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Ratios and Proportions
Knowing how to work with ratios and proportions is very handy in chemistry classes, especially when working with different units of measurement. Let's start with some dictionary definitions:
The relative size of two quantities expressed as the quotient of one divided by the other; the ratio of a to b is written as a:b or a/b.
So what are these things really? Consider the following situation.
In 1995, 78 women were enrolled in chemistry at a certain high school while 162 men were enrolled. What was the ratio of women to men? Men to women?
Let's answer the questions using the definition of ratio. Filling in what we know:
men : women is 162:78 or 162/78
We could have reduced the fractions (cancelling out a factor of 6) or used our calculators to get a decimal equivalent for these fractions using the divide key:
men : women is 162 ÷ 78 or 27 ÷ 13 or 2.07692308
By writing the answer in these ways we have lost information, namely the specific number of men and women. Be careful! When given a ratio such as 13:27, the fractions may have been reduced so the original quantities could have been larger. This brings us to the idea of proportion.
Ratios are said to be in proportion when their corresponding fractions are equal. What we really did above was notice that the fraction 78/162 was equal to the fraction 13/27 - because we could divide both numbers in the first ratio by six (6) to get the second ratio - so the ratios are equal as well, i.e.,
These two (2) equalities are examples of proportions (equal ratios); it is as simple as that. How are proportions used? Let's add another question to our problem:
In 1996 the number of men enrolled was 193 while the ratio of women to men enrolled in chemistry stayed the about same as in 1995. How many women were enrolled in chemistry in 1996?
To answer this, we build a proportion equating the ratio of women to men in the two (2)
These are easiest to solve when written in fraction form. Notice that we've used
x for the unknown number of women since
it is common in algebra to use
the letter x as the variable.
We can then use the
So the number of women enrolled in 1996 was 92.9259259??? Use your common sense! There are no fractions of women walking around, so we will report 93 (rounding 92.9259259 correctly). It is probably wise to say "There are about 93 women enrolled in chemistry in 1996" since we were told the proportions were about the same. The issue of when to round will come up in chemistry, too. Often the objects being counted will be atoms or atomic particles like protons, neutrons and electrons; only whole number answers make sense in this case. Sometimes, however, we're measuring amounts (such as masses) which can be fractional. Then you should use the rules for correct rounding and significant figures reviewed in Session 1.
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[Numbers and their Properties] [Numbers in Science] [Ratios and Proportions]
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