I'm sure I mentioned this once, but I couldn't locate the message, so I thought it might be interesting to give the topic certain focus, since it seems beginners' books never mention this.
Parts of the following quotes were in romanised Japanese, but I've added kana / kanji myself.
[…] You can move all and both in English like this:
1. All students are healthy.
2. Students are all healthy.
You can move any quantifiers in Japanese, and they have different meanings when they are put before a noun and put before a predicate.
3. 猫が二匹いる。 [Neko ga ni-hiki iru.] (There are two cats.)
4. 二匹の猫がいる。 [Ni-hiki no neko ga iru.] (The two cats are there.)
A floating quantifier means the noun is indefinite. If the noun is definite, quantifier float is not common. Sentence 4 can be used for "two cats", but sentence 3 cannot be used for "the two cats".
You have to use quantifier float if the noun is indefinite and the number is a focus.
5. 五十円切手を三枚ください。 [Go-jû-en kitte o san-mai kudasai.] (Please give me three 50-yen stamps.)
6. *三枚の五十円切手をください。 [San-mai no go-jû-en kitte o kudasai.] (wrong)
Sentence 6 is wrong when you buy stamps in a post office. You can say:
7. その三枚の五十円切手をください。 [Sono san-mai no go-jû-en kitte o kudasai.] (Please give me the three 50-yen stamps.)
if you want three stamps someone has.
8. アジアの言語をもう一つ学ぶ。 [Ajia no gengo o mô hitotsu manabu.] (I learn another Asian language.)
9. もう一つのアジアの言語を学ぶ。 [Mô hitotsu no ajia no gengo o manabu.] (I learn the other Asian language.)
[…] Sentence 9 is all right if you think Japanese and Chinese are the two major Asian languages and you learn both of them.
You can use quantifier float for the object of a transitive verb and the subject of an intransitive verb.
侍七人 [samurai shichi-nin] is quite different from 七人の侍 [shichi-nin no samurai], because it is understood that the latter focuses on the particular group of seven samurai like implicitly saying その七人の侍 [sono shichi-nin no samurai] and no other, while the former means just any seven samurai.