2/3 = две третьих or две трети
The numerator of a fraction is always a cardinal number and the denominator is an ordinal number in Genitive (singular if the numerator ends in "одна" and plural if that's not the case). Always use feminine when the form exposes gender.
For quarters and thirds you can also use "одна треть" and "две четверти". Russian has words "треть" and "четверть" which mean "a third" and "a quarter" respectively. Won't work for other numbers, though—there are no such words.
Examples of other fractions:
- 5/3 = пять третьих
- 4/10 = четыре десятых
- 1/8 = одна восьмая
- 3/8 = три восьмых
- 5/9 = пять девятых
- 21/27 = двадцать одна двадцать седьмая
- 49/1000 = сорок девять тысячных
- 22/232 = двадцать две двести тридцать вторых
Note that ordinal "третий"(3rd) has a slightly deviant ending patter with "ь", typical of animal-possessive adjectives (лисий, волчий, цыплячий, кошачий). That probably has much to do with the fact that other than animal-adjectives -сий/-тий are never encountered (at least, I could not find any such adkective) and -чий is pretty rare.
When reading mathematical expressions or if you actually mean the division of x by y with numbers (especially large), use "x поделить на y". Or just "x на y" where the context is explicit — for instance, if you are writing out the same fraction as you pronounce it, so your viewers know that you mean division and not multiplication.
For numbers (at least, small enough) you typically treat a fraction as a whole unit. When you read expressions, the latter method is the only way to go.
It may look like that:
- 581/1035 * (x + 1.2) → пятьсот восемьдесят один ... на тысячу тридцать пять... (и) умножить на икс плюс одна целая две десятых (when spelling the expression)
- (x²+2)/(x³ + 7x - 4) → икс квадрат плюс два (поделить) на икс куб плюс семь икс минус четыре.
Again, if you are writing a fraction for everyone to see or are just speaking to yourself, single "на" is enough. However, if a listener has no reason to assume it is division and not multiplication, it sounds ambiguous, and I would probably think of multiplication first.