Das Kind rechnet richtig.

Because Kind is a neuter noun in German. Its basic article in the singular is das.

So in the nominative singular:

• das Kind = the child

This is grammatical gender, not biological sex. Even if the child is a boy or a girl, the noun Kind itself is still grammatically neuter.

It is in the nominative case because it is the subject of the sentence — the one doing the action.

In Das Kind rechnet richtig:

• das Kind = the subject
• rechnet = the verb
• richtig = describes how the action is done

So das Kind is nominative.

Because all nouns are capitalized in German, not just proper names.

So:

• das Kind
• der Mann
• die Frau
• das Haus

This is one of the most noticeable spelling differences between German and English.

Because the subject is das Kind, which is third person singular. In the present tense, rechnen changes to rechnet for er/sie/es.

Present tense of rechnen:

• ich rechne
• du rechnest
• er/sie/es rechnet
• wir rechnen
• ihr rechnet
• sie/Sie rechnen

Since das Kind matches es, the correct form is rechnet.

Here rechnen means something like:

• to do arithmetic
• to calculate
• to work with numbers

So the sentence suggests the child is doing sums or calculations correctly.

Be careful: rechnen is not the general verb for thinking. It is more specifically about numbers, calculation, or sometimes figuring something out mathematically.

Because richtig is being used adverbially here: it describes the verb rechnet, not the noun Kind.

So it means:

• rechnet richtig = calculates correctly

In German, adjectives used as adverbs usually do not take endings.

Compare:

• Das ist ein richtiges Ergebnis.
  Here richtiges describes the noun Ergebnis, so it takes an ending.
• Das Kind rechnet richtig.
  Here richtig describes the action, so it stays unchanged.

In this sentence it means correctly.

That is because it modifies the verb:

• rechnet richtig = calculates correctly

As an adjective with a noun, richtig often means right or correct:

• die richtige Antwort = the correct answer

So the exact English translation depends on what the word is describing.

Yes. This is a very normal German main clause word order:

• Das Kind = subject
• rechnet = finite verb
• richtig = adverb

A key German rule is that in a main clause, the finite verb usually comes in second position.

So this sentence follows the standard pattern:

• Subject + verb + other information

In a yes/no question, German usually puts the finite verb first:

• Rechnet das Kind richtig? = Is the child calculating correctly?

So the statement:

• Das Kind rechnet richtig.

becomes:

• Rechnet das Kind richtig?

That verb-first pattern is very common in German questions.

Yes, but the verb still has to stay in second position in a normal statement.

For example, you could say:

• Richtig rechnet das Kind.

This is grammatical, but it sounds marked or emphatic, as if you are emphasizing richtig.

The most neutral version is still:

• Das Kind rechnet richtig.

So yes, German word order can be flexible, but not random.

In both words, the ch is the soft German sound often called the ich-Laut.

So:

• rechnet
• richtig

both use a soft sound similar to a gentle hiss made high in the mouth, not like English ch in chair.

Very roughly:

• rechnet sounds like REKH-net with a soft ch
• richtig sounds like RIKH-tikh with the same soft sound at the end

This sound is difficult for many English speakers at first, but it is very common in German.

Yes, grammatically you can, because Kind is a neuter noun.

So:

• Das Kind rechnet richtig.
• Es rechnet richtig.

Both are grammatical.

However, in real conversation, once people know whether the child is a boy or girl, they often switch to er or sie based on natural gender, especially in less formal speech. But strictly by grammar, es matches das Kind.