What’s the diﬀerence between “to reduce ʙʏ one-third” and “to reduce ɪɴᴛᴏ one-third”?

Question

A sam­ple of fluo­rine gas oc­cu­pies a vol­ume of 600 mL at 760 torr.
Given that the tem­per­a­ture re­mains the same, cal­cu­late
the pres­sure re­quired to re­duce its vol­ume by one-third.

I don't need an an­swer. I just want to know what op­er­a­tion the
ques­tion is re­fer­ring to.
What con­fuses me is the part at the end of the ques­tion: does re­duce its
vol­ume by one-third re­fer to re­duc­ing the vol­ume by one-third? Like you
sub­tract one-third of 600 into 600?
Or does it re­fer to re­duc­ing the vol­ume of 600 into one-third
meaning that 600 should be di­vided by three?

Anton · Answer

by is a very versatile preposition. Most comments so far could easily have been made into answers, so I claim no greater authority in setting out this understanding:

by: Preposition
If something increases or decreases by a particular amount, that amount is gained or lost.
"Violent crime has increased by 10 percent since last year."
"Their pay has been cut by one-third."
Collins dictionary

A reduction by one third is a decrease of one third: so 600 ml is to be decreased by 600/3 ml (= 200 ml) to a final volume of 400 ml.
As commented by others, a reduction into one third would be a reduction to 600/3 ml (= 200 ml).
I draw your attention to the careful exclusion of ambiguity by the formulation of the question. The volume is expressed in units of ml. The reduction is expressed only as a number (1/3); it has no units. There is therefore no reason to interpret the question as meaning a reduction of 600 ml by 1/3 ml to 599.666... ml. Nor may we imagine that the 600 ml is to be compressed to 1/3 ml.

What’s the diﬀerence between “to reduce ʙʏ one-third” and “to reduce ɪɴᴛᴏ one-third”?

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What’s the diﬀer­ence be­tween “to re­duce ʙʏ one-third” and “to re­duce ɪɴᴛᴏ one-third”?

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