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Fim de semana vs. final de semana

In Portuguese, fim de semana and final de semana are synonymous phrases that both mean "weekend". While they are used interchangeably to refer to Saturday and Sunday, there are slight distinctions regarding regional preference and formal acceptance.

Fim de semana

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This is the most standard, grammatically traditional way to say "weekend". It is used in all Portuguese-speaking countries and is the preferred form in Portugal and formal writing. The word fim serves as the noun for "end".
Eu vou viajar neste fim de semana.
(I am going to travel this weekend.)
Tenha um bom fim de semana!
(Have a good weekend!)
Eles gostam de descansar no fim de semana.
(They like to rest on the weekend.)
O escritório não abre durante o fim de semana.
(The office does not open during the weekend.)

Final de semana

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This variation is extremely common in spoken Brazilian Portuguese. While it has the exact same meaning, it is rare in European Portuguese. Here, final functions as a noun synonymous with "end".
O que você vai fazer no final de semana?
(What are you going to do on the weekend?)
Nós vamos ao cinema no final de semana.
(We are going to the movies on the weekend.)
O parque fica cheio todo final de semana.
(The park gets full every weekend.)
Estou ansioso para o próximo final de semana.
(I am looking forward to the next weekend.)

Summary

Both terms are correct and understood universally. Fim de semana is the standard usage in Portugal and formal contexts, while final de semana is a very popular alternative in everyday conversation within Brazil.