How to solve the proportion.

How to solve the proportion.

Proportion says that two ratio (or fractions) are equal.

Example:

1\3 is equal to 2/6

So 1-out-of-3 is equal to 2-out-of-6

The ratios are the same, so they are in proportion.

Example: Rope

A rope's length and weight are in proportion.

When 20m of rope weighs 1kg, then:

·         40m of that rope weighs 2kg

How to solve the proportion.

Proportion says that two ratio (or fractions) are equal.

Example:

1\3 is equal to 2/6

So 1-out-of-3 is equal to 2-out-of-6

The ratios are the same, so they are in proportion.

Example: Rope

A rope's length and weight are in proportion.

When 20m of rope weighs 1kg, then:

·         40m of that rope weighs 2kg

·         200m of that rope weighs 10kg

Sizes

When shapes are "in proportion" their relative sizes are the same.

Here we see that the ratios of head length to body length are the same in both drawings. So they are proportional. Making the head too long or short would look bad!

Working With Proportions

NOW, how do we use this?

Example: you want to draw the dog's head ... how long should it be?

Let us write the proportion with the help of the 10/20 ratio from above:

?/42 = 10/20

Using Proportions to Solve Percents

A percent is actually a ratio! Saying "25%" is actually saying "25 per 100":

25% = 25/100

We can use proportions to solve questions involving percents.

The trick is to put what we know into this form:

Part/Whole = Percen/t100

We can also use cross products to find a missing term in a proportion. Here's an example. 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?

First, write the proportion, using a letter to stand for the missing term. We find the cross products by multiplying 20 times x, and 50 times 30. Then divide to find x. Study this step closely, because this is a technique we will use often in algebra. We are trying to get our unknown number, x, on the left side of the equation, 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 building will appear to be 75 feet tall.

Note that we're using the inverse of multiplying by 20-that is, dividing by 20, to get x alone on one side.