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In a sentence
to give out
Dobrovoľníci rozdávajú ľuďom teplé jedlo.
Volunteers are handing out hot food to people.
to distribute
Po koncerte rozdávali autogramy fanúšikom.
After the concert they handed out autographs to fans.
Other
Na námestí rozdávajú letáky o festivale.
In the square they are handing out leaflets about the festival.
Každú zimu rozdáva teplé čiapky bezdomovcom.
Every winter she distributes warm hats to the homeless.
Source
Slovak National Corpus (SNK) ↗English gloss from the frequency publish path. Hand-reviewed example sentences.
Full attribution on References.