I think in order to do much of anything with this, we will have to make some assumptions about what is meant.
SCENARIO A Let's assume each jar literally has 96 screws inside it; the screws "being used" are outside each jar; the fractions being used are fractions of each total inside and outside the jar; and the fraction of total screws not being used is the fraction of all screws inside and outside the jars. In that case: Jar 1 has 96 inside and 32 outside in use. Jar 2 has 96 inside and 57.6 screws outside in use -- No, that cannot be right.
SCENARIO B The only other scenario I can think of currently that might be intended would be four groups of 96 screws: where one group has 1/4 in use; another group has 5/8 in use; another group has 3/4 in use; and the remaining group has 1/2 in use.
The fastest way to solve this is to recognize that if each group has 96 screws then the 1/4, 5/8, 3/4, 1/2 are proportionate and the number of screws is irrelevant (as long as all the fractions are whole numbers of screws). Add up the fractions; divide by 4; and then subtract the result from 1. (1/4)+(5/8)+(3/4)+(1/2) = 17/8 ; 17/8 divided by 4 = 17/32 ; 1-(17/32) = 15/32.
===== I think the intended answer is 15/32.
EDIT -- actually, an even faster way to solve this would be to recognize that since the fractional parts are all proportionate and since they would average to 1/2 if the 5/8 were 1/2 instead -- the extra 1/8 divided by 4 is 1/32, and then since it's how many are not being used subtract the 1/32 from a 1/2 instead of adding it. That's 15/32. But that requires a high degree of confidence in one's logic to do that without using another method to check the result.
I can't find my calculator, and I did the following quickly so I might have made a mistake. But I think 15/32 = 0.46875 (.46875 if no leading zero prior to the decimal point). If that was the decimal, then the decimal was probably the intended answer.
(Of course, the whole thing could have been messed up for all I know.)
Sure, but the problem seems to say the answer is supposed to be fraction of the total. That's why I thought divide by 4. So using your numbers, 2 1/8 used and 1 7/8 left -- divide both parts by 4 -- 17/32 of the total used and 15/32 of the total left.
You guys are looking at this all wrong. 1/4, 1/2, 3/4, and 5/8 are all standard screw sizes. Subtract these sizes from the totality of screw sizes available in the world, and you are left with the percentage of screws not being used. I would assume that this includes both standard and metric sizes.
The four jars are different sizes. The fractions given are the fraction of the volume of the jar that is being used up by the 96 screws and is thus fairly extraneous to the solution of the problem. The answer is that 1/1 of the screws are not being used since they are all in jars (either a screw is in a jar or it is being used, not both).
But the question part of the question is "...what is the fraction of total screws not being used?". The fraction of the total would be the fraction of all four jars, not the fraction of one jar. 15/8 divided by 4 = 15/32 which is the answer the OP, myself, and a few other people came up with.
SCENARIO A Let's assume each jar literally has 96 screws inside it; the screws "being used" are outside each jar; the fractions being used are fractions of each total inside and outside the jar; and the fraction of total screws not being used is the fraction of all screws inside and outside the jars. In that case: Jar 1 has 96 inside and 32 outside in use. Jar 2 has 96 inside and 57.6 screws outside in use -- sure, what the hell. Jar 3 has 96 inside and 288 screws outside in use. Jar 4 has 96 inside and 96 outside in use.
384 screws in the jars not being used; 857.6 total screws (or maybe 858 total screws).
384/858 = 64/143 = just under 0.448 384/857.6 = 30/67 = just under 0.448
Were any of -- 384/858 384/857.6 3840/8576 64/143 30/67 0.448 .448 0.447 something .447 something -- among the choices?