Things Proportional

J /roportions are nothing more than two ratios or fractions set equal to V one another. Proportions have several very handy properties that make working with them much easier to manage. In this chapter, you see how to set up the proportions correctly and how to solve the problems you ve created with the proportions. You see how to apply the properties of proportions to make the solutions easier. 

A proportion is an equation involving two fractions. The ratio of the numerators and denominators of the fractions must be equal. A proportion is a statement saying that two fractions are equivalent or equal in value. The fractions can be reduced in the normal way — the way you ve see since third grade — and they can be reduced in some rather unique ways, too. You use this prop-erty and several others to solve for unknown parts of a proportion. 

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Modern medicine offers many wonderful options to reduce pain and suffering. The amount of the medication for a particular person has to be correct, though. The amount of medicine prescribed may depend on a person s weight, age, or current health status — or, often, a mixture of all these things. Proportions are used to determine dosages of many medications and the number of tablets needed per dose. 

If there is no band overlap in a spectrum, the absorbance at a characteristic wavelength is proportional to the concentration of chromophores present. This is the basis of quantitative analysis using spectra. With band overlap, things are more complicated but still possible. 

Equation 1-4 (Beer s Law) deals only with the absorbed and the transmitted beam in particular, it is not concerned with the history of a quantum subsequent to absorption. Because the number of quanta disappearing from the incident beam by whatever process is proportional, other things equal, to the number of quanta present, we may group under absorption all the processes that reduce this number of quanta. This procedure is convenient, though not strictly rigorous. The trans-... 

That Bar, at 116 Smith Street in Brooklyn, serves a perfectly proportioned stinger with a green-dyed-sugar rim and a mint chocolate, which reminds me of one of the few things that I ve learned in life only beautiful people can get away with ugly clothes. 

Several things are immediately obvious the problem is much worse at the edge of the parabola than near the center and gets worse as pIRvertex ) Since p/Rvertex) is proportional to the // of the primary, the difficulty as the primary gets faster is clear. Of course, this must be traded off with the cost of the dome and other lesser issues that depend on the // of the primary. 

They get up and go over to the workbench, and I wonder if Mark can see in Gareth what I can so clearly that he still touches paper as if he loves it, handles the machines like a patient groom or shepherd, judges space and proportion and form as naturally as breathing, his eyes sharp even as he shows Mark things he s already looked at himself for hours each day. How can he give it up ... 

Furthermore, the price elasticities of demand for pharmaceuticals are likely to differ depending on individuals income. If low-income households have a more price-elastic demand, an increase in co-payment will cause them to make a proportionally larger reduction in their pharmaceutical consumption than high-income households. The same thing could happen if we make the comparison in terms of levels of health. We are faced with equity problems, to which we will return below. 

The crops and livestock look after themselves. Nature has never found it necessary to design the equivalent of the spraying machine and the poison spray for the control of insect and fungus pests. There is nothing in the nature of vaccines and serums for the protection of the livestock. It is true that all kinds of diseases are to be found here and there among the plants and animals of the forest, but these never assume large proportions. The principle followed is that the plants and animals can very well protect themselves even when such things as parasites are to be found in their midst. Nature s rule in these matters is to live and let live (Howard, 1943). 

Ratios are numbers that are used to compare things. Ratios play an important role in mathematics because they quantify all of the items that we compare on a day-to-day basis. Ratio and proportion are evident in numerous mathematical problems. Before you begin learning about ratios and proportions, take a few minutes to take this ten-question Benchmark Quiz. These questions are similar to the type of questions that you will find on important tests. When you are finished, check the answer key carefully to assess your results. Your Benchmark Quiz analysis will help you determine how much time you need to spend on ratios and proportions, and the specific areas in which you need the most careful review and practice. 

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