4-3 Identifying and Writing Proportions

Warm Up

Lesson Presentation

Problem of the Day

Lesson Quizzes

4-3 Identifying and Writing Proportions

Warm Up Find the unit rate. 1. 18 miles in 3 hours

2. 6 apples for $3.30

3. 3 cans for $0.87

4. 5 CD’s for $43

6 mi/h

$0.55 per apple

$0.29 per can $8.60 per CD

4-3 Identifying and Writing Proportions

Learn to find equivalent ratios and to identify proportions.

4-3 Identifying and Writing Proportions

Vocabulary

equivalent ratios proportion

4-3 Identifying and Writing Proportions

Students in Mr. Howell’s math class are measuring the width w and the length l of their faces. The ratio of l to w is 6 inches to 4 inches for Jean and 21 centimeters to 14 centimeters for Pat.

4-3 Identifying and Writing Proportions

6 4

21 14

These ratios can be written as the

fractions and . Since both simplify

to , they are equivalent. Equivalent

ratios are ratios that name the same comparison.

3 2

4-3 Identifying and Writing Proportions

An equation stating that two ratios are equivalent is called a proportion. The equation, or proportion, below states that the ratios and are equivalent. 6

4 21 14

6 4

= 21 14

Read the proportion by saying “six is to four

as twenty-one is to fourteen.”

Reading Math

6 4

= 21 14

4-3 Identifying and Writing Proportions

If two ratios are equivalent, they are said to be proportional to each other, or in proportion.

4-3 Identifying and Writing Proportions

Determine whether the ratios are proportional.

Additional Example 1A: Comparing Ratios in Simplest Forms

, 24 51

72 128

72 ÷ 8 128 ÷ 8

= 9 16

24 ÷ 3 51 ÷ 3 = 8

17 Simplify . 24

51

Simplify . 72 128

8 17 Since = , the ratios are not proportional. 9

16

4-3 Identifying and Writing Proportions

4-3 Identifying and Writing Proportions

Determine whether the ratios are proportional.

Additional Example 1B: Comparing Ratios in Simplest Forms

, 150 105

90 63

90 ÷ 9 63 ÷ 9

= 10 7

150 ÷ 15 105 ÷ 15 = 10

7 Simplify . 150

105

Simplify . 90 63

4-3 Identifying and Writing Proportions

Determine whether the ratios are proportional.

Check It Out: Example 1A

, 54 63

72 144

72 ÷ 72 144 ÷ 72

= 1 2

54 ÷ 9 63 ÷ 9 = 6

7 Simplify . 54

63

Simplify . 72 144

4-3 Identifying and Writing Proportions

Determine whether the ratios are proportional.

Check It Out: Example 1B

, 135 75

9 4

9 4

135 ÷ 15 75 ÷ 15 = 9

5 Simplify . 135

75

is already in simplest form. 9 4

4-3 Identifying and Writing Proportions

Directions for making 12 servings of rice call for 3 cups of rice and 6 cups of water. For 40 servings, the directions call for 10 cups of rice and 19 cups of water. Determine whether the ratios of rice to water are proportional for both servings of rice.

Additional Example 2: Comparing Ratios Using a Common Denominator

Write the ratios of rice to water for 12 servings and for 40 servings.

Ratio of rice to water, 12 servings: 3 6

Ratio of rice to water, 40 servings: 10 19

3 6

= 3 · 19 6 · 19

= 57 114

10 19

= 10 · 6 19 · 6

= 60 114

57 114

60 114

Write the ratio as a fraction.

Write the ratio as a fraction

Write the ratios with a common denominator, such as 114.

Since = , the two ratios are not proportional.

19 10 40 6 3 12

Cups of Water

Cups of Rice

Servings of Rice

4-3 Identifying and Writing Proportions

Use the data in the table to determine whether the ratios of beans to water are proportional for both servings of beans.

Check It Out: Example 2

Write the ratios of beans to water for 8 servings and for 35 servings.

Ratio of beans to water, 8 servings: 4 3

Ratio of beans to water, 35 servings: 13 9

4 3

= 4 · 9 3 · 9

= 36 27

13 9

= 13 · 3 9 · 3

= 39 27

36 27

39 27

Write the ratio as a fraction.

Write the ratio as a fraction

Write the ratios with a common denominator, such as 27.

9 13 35 3 4 8

Cups of Water Cups of Beans Servings of Beans

Since = , the two ratios are not proportional.