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I want to say the speed reduces by half. Do I say "it is slowed down by half" or "it is slowed down by twice"?
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How about, "It becomes half as much as before"?
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« "it is slowed down by half" or "it is slowed down by twice"»
Neither is correct. To keep as close to them as possible, I'd suggest:

1. «It (is) slowed down [or decreased] twice»

Another way:
«It is now half the speed I had before.»

Ruslana's sentence
«It becomes half as much as before» by dint of double negation can be converted to:
«It becomes twice_ as _low as before» — a funnier way to express the thought.

Or just:
«It became twice lower» and, analogously,
«It became half higher/faster»
AnonymousI want to say the speed reduces by half. Do I say "it is slowed down by half" or "it is slowed down by twice"?

down by half is a fine expression

the problem is slow down

it is reduced by half is OK

the speed is reduced by half is fine as well

slow [down] by is rarely used the way you need it here. Usually it is

We were slowed down by the bad weather.

Almost always when for example slowed by 20% is used, it is better reduced by 20% or decreased by 20%

They slow down the speed by half is fine as well

So it is your combination passiv of (slow down) + by half that is not ok.