教授がみんなの勘定を払ってくれた。

professor; teaching; instruction

indicates sentence subject (occasionally object); indicates possessive (esp. in literary expressions); but; however; still; and

all; everyone; everybody; everything

indicates possessive; nominalizes verbs and adjectives; substitutes for "ga" in subordinate phrases; (at sentence-end, falling tone) indicates a confident conclusion; (at sentence-end) indicates emotional emphasis; (at sentence-end, rising tone) indicates question

calculation; computation; counting; reckoning; count; bill; check; account; payment (of a bill); settlement (of an account); consideration; allowance

indicates direct object of action; indicates subject of causative expression; indicates an area traversed; indicates time (period) over which action takes place; indicates point of departure or separation of action; indicates object of desire, like, hate, etc.

to pay (e.g. money, bill); to brush off; to wipe away; to clear away; to dust off; to cut off (e.g. branches); to drive away (e.g. one's competitors); to sell off (something unneeded); to dispose of; to pay (e.g. attention); to show (e.g. respect, concern); to make (e.g. effort, sacrifice); to expend; to exert; to move out (of one's own place); to vacate; to sweep (e.g. one's legs); to knock aside; to make a sweeping stroke (in Japanese calligraphy); to reset (an abacus)