Michael S. answered • 12d
Chemistry B.S. from Indiana University, A's in College Physics I & II
These are apothecaries' units, so use the apothecaries' equivalents:
1 yard = 36 inches
1 gallon = 128 fluid ounces, and 1 fluid ounce = 8 fluidrams
1 drachm (dram) = 60 grains
1 fluidram = 60 minims
The question asks for ratio and proportion, so set each one up as two equal ratios and cross-multiply.
a) 0.25 yards to inches
1 yd / 36 in = 0.25 yd / x in
x = 0.25 x 36 = 9 inches
b) 1.2 gallons to fluidrams
Chain it in two steps, or combine first. Combining: 128 fl oz x 8 fluidrams = 1024 fluidrams per gallon.
1 gal / 1024 fluidrams = 1.2 gal / x
x = 1.2 x 1024 = 1228.8 fluidrams
c) 160 grains to drachms
1 drachm / 60 grains = x drachms / 160 grains
x = 160 / 60 = 2.67 drachms (exactly 2 and 2/3)
d) 380 minims to fluidrams
1 fluidram / 60 minims = x fluidrams / 380 minims
x = 380 / 60 = 6.33 fluidrams (exactly 6 and 1/3)
Two things that make this system less painful
The 60s line up. A drachm is 60 grains by weight and a fluidram is 60 minims by volume. Once you notice that, parts (c) and (d) are the same arithmetic, and you only have to remember one number instead of two.
Sanity-check the direction every time. Going to a smaller unit means the number must get bigger: gallons into fluidrams gave 1228.8, which is far larger than 1.2, so that is right. Going to a larger unit means the number gets smaller: grains into drachms gave 2.67 from 160. If a conversion moves the wrong way, you set the proportion up upside down.
One warning worth carrying
"Dram" means two different things. The apothecaries' drachm used here is 60 grains, but the avoirdupois dram is only 27.34 grains - about 45% as large. Part (c) would come out 5.85 instead of 2.67 under the wrong one. Since this problem set mixes in minims and fluidrams, which are purely apothecaries' units, the apothecaries' drachm is the intended one. In pharmacy work, always check which system a source is using before trusting a dram.
