Η προσαύξηση είναι γελοία.

Η is the feminine singular definite article, so here it means the.

It matches προσαύξηση, which is a feminine singular noun:

• η προσαύξηση = the increase / the raise / the surcharge, depending on context

Greek articles must agree with the noun in gender, number, and case.

Because προσαύξηση is simply a noun that belongs to the feminine gender in Greek. Grammatical gender is something you usually have to learn together with the noun.

A useful clue is the ending:

• many nouns ending in -ηση are feminine

So you learn it as:

• η προσαύξηση

That is why the article is η and the adjective later is also in the feminine form.

Because adjectives in Greek must agree with the noun they describe.

The noun προσαύξηση is:

• feminine
• singular
• nominative

So the adjective must also be:

• feminine
• singular
• nominative

That gives:

• masculine: γελοίος
• feminine: γελοία
• neuter: γελοίο

So:

• Η προσαύξηση είναι γελοία. = correct
• Η προσαύξηση είναι γελοίο. = incorrect, because γελοίο is neuter

Είναι is the present-tense form of είμαι, meaning to be.

Here it means is.

A helpful thing to know is that είναι is used for:

• he/she/it is
• and also they are

So Greek does not distinguish those two with different present-tense forms the way English does.

In this sentence:

• Η προσαύξηση είναι γελοία.
• literally: The increase is ridiculous.

The main noun phrase Η προσαύξηση is in the nominative, because it is the subject of the sentence.

The adjective γελοία is also in the nominative, because it is a predicate adjective after είναι.

So:

• η προσαύξηση = nominative feminine singular
• γελοία = nominative feminine singular

This is normal after a verb like είμαι.

A rough pronunciation is:

i pro-SAF-ksi-si EE-ne ye-lo-EE-a

More carefully:

• Η = i
• προσαύξηση = pro-SAF-ksi-si
• είναι = EE-ne
• γελοία = ye-lo-EE-a

Two especially useful pronunciation points:

• αυ is pronounced af before a voiceless sound, and in προσαύξηση it comes before ξ, so it sounds like af
• γ before ε sounds like a soft y-like sound, so γε sounds roughly like ye

Because this is the normal pattern for a sentence with to be:

• subject + είναι + adjective

So:

• Η προσαύξηση είναι γελοία.

This is the most neutral word order.

Greek word order is somewhat flexible, though. You could change it for emphasis, for example:

• Γελοία είναι η προσαύξηση.

That sounds more marked, like Ridiculous is the increase or The increase is what’s ridiculous.

In this sentence, η is the natural choice because the speaker is talking about a specific increase, raise, or surcharge: the increase.

Greek also uses the definite article quite often, sometimes more often than English does. With a specific noun like this, leaving the article out would usually sound unnatural.

So the normal version is:

• Η προσαύξηση είναι γελοία.

Not necessarily. Προσαύξηση can refer to different kinds of increases depending on context, such as:

• a pay raise
• an increase in an amount
• an extra charge
• a surcharge
• an increment

So even if the grammar is straightforward, the exact English word can vary with context.

English often uses it is, but Greek does not need a dummy subject like it in the same way.

In this sentence, the actual subject is already there:

• Η προσαύξηση = the increase

So Greek simply says:

• Η προσαύξηση είναι γελοία.

There is no need for an extra pronoun.

A very useful pattern is:

• Η/Ο/Το + noun + είναι + adjective

For example:

• Η ιδέα είναι καλή. = The idea is good.
• Ο νόμος είναι άδικος. = The law is unfair.
• Το μέτρο είναι γελοίο. = The measure is ridiculous.

The main thing to remember is:

• the article agrees with the noun
• the adjective also agrees with the noun
• είναι links them, like is in English