رقم الوثيقة مع السائق الآخر.

Yes. In Arabic, especially in the present tense, the verb “to be” is often left out.

So رقم الوثيقة مع السائق الآخر is a normal nominal sentence. Arabic understands it as something like:

• رقم الوثيقة = the document number
• مع السائق الآخر = with the other driver

So the missing idea of is is simply understood from context.

This is an iḍāfa construction, often called a genitive/possessive construction.

It is made of:

• رقم = number
• الوثيقة = the document

Together, رقم الوثيقة literally means the number of the document, or more naturally the document number.

In Arabic, this kind of structure is very common:

• باب البيت = the door of the house
• اسم الطالب = the student’s name
• رقم الوثيقة = the document number

The first noun comes first, and the second noun specifies it.

Because in an iḍāfa, the first noun usually does not take ال.

So you say:

• رقم الوثيقة not
• الرقم الوثيقة

The definiteness of the whole phrase comes from the second noun. Since الوثيقة is definite, رقم الوثيقة is understood as definite too: the document number.

This is a very important pattern in Arabic.

Because it has الـ, the definite article.

• وثيقة = a document
• الوثيقة = the document

In رقم الوثيقة, the second noun is definite, so the entire iḍāfa phrase becomes definite.

So:

• رقم وثيقة = a document number / the number of a document
• رقم الوثيقة = the document number / the number of the document

مع means with.

Here it shows location or possession in the sense of being in someone’s possession:

• مع السائق الآخر = with the other driver

So the phrase means that the document number is with that person.

مع is a preposition, so the noun after it is in the genitive case.

Because مع is a preposition, and prepositions in Arabic make the following noun genitive.

So in full case-marked Arabic, it would be:

• مَعَ السَّائِقِ الآخَرِ

Notice the kasra-type ending in careful pronunciation:

• السائقِ
• الآخرِ

In normal everyday writing, those short vowels are usually not written, but the grammar is still there.

Because الآخر is an adjective describing السائق, and adjectives in Arabic must agree with the noun they describe in:

• gender
• number
• definiteness
• case

Here:

• السائق is masculine singular definite
• so the adjective must also be masculine singular definite

That gives:

• السائق الآخر = the other driver

If the noun were feminine, you would use الأخرى:

• السيارة الأخرى = the other car

Its basic meaning here is other.

So:

• السائق الآخر = the other driver

In some contexts, forms from this root can also suggest another, the last, or the latter, depending on structure and context. But in this sentence, the natural reading is simply the other driver.

A careful full pronunciation would be:

رَقْمُ الوَثِيقَةِ مَعَ السَّائِقِ الآخَرِ

Breaking it down:

• رَقْمُ = raqmu
• الوَثِيقَةِ = al-wathīqati
• مَعَ = maʿa
• السَّائِقِ = as-sāʾiqi
• الآخَرِ = al-ākhari

A learner should also notice that رقم is nominative here because it is the topic/subject of the nominal sentence.

It can sound a bit brief or report-like, which is very common in Arabic administrative, police, or form-based language.

Arabic often allows concise statements like this, especially when the context is already clear.

A fuller version could be something like:

• رقم الوثيقة موجود مع السائق الآخر
  The document number is with the other driver / is in the possession of the other driver

But the shorter version is perfectly natural in the right context.

Yes, but the meaning or emphasis may shift slightly.

The given order:

• رقم الوثيقة مع السائق الآخر

starts with رقم الوثيقة, making that the main topic.

A different order like:

• مع السائق الآخر رقم الوثيقة

is less neutral and would sound more marked or context-dependent.

In standard straightforward Arabic, the original order is the most natural if you are simply stating where the document number is.