Ratios and ProportionsSolve each equation1. 2.

3. 4.

15538 yy 171434 xx

8.0538.2 ww 175235 xx

4y321

3

5x

1w NUMBERS ALL

Ratios and Proportions

Ratios and Proportions

A ratio is a comparison of two numbers by division.

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

y

xyxyx :to

Ratios and Proportions

Ratios 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

2

4

1

2

Ratios and Proportions

Suppose 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.

4

8

1

2

Ratios and Proportions

An equation stating that two ratios are equal is called a proportion.

So we can state that is a proportion.4

8

2

4

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

49

40

8

6

5

not8

Ratios and Proportions

Another 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.

4

2

6

3

64

26

6

3

4

123

44

1243

1212

You are using the Multiplicative Property of Equality!!