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It is hard for me to pronounce all the "R" in following words or sentences like

"Northern" or "eight dollar metro card"

Do native people usually pronounce all the "R"s? or skip some of them?

Plus, it is also hard for me to pronounce flap t or d after R

(I tend to use flab t or d because people understand me better with those, by the way. so please dont tell me to use flab t or d if you are not a native).

for example, in case of "Fort Lee", t seems almost unvoiced(?). Is it just For Lee or Fort lee with a gentle touch at the upper aveolar ridge? If the latter one is right, could you tell me how to do it smoothly without any stresses. Can I just slow lick(?) from the ridge to the back of the teeth? I hope you know what I mean. What about "Fordham"?

Thank you!
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There is /r/ dissimilation, a phenomenon observed in rhotic dialects.
Comments  
The "r" is not usually pronounced after "a,o,i" in most British varieties of pronunciation. Some American accents articulate the "r" sound, kind of by moving your jaw sideways a little.

"t" and "d" are often reduced or omitted in fluent speech if the sound before them is a consonant.
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In the States, most people promounce those R's - although not so much in the northeast, especially New England, where "northern" = "NAW-thun" and "dollar" = "DAWL-uh" and would call the NJ town "Fought Lee". I have horible trouble in Spanish with "dolares" as the plural of "dollar", but "dollars" sounds bad/wrong. So, I understand! Try practicing words like "northern" slowly , and build up speed with the shifts later.

"Fordham" (as in the University) is pronounced "for-dum", again if you need a slight pause between syllables, take one as though it were actually written For Dum.
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