Ratios and ProportionsSolve each equation1. 2.

3. 4.

15538 yy 171434 xx

8.0538.2 ww 175235 xx

4y321

35

x

1w NUMBERS ALL

Ratios and Proportions

Ratios and ProportionsA ratio is a comparison of two numbers by division.

The ratio of x to y can be expressed in the following ways:

yxyxyx :to

Ratios and ProportionsRatios are often expressed in simplest form.

For example, the recipe stated that for 4 servings you need 2 cups of milk.

The ratio of serving to milk may be written as:

4 to 2 4 : 2 or

Written in simplest form, the ratio of servings to milk would be:

2 to 1 2 : 1 or

24

12

Ratios and ProportionsSuppose you wanted to double the recipe to have 8 servings.

The amount of milk required would be 4 cups.

The ratio of servings to milk is

When this ratio is simplified, the ratio is

Notice that this ratio is equal to the original ratio.

48

12

Ratios and ProportionsAn equation stating that two ratios are equal is called a proportion.

So we can state that is a proportion.48

24

Answer: The ratios are equal. Therefore, they form a proportion.

Determine whether the ratios and form a proportion.

Determine Whether Ratios Form a Proportion

Do the ratios and form a proportion?

Answer: The ratios are not equal. Therefore, they do not form a proportion.

Determine Whether Ratios Form a Proportion

4940

8

65

not8

Ratios and ProportionsAnother way to determine whether two ratios form a proportion is to use cross products.

If the cross products are equal, then the ratios form a proportion.

42

63

6426

63

4123

44

1243

1212

You are using the Multiplicative Property of Equality!!