turn down

turn somebody/something ↔ down phrasal verb
1. to turn the switch on a machine such as an oven, radio etc so that it produces less heat, sound etc OPP turn up:
Can you turn the TV down? I’m trying to work.
2. to refuse an offer, request, or invitation:
They offered her the job but she turned it down.
I’m not going to turn down an invitation to go to New York!
Josie’s already turned him down (=refused his offer of marriage).

Cambridge Advanced Learner's Dictionary

Cambridge Advanced Learner's Dictionary - 4th Edition

turn sth/sb down — phrasal verb with turn / tɜːn / / tɝːn / verb

B2 to refuse an offer or request:

He offered her a trip to Australia but she turned it/him down.

He turned down the job because it involved too much travelling.

Collins Advanced Learner’s English Dictionary

turn down

1) PHRASAL VERB If you turn down a person or their request or offer, you refuse their request or offer.
  [V n P] Before this I'd have smiled and turned her down...
  [V n P] I thanked him for the offer but turned it down...
  [V P n (not pron)] Would you turn down $7,000,000 to appear nude in a magazine?
  Syn:
  refuse
2) PHRASAL VERB When you turn down a radio, heater, or other piece of equipment, you reduce the amount of sound or heat being produced, by adjusting the controls.
  [V n P] He kept turning the central heating down...
  [V P n (not pron)] She could not bear the relentless music and turned down the volume.
  Ant:
  turn up
3) PHRASAL VERB If the rate or level of something turns down, it decreases. [BRIT, JOURNALISM]
  [V P] The divorce rate turned down in the 1950s.(in AM, use fall)