العمر مهم.

Because Arabic often leaves out the verb to be in the present tense.

So in a simple sentence like العمر مهم:

• العمر = the subject
• مهم = the predicate / description

Arabic understands this as Age is important without needing a separate word for is.

If you wanted a past or future meaning, then Arabic would use a verb:

• كان العمر مهمًّا = age was important

A careful MSA pronunciation is:

العُمْرُ مُهِمٌّ
al-ʿumru muhimmun

In normal pause, it is often said more like:

al-ʿumr muhimm

A few pronunciation notes:

• ع is the letter ʿayn, a sound English does not have.
• مهم is pronounced mu-himm, with a doubled m at the end.
• In everyday reading, the short final case vowels are often not pronounced.

الـ is the Arabic definite article, like the in English.

So:

• عمر can be a proper name, Umar
• العمر means the age or age in a general sense, depending on context

In this sentence, العمر is definite, which is very common for the first part of a nominal sentence.

Because ع is a moon letter, not a sun letter.

With moon letters, the ل in الـ is pronounced:

• العمر = al-ʿumr

With sun letters, the ل would assimilate, as in:

• الشمس = ash-shams

So here you say the l sound clearly.

Because مهم here is not an attributive adjective inside a noun phrase. It is the predicate of the sentence.

In other words:

• العمر مهم = Age is important
• العمر المهم = the important age / the important lifetime, which is a different structure

This is a very common pattern in Arabic:

• definite subject + indefinite predicate

So العمر is definite, but مهم usually stays indefinite.

It is an adjective in meaning, but in the sentence it functions as the predicate (خبر) of the nominal sentence.

So grammatically, it is describing العمر, but it is not attached to it the way an ordinary adjective is in a phrase like:

• العمر المهم = the important age

In العمر مهم, it stands as the second main part of the sentence.

Because العمر is grammatically masculine, so the adjective/predicate agrees with it in gender.

So:

• العمر مهم = masculine
• الحياة مهمة = feminine

Even though مهم is the predicate, it still agrees with the subject in gender and number.

In fully vocalized MSA, it is:

العُمْرُ مُهِمٌّ

Both words are in the nominative here:

• العُمْرُ ends in -u
• مُهِمٌّ ends in -un

Why?

• العمر is the subject of a nominal sentence
• مهم is the predicate

In normal Arabic writing, these short endings are usually not written, so you normally see only:

العمر مهم

That mark is shadda (ّ). It means the consonant is doubled.

So:

• مهم is pronounced muhimm
• not muhim

The last م is held a little longer because it is doubled.

This is important for correct pronunciation.

For a normal, neutral sentence, العمر مهم is the standard order.

Arabic can sometimes put the predicate first for emphasis or style, but that is less basic and less neutral. A learner should use:

العمر مهم

as the default pattern.

So if your goal is clear standard Arabic, keep the original order.

They are written with the same basic letters ع م ر, but they are different words in practice.

• عُمَر = Umar (the male name)
• العُمْر = the age / age / lifetime

The presence of الـ and the different pronunciation make the meaning clear in context.

So in this sentence, العمر is definitely not the name Umar.