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Solving Proportions: Examples (page 5 of 7) Sections: Ratios, Proportions, Checking proportionality, Solving proportions
Rain gutters have to be slightly sloped so the rainwater will drain toward and then down the downspout. As I go from the high end of the guttering to the low end, for every fourfoot length that I go sideways, the gutters should decline [be lower by] onequarter inch. So how much must the guttering decline over the thirtyseven foot span? I'll set up the proportion.
For convenience sake (because my tape measure isn't marked in decimals), I'll convert this answer to fractional form: Copyright © Elizabeth Stapel 20012011 All Rights Reserved The lower end should be 2 ^{5}/_{16} inches lower than the high end. As is always the case with "solving" exercises, you can check your answer by plugging it back into the original problem. In this case, you can verify the size of the "drop" from one end of the house to the other by checking the means and the extremes. Converting the "onefourth" to "0.25", we get: (0.25)(37)
= 9.25
Since the values match, then the proportionality must have been solved correctly, and the solution must be right.
As far as I know, this is a technique that biologists and park managers actually use. The idea is that, after allowing the tagged fish to circulate, they are evenly mixed in with the total population. When the researchers catch some fish later, the ratio of tagged fish in the sample is representative of the ratio of the 96 fish that they tagged with the total population. I'll use " f
" to stand
for the total number of fish in the lake, and set up my ratios with
the numbers of "tagged" fish on top. Then I'll set up and
solve the proportion: f
× 4 = 72 × 96 There are about 1728 fish in the lake. A related type of problem is unit conversion, which looks like this:
For this, I will need conversion factors, which are just ratios. If you're doing this kind of problem, then you should have access (in your text or a handout, for instance) to basic conversion factors. If not, then your instructor is probably expecting that you have these factors memorized. I'll set everything up in a long multiplication so that the units cancel: Then the answer is 88 feet per second. Note how I set up the conversion factors in notnecessarilystandard ways. For instance, one usually says "sixty minutes in an hour", not "one hour in sixty minutes". So why did I enter the hourminute conversion factor (in the second line of my computations above) as "one hour per sixty minutes"? Because doing so lined up the fractions so that the unit "hour" would cancel off with the "hours" in "60 miles per hour". This cancellingunits thing is an important technique, and you should review it further if you are not comfortable with it. << Previous Top  1  2  3  4  5  6  7  Return to Index Next >>



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