Untuk menenangkan bayi itu, nenek mengelus kepalanya dan bernyanyi pelan.

Here, untuk introduces a purpose phrase: untuk menenangkan bayi itu = to calm/soothe the baby or in order to calm the baby.

So the sentence structure is:

• Untuk menenangkan bayi itu, = To calm the baby,
• nenek mengelus kepalanya dan bernyanyi pelan. = grandmother stroked his/her head and sang softly.

In Indonesian, untuk + verb is a very common way to express purpose.

Tenang means calm or peaceful.

menenangkan comes from the root tenang with affixes:

• meN- ... -kan

This makes it into a verb meaning to make someone calm, to calm, or to soothe.

So:

• tenang = calm
• menenangkan = to calm someone / to soothe someone

This is a very common Indonesian pattern:

• bersih = clean
• membersihkan = to clean something
• tenang = calm
• menenangkan = to calm something/someone

In Indonesian, demonstratives like ini and itu usually come after the noun.

So:

• bayi itu = that baby / the baby
• rumah itu = that house
• buku ini = this book

This is different from English, where this/that come before the noun.

Also, in many contexts itu can make the noun feel definite, so bayi itu may mean either that baby or simply the baby, depending on context.

Because Indonesian often does not repeat the subject when it is already clear.

So:

• nenek mengelus kepalanya dan bernyanyi pelan

literally looks like:

• grandmother stroked his/her head and sang softly

The subject nenek applies to both verbs:

• mengelus
• bernyanyi

English also does this sometimes:
Grandma stroked the baby's head and sang softly.

Indonesian does it very naturally and often.

Mengelus means something like:

• to stroke
• to caress
• to gently rub

In this sentence, it suggests a soft, comforting motion, which fits the idea of calming a baby.

It is gentler than a verb meaning to hit or to pat sharply.
So mengelus kepalanya suggests stroking the baby's head gently.

Because -nya is attached directly to the noun.

• kepala = head
• kepalanya = his head / her head / its head / the head

In Indonesian, pronoun-like endings such as -nya are suffixes, so they are written together with the word.

Other examples:

• bukunya = his/her book, the book
• rumahnya = his/her house, the house

So kepalanya is not two separate words.

In this sentence, -nya most naturally means his/her, referring to the baby:

• kepalanya = his/her head

Since bayi does not mark gender, English may translate this as the baby's head, his head, or her head, depending on context.

Important: -nya can do more than one job in Indonesian. It can mark:

• possession: bukunya = his/her book
• definiteness in some contexts: rumahnya besar = the house is big / his house is big
• an object pronoun in some constructions

But here, the most straightforward reading is the baby's head.

Grammatically, -nya can sometimes be ambiguous, because it does not show gender and can refer back to someone already mentioned.

But in this sentence, the most natural interpretation is that it refers to the baby's head, because:

• the purpose is to soothe the baby
• stroking the baby's head fits that situation naturally

If it meant the grandmother's own head, the sentence would sound odd in context.

So learners should understand kepalanya here as the baby's head.

In Indonesian, words like pelan can function adverbially without needing a separate word like dengan.

So:

• bernyanyi pelan = sing softly / sing quietly

This is very natural.

You may also hear:

• bernyanyi dengan pelan
• bernyanyi pelan-pelan

But bernyanyi pelan is simple and idiomatic.

A useful thing to remember is that Indonesian often uses adjective-like words directly as adverbs:

• bicara pelan = speak softly
• lari cepat = run fast
• tidur nyenyak = sleep soundly

Pelan basically means slow or soft/gentle, depending on context.

In bernyanyi pelan, it means something like:

• softly
• quietly
• in a gentle voice

It does not mean that the grandmother sang at a slow musical tempo.
The meaning here is about volume/gentleness, not speed.

The comma is used because the purpose phrase has been moved to the front of the sentence.

So the structure is:

• Untuk menenangkan bayi itu, = fronted purpose phrase
• nenek mengelus kepalanya dan bernyanyi pelan. = main clause

This is similar to English:

• To calm the baby, Grandma stroked the baby's head and sang softly.

You could also say the sentence without fronting the purpose phrase, for example:

• Nenek mengelus kepalanya dan bernyanyi pelan untuk menenangkan bayi itu.

That would also be grammatical, though the focus is slightly different.

Usually, nenek means grandmother.

But depending on context, it can also refer to an old woman. In real life, Indonesian kinship words are often used more broadly than in English.

In this sentence, if the translation already gives grandmother, that is the natural reading.
So here:

• nenek = grandmother / grandma

Yes, it could, if the baby has already been clearly identified in context.

• Untuk menenangkan bayi itu = To calm the baby
• Untuk menenangkannya = To calm him/her

Here, -nya on menenangkannya would mean him/her.

The version in your sentence uses the full noun phrase bayi itu, which is often clearer for learners and for standalone sentences.

A useful breakdown is:

• Untuk menenangkan bayi itu = purpose phrase
• nenek = subject
• mengelus kepalanya = first verb phrase
• dan bernyanyi pelan = second coordinated verb phrase

So overall:

[Purpose] + [Subject] + [Verb phrase 1] + dan + [Verb phrase 2]

More literally:

• To soothe the baby, grandmother stroked his/her head and sang softly.

This is a very normal Indonesian sentence pattern.