Ostatak hrane je u frižideru.

Because after ostatak (the rest / remainder), Serbian normally uses the genitive case.

• hrana = food (dictionary form, nominative)
• hrane = of food (genitive singular)

So ostatak hrane literally means the rest of the food.

This is very common in Serbian:

• čaša vode = a glass of water
• kilo šećera = a kilo of sugar
• ostatak dana = the rest of the day

Ostatak means the rest, the remainder, or what is left.

In this sentence, ostatak hrane means:

• the rest of the food
• the leftover food
  depending on context

A useful distinction:

• ostatak hrane = the remaining food
• ostaci hrane = food scraps / leftovers / remains

So this sentence sounds like the remaining food is in the fridge.

Je is the 3rd person singular form of the verb biti (to be), meaning is.

So:

• Ostatak hrane = the rest of the food
• je = is
• u frižideru = in the fridge

Serbian often uses forms of biti just like English uses to be:

• On je ovde. = He is here.
• Knjiga je na stolu. = The book is on the table.

Because u can take different cases depending on meaning.

Here it means location: in the fridge, so it uses the locative case:

• frižider → frižideru

Compare:

• u frižideru = in the fridge (where something is)
• u frižider = into the fridge (movement toward the inside)

So:

• Ostatak hrane je u frižideru. = The rest of the food is in the fridge.
• Stavi hranu u frižider. = Put the food into the fridge.

It is the locative singular of frižider.

The preposition u with a meaning of location requires the locative:

• u kući = in the house
• u školi = at school / in school
• u frižideru = in the fridge

For many masculine nouns, the locative singular often ends in -u:

• grad → u gradu
• park → u parku
• frižider → u frižideru

Yes. Serbian word order is more flexible than English, although some versions sound more neutral than others.

The most neutral version here is:

• Ostatak hrane je u frižideru.

But you could also hear:

• U frižideru je ostatak hrane.
  This puts more focus on where it is.

Because Serbian uses cases, the role of each word is usually still clear even when the order changes.

Serbian does not have articles like English a / an / the.

So ostatak hrane can mean:

• the rest of the food
• sometimes just rest of the food

You understand whether it is definite or not from context.

This is normal in Serbian:

• Knjiga je na stolu. = The book is on the table.
• Imam auto. = I have a car.

There is no separate word for the.

Yes, frižider is a very common everyday word in Serbian.

It comes from the same source as English Frigidaire, and in normal speech it simply means fridge / refrigerator.

You may also encounter:

• hladnjak in some regional standards, especially outside Serbian usage

But in Serbian, frižider is completely natural and very common.

A simple approximation is:

Ostatak hrane je u frižideru
oh-STAH-tahk HRAH-neh yeh oo free-ZHEE-deh-roo

A few notes:

• j is pronounced like English y
  • je sounds like ye
• ž sounds like the s in measure
• r in Serbian is usually rolled or tapped

So:

• hrane ≈ HRAH-neh
• frižideru ≈ free-ZHEE-deh-roo

Yes, depending on context, that is a natural English translation.

Literally, it is the rest of the food is in the fridge, but in real usage it may refer to:

• the remaining portion of a meal
• leftovers from earlier
• food that wasn’t eaten

If you specifically wanted leftovers as a plural idea, Serbian might also use:

• ostaci hrane

But ostatak hrane is perfectly natural for the remaining food.

Because Serbian is organizing the idea differently.

In this sentence:

• hrana = food, an uncountable singular noun
• ostatak hrane = the remaining amount of food

English often uses a plural noun like leftovers, but Serbian can express the same idea with a singular mass noun:

• food
• the rest of the food

So the grammar does not have to match English word-for-word.

Yes, but it is slightly different.

• Ostatak hrane = the rest of the food
• Ostala hrana = the remaining food

Both are natural, but:

• ostatak hrane focuses on what is left over
• ostala hrana sounds a bit more like the remaining food as a description

So both can work, but they are not always perfectly interchangeable in every context.