kodomo ha suizokukan yori hakubutukan no hou ga sizuka da to itte imasita.

は marks 子供 as the topic of the whole sentence.

So the sentence is talking about the child / children, and then telling us what that person or group said.

It does not necessarily mean 子供 is the grammatical subject of the quoted statement. The main structure is:

• 子供は = as for the child / children
• …と言っていました = was saying / said that …

So 子供は belongs to the outside sentence, not to the inside quoted clause.

It can mean either child or children. Japanese nouns usually do not show singular vs. plural unless the context makes it clear.

So 子供は could mean:

• the child
• children
• the children

You have to rely on context, or on the translation already given to you.

This is a very common comparison pattern:

A より B のほうが + adjective

It means:

• B is more adjective than A
• or more naturally, B is adjective-er than A

In this sentence:

• 水族館より = than aquariums / than the aquarium
• 博物館のほうが = museums / the museum, more so

So the pattern is:

• 水族館より = compared with the aquarium/aquariums
• 博物館のほうが = the museum/museums are the side that is more quiet

ほう literally means something like side or direction, but in comparisons it is often best understood as the one that is more….

So:

• 博物館のほうが does not literally mean the side of museums in a natural English sense
• it means museums rather than aquariums / museums are the one that is more…

This is just standard Japanese comparison grammar.

A very common pattern is:

• AよりBのほうがいい = B is better than A

In this comparison pattern, B のほうが is treated as the thing that has the property being described.

So in:

• 水族館より博物館のほうが静かだ

the part 博物館のほうが is the thing being described as quiet.

That is why が appears there. It marks the item that is being singled out in the comparison.

You can think of it like this:

• As for the two, the museum side is the one that is quiet(er).

静か is a na-adjective.

Na-adjectives work differently from i-adjectives:

• 静かだ = is quiet
• 静かな博物館 = a quiet museum

So:

• 静かだ is used when 静か is the predicate of the sentence
• 静かな is used when 静か directly modifies a noun

Here, 静か is the predicate inside the quoted clause, so 静かだ is correct.

Because the quoted statement is a plain-form clause, and 静か needs the copula だ in plain style.

The quoted part is:

• 水族館より博物館のほうが静かだ

Then と marks that whole clause as the content of what was said:

• …静かだ と 言っていました

So だ is not there because of と specifically; it is there because the sentence inside the quote needs to end properly in plain form.

Compare:

• 安いと言った = said that it is cheap
• 静かだと言った = said that it is quiet

For i-adjectives, no だ is needed:

• 高いと言った

But for na-adjectives and nouns, plain だ appears in this kind of quotation.

と marks the content of what was said or thought. It often works like that in English.

So:

• 水族館より博物館のほうが静かだ = the statement
• と = marks that statement as a quotation/content clause
• 言っていました = was saying / said

Together:

• …だと言っていました = was saying that …

Even when there are no quotation marks in Japanese, と often tells you this is the thing being said.

言っていました is the ている form of 言う, in polite past:

• 言う = say
• 言っている = is saying / says / has been saying, depending on context
• 言っていました = was saying / said

With verbs like 言う, ている can sometimes suggest:

1. an action in progress
   
   • was saying
2. a continuing state resulting from speaking
   
   • roughly, had said / was saying
3. a softer or more descriptive way of reporting speech

In many real sentences, 言っていました and 言いました can both be translated as said, but the nuance is a little different.

• 言いました = a more simple completed action: said
• 言っていました = often sounds more like was saying, had said, or was telling me

Yes. The quoted content is:

• 水族館より博物館のほうが静かだ

Then that entire clause is followed by:

• と 言っていました

So the structure is:

• [quoted statement] と 言っていました

This is extremely common in Japanese.

Here 静か is being used as the predicate, not directly before a noun.

Japanese adjectives can either:

1. modify a noun
   • 静かな博物館 = a quiet museum
2. end the predicate
   • 博物館は静かだ = the museum is quiet

In this sentence, the comparison is about which is quieter, so 静かだ is acting as the predicate of the quoted statement.

Normally, no. Because 子供は is attached to 言っていました, it is most naturally understood as:

• The child / children said that …

For 子供は to mean something like for children, you would usually expect a different structure, such as:

• 子供には …
• 子供にとって …

So in this sentence, 子供は is the topic of the speaker/sayer, not the standard of comparison or the point of view.

Usually in comparisons, yes, より is the part that corresponds to than.

But it is good to think of it more broadly as compared with. That helps explain the grammar better.

So:

• 水族館より博物館のほうが静かだ

is literally closer to:

• Compared with aquariums, museums are more quiet

Natural English then becomes:

• Museums are quieter than aquariums

Thinking of より as compared with can make the Japanese structure easier to understand.