Meaning
To make a fool of oneself / to commit a gaffe
Example
Acabei de dar uma rata daquelas na frente de todo mundo.
I just made a complete fool of myself in front of everyone.
Origin
The noun rata means a public blunder or gaffe. Standard reference dictionaries (Priberam, Infopédia) classify the etymology as uncertain — possibly related to ratão.
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More idioms
Acertar na moscaTo guess correctly / To hit the nail on the headAmigo da onçaA fake/false friendAndar na linhaTo toe the line / To behave properlyArmar um barracoTo cause a public sceneRodar a baianaTo cause a public scene / To go ballisticArrumar sarna pra se coçarTo ask for troubleArrastar as asasTo hit on someone / To flirtAbrir o jogoTo come clean / To open upArregaçar as mangasTo roll up one's sleeves / To get to workAgarrar com unhas e dentesTo hold on for dear life / To seize an opportunity