I need some help. So, I have been doing some work with fractions, and this came up: 3/21. I have no idea how to pronounce the 21 part. Is it twenty-oneth or..? I have no clue, so can someone give me the correct pronunciation?
How you say it depends on the context.
If it comes up in a discussion of mathematics you would say "three over twenty-one". Since you asked while you're thinking about fractions that's the answer.
In everyday speech, that or "three twenty-firsts" would do. (I wonder where it might come up in everyday speech.)
Of course 3/21 = 1/7, so "one seventh" might work too.
When you get to algebra and want to talk about (ax+b)/(cx+d) you have no other way than to say "a x plus b over c x + d".
In mathematics, the numerator is always pronounced as a cardinal number and the denominator is always pronounced as an ordinal number. This answer may be helpful for further clarification.
So the pronunciation should be "three twenty-firsts." In common speech, though, you could say, "Three out of twenty-one," or something similar. You will even hear from some people, "Three on twenty-one," or "Three by twenty-one."
If it's a date rather than a fraction, a US speaker would likely say "three twenty-one" when the context was clear, or "March 21st" if the context were not unambiguously a date. In American English (the military being a notable exception) the standard numeric format for dates is typically
dd/mm/yyyy. Absent other cues, I'd assume 3/21 is a date and say it that way.
Other answers have addressed fractions, so I can add little there, but "three twenty-firsts" or "3 out of 21" would not be uncommon ways to express this conversationally. However, this is simply unlikely to come up often in casual conversation as the number of items that come in packs of 21 is...well, I can't even think of one offhand.
In conversation, I'd usually expect to hear "I'll have three of those [uncounted items]" or (assuming it's a cake or pizza in 21 slices) "I'll take three slices, please!" without reference to what fraction of the whole that represents. Numeric precision isn't generally required in casual contexts, but your situation may differ.