Letter R is the only letter in Serbian alphabet which might be both - a vowel and a consonant. Normally it's a consonant. But when there is no other vowel in a group of consonants, R takes over that role.
There are some facts and tricks which might be helpful for improving our pronunciation of Serbian letter R.
1)R in Serbian is a vibrant sound (Spanish Oscar, Serbian
Oscarrrr). When you pronounce it properly, you should feel the vibration on the surface of your tongue.
2)The position of speech organs should be this: the top of the tongue is above the upper teeth, slightly touching it or not touching it at all.
3)Words for practicing R in clusters PR and TR: PRVI, PRAVI, PROMET, PRIČA, PREDMET, TRAVA, VATRA, TRAJATI, TRAŽITI.
4) Words for practicing R when R has a role of a vowel: SRBIJA, PRTLJAŽNIK, PRŽITI, CRKVA, KRST, TRG, CRVENO.
5)This is a good trick to check if you are doing it properly: put your hand in front of the mouth; say R several times; if you feel your breath on your
palm, the pronunciation is good. Try this as many times as needed, until you clearly feel your breath.
6)Sing in house RRRRRRRRR, SIRRRRRR, PRRRRRAVI… Maybe you may make up your personal song with words that contain R.
Enjoy in learning Serbian (that is the most important) !