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How do we say if I had already switched on the fan, I want to "turn up" the number from 1 to 4 ?

Dialogue

A: Today is very hot, please turn up the speed of the fan. / please turn the number 4.

B: Ok, I will.

How do we say If I want to lower down the speed of the fan? from 4 to 1?

Dialogue

A: Today is cold, please turn down to number 1 for the fan.

B: Yes.

==

Do we say,

(a) Please lower down the fan. It's cool.
(b) Please speed up the fan,it's quite hot.

Thanks!!
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It's much easier...

Please turn up the fan (to number 3).

Please turn down the fan (to number 1).

Speed is implied, so we don't need to say it. The only confusion possible is if someone wants to change the angle of the fan: then we usually say "Please angle the fan down/up/to the left."

Also, don't use "Today is cold." You should say "It is cold today."
Comments  
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Thanks, but do we say:

(i) Turn up the fan / Turn the fan up / Turn it up to make it on a higher number.

(ii) Turn down the fan / Turn the fan down / Turn it down to make it on a lower number.

(i) yes/yes/no...turn it up to a higher number (higher speed sounds better, but is not necessary).

(ii) yes/yes/no...turn it down to a lower number (lower speed sounds better...).

Could anyone tell me whether it would be grammatically correct if I say,

"Please turn down or lower (or turn up) the speed of the fan."

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If i want to permission to someone for turn down the speed of the fan.what i will say?

1) Do you think I can turn down the fan?

2) Do you mind if I turn down the fan?

3) Can I turn down the fan?