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

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?

• You must focus on the little word "by" to tell you what to do. First you calculate 1/3 as you expected, Subtract that amount from 600, to "reduce its volume by" 200. Then figure the pressure you need to produce 400. Nov 22, 2020 at 14:29
• ...and "reduce into 1/3" would be to a volume of 200 (much greater pressure). Nov 22, 2020 at 14:31
• To reduce a volume by 1/3 is to end up with a volume 2/3 of the original, to reduce a volume to 1/3 means to reduce by 2/3 leaving a volume of 1/3. In more mathematecal language if V is the original volume then reducing V by y/x is to end up with a volume of V-yV/x. I'm actualy more confused by the term "reduce into 1/3" which mixes two mathematical terms to me. Nov 22, 2020 at 14:31
• Similarly, when you buy something at a 10% discount, you end up paying 90% of the original price by subtracting. You do not buy it for 10% of the original price. Nov 22, 2020 at 15:10
• @Anton I don't think OP or anyone else has suggested that it means either 1/3 ml or 599.666 ml. In fact OP asks if the 1/3 of 600 ml is to be taken off, or is the result. Nov 22, 2020 at 17:22

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.