Ratios,+Proportions,+and+Percents

=Ratios, Proportions, and Percents =  =Ratios=

To change a ratio into a decimal is a simple process. All you really have to do is divide the numerator by the denominator.

__Example #1__

math \frac{1}{4} math

1 is the numerator and 4 is the denominator. So we would do 1 divided by 4 which =.25

When two ratios are equal, then the cross products are equal.

That is, for the proportion, a:b = c:d, a * d = b * c

__Example #2__

math \frac{3}{5}=\frac{21}{35} math

3 * 35 = 105 5 * 21= 105

 =Proportions=

A proportion is a name we give to a statement that two ratios are equal. It can be written in two ways:

(1) Two equal fractions,

math \frac{a}{b}=\frac{c}{d} math

or, (2) Using a colon,

math a:b=c:d math

In problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. We can also use cross products to find a missing term in a proportion.

__Example #3__

In a horror movie featuring a giant beetle, the beetle appeared to be 50 feet long. However, a model was used for the beetle that was really only 20 inches long. A 30-inch tall model building was also used in the movie. How tall did the building seem in the movie?

math \frac{50}{x}=\frac{20}{30} math

 =Percents=

__Example #4__

How to change Fractions into Percents? Lets say your fraction is 28/40. So all you have to do is set it up like this:

math \frac{28}{40}=\frac{x}{100} math

Just cross multiply and you have your answer! So in simpler terms you could say the numerator (top number) multiplied by 100 divided by the denominator (bottom number) equals your percent. In this case you would do this:

28 *100 = 40 * N 2800 ÷ 40 = 70

So 28/40 equals 70%