Min mors fødselsdag er den femtende oktober.

Mors is the genitive form of mor (mother), and it means mother's.

So:

• min mor = my mother
• min mors fødselsdag = my mother's birthday

In Danish, you usually make possession by adding -s:

• Peters bog = Peter's book
• min søsters bil = my sister's car
• min mors fødselsdag = my mother's birthday

This is very similar to English 's, but in Danish it is written directly as s without an apostrophe in normal cases.

Because when a noun is already made definite by a possessor, Danish normally does not add the definite ending.

So:

• fødselsdag = birthday
• fødselsdagen = the birthday

But:

• min mors fødselsdag = my mother's birthday, not min mors fødselsdagen

This is a very important Danish pattern:

• bilen = the car
• min bil = my car
  not min bilen

Likewise:

• huset = the house
• Peters hus = Peter's house
  not Peters huset

Fødselsdag is a compound noun, which is very common in Danish.

It is made from:

• fødsel = birth
• dag = day

So literally it is birth-day, just like English birthday.

There is also an -s- in the middle: fødsel + s + dag. This linking s often appears in Danish compounds, and you usually just learn the whole compound as one word.

In Danish, when saying a date with an ordinal number, you normally use den before it.

So:

• den første januar = the first of January
• den femtende oktober = the fifteenth of October

Here:

• den = a marker used with the date
• femtende = fifteenth

This is the normal way to say dates in full.

Because femten is the cardinal number (fifteen), while femtende is the ordinal number (fifteenth).

Compare:

• femten = fifteen
• femtende = fifteenth

Dates in Danish are usually said with ordinal numbers:

• den tredje marts = the third of March
• den tiende april = the tenth of April
• den femtende oktober = the fifteenth of October

Danish often does not use a preposition where English uses on with dates.

So English says:

• My mother's birthday is on the fifteenth of October

But Danish simply says:

• Min mors fødselsdag er den femtende oktober

That is normal Danish. The date expression can come directly after er.

No. In Danish, months are not normally capitalized.

So you write:

• oktober
• januar
• mandag
• dansk

not:

• Oktober
• Januar
• Mandag
• Dansk

This is different from English, where months and days are capitalized.

Yes. In writing, Danish often uses numerals for dates.

For example:

• Min mors fødselsdag er den 15. oktober.
• Min mors fødselsdag er 15. oktober.

You may see slight variation in style, but 15. oktober is very common in writing.

In full spoken Danish, den femtende oktober sounds natural and standard.

Min means my and is the common-gender singular possessive form.

Danish has different forms of my depending on the gender/number of the noun:

• min for common gender singular
• mit for neuter singular
• mine for plural

Since mor is a common-gender noun, you say:

• min mor = my mother

Compare:

• min bil = my car
• mit hus = my house
• mine bøger = my books

The sentence follows the normal Danish main-clause word order:

• Min mors fødselsdag = subject
• er = verb
• den femtende oktober = complement

So the structure is basically:

Subject + verb + date expression

This is very similar to English:

• My mother's birthday
  • is
    • the fifteenth of October

A careful pronunciation would be approximately:

Min mors fødselsdag er den femtende oktober

A few helpful points:

• min often sounds like meen
• mors has a Danish r, not an English one
• fødselsdag can be tricky because of the ø and the consonant cluster
• femtende is often pronounced more smoothly than it looks on the page
• oktober has stress on the last part: roughly ok-to-BER

The hardest word for many learners is often fødselsdag. It helps to practice it slowly first:

fød-sels-dag

and then speed it up.

Usually, no, unless you are using a dialect, speaking informally in a specific regional way, or using a Swedish/Norwegian-influenced form.

In standard Danish, the usual word is:

• mor = mother / mum

So standard Danish is:

• Min mors fødselsdag

You might also hear:

• min mor har fødselsdag den femtende oktober
  = my mother has her birthday on the fifteenth of October / my mother's birthday is on the fifteenth of October

That is also very natural Danish.