the knife
• Я ножем ріжу огірок — emphasizes the instrument a bit more

So changing the order usually changes emphasis, not the basic meaning.

Because Ukrainian has no articles.

So огірок can mean:

• a cucumber
• the cucumber

And ніж / ножем can mean:

• a knife / with a knife
• the knife / with the knife

Context tells you which meaning is intended. If Ukrainian speakers want to be more specific, they can use words like цей (this) or other context clues.

A helpful stress pattern is:

• Я
• рі́жу
• огіро́к
• ноже́м

A rough pronunciation guide:

• Я ≈ ya
• рі́жу ≈ REE-zhu
• огіро́к ≈ o-hee-ROK
• ноже́м ≈ no-ZHEM

One important point: Ukrainian г in огірок is not a hard English g. It sounds more like a voiced h.