Proportions
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Proportions: |
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A proportion is simply a statement that two ratios are equal. It can be written in two ways: as two
equal fractions a/b = c/d; or using a colon, a:b = c:d.
The following proportion is read as "twenty is
to twenty-five as four is to five."
In problems involving proportions, we can use cross products to test whether two ratios are equal
and form a proportion. To find the cross products of a proportion, we multiply the outer terms,
called the extremes, and the middle terms, called the means.
Here, 20 and 5 are the extremes, and 25 and 4
are the means. Since the cross products are both
equal to one hundred, we know that these ratios are equal and that this is a true proportion.
Example: A dog walks 8 km at 4 km per hour, then chases a rabbit for 2 km at 20 km per hour.
What is the dog's average rate of speed for the distance he traveled?
Solution: The total distance traveled is 8 + 2 = 10 km.
Now we must figure the total time he was traveling.
For the first part of the trip, he walked for 8 ÷ 4 = 2 hours.
He chased the rabbit for 2 ÷ 20 = 0.1 hour.
The total time for the trip is 2 + 0.1 = 2.1 hours.
The average rate of speed for his trip is 10/2.1 = 100/21 kilometers per hour.
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