PROPORTIONALLY SPEAKING!!

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

two equal fractions,

or, using a colon, a:b = c:d

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

That means, for the proportion,

a x d = b x c

EXAMPLE:

21 x 15 is equal to 7 x 45

We can also use cross products to find a missing term in a proportion.

Here's an example.
In a movie featuring a giant tiger, the tiger appeared to be 50 feet long. However, a model was used for the tiger that was really only 20 inches long. A 30-inch tall model cage was also used in the movie. How tall did the cage seem in the movie?

First, write the proportion, using a letter to stand for the missing term. In this case that would be the cage.

We find the cross products by multiplying 20 times x, and 50 times 30. Then divide to find x.

Remember: We are trying to get our unknown number, x, all by itself. Since x is multiplied by 20, we can use the "inverse" of multiplying, which is dividing, to get rid of the 20. We can divide both sides of the equation by the same number, without changing the meaning of the equation. When we divide both sides by 20, we find that the cage will appear to be 75 feet tall.

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These pages were made through TeacherTECH, the teacher professional development component of GirlTECH, which is sponsored by the Center for Excellence and Equity in Education (CEEE) with support from the National Science Foundation through EOT-PACI, RGK Foundation, the Verizon Foundation, Rice University, and HiPerSoft.