1. Holt CA Course 1 5-3 Identifying and Writing Proportions Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

2. Holt CA Course 1 5-3 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 CDs for $43 6 mi/h $0.55 per apple $0.29 per can $8.60 per CD

3. Holt CA Course 1 5-3 Identifying and Writing Proportions NS1.2 Interpret and use ratios in different contexts (e.g., batting averages, miles per hour) to show the relative sizes of two quantities, using appropriate notations (, a to b, a:b). California Standards abab

4. Holt CA Course 1 5-3 Identifying and Writing Proportions Students are measuring the width w and the length l of their heads. The ratio of l to w is 10 inches to 6 inches for Jean and 25 centimeters to 15 centimeters for Pat.

5. Holt CA Course 1 5-3 Identifying and Writing Proportions 10 6 25 15 These ratios can be written as the fractions and. Since both ratios simplify to, they are equivalent. Equivalent ratios are ratios that name the same comparison. 5353

6. Holt CA Course 1 5-3 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. 10 6 25 15 10 6 = 25 15 If two ratios are equivalent, they are said to be proportional to each other, or in proportion. Reading Math

7. Holt CA Course 1 5-3 Identifying and Writing Proportions Determine whether the ratios are proportional. Teacher Example 1: 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

8. Holt CA Course 1 5-3 Identifying and Writing Proportions Determine whether the ratios are proportional. Student Practice 1:, 54 63 72 144 72 ÷ 72 144 ÷ 72 = 1 2 54 ÷ 9 63 ÷ 9 = 6767 Simplify. 54 63 Simplify. 72 144 6767 Since =, the ratios are not proportional. 1212

9. Holt CA Course 1 5-3 Identifying and Writing Proportions Determine whether the ratios are proportional. Teacher Example 2: 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 10 7 Since =, the ratios are proportional. 10 7

10. Holt CA Course 1 5-3 Identifying and Writing Proportions Determine whether the ratios are proportional. Student Practice 2:, 135 75 9494 9 4 135 ÷ 15 75 ÷ 15 = 9 5 Simplify. 135 75 is already in simplest form. 9 4 9595 Since =, the ratios are not proportional. 9494

11. Holt CA Course 1 5-3 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. Teacher Example 3: 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: 3636 Ratio of rice to water, 40 servings: 10 19 3636 = 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 ratios with a common denominator, such as 114. Since =, the two ratios are not proportional. Servings of Rice Cups of Rice Cups of Water 1236 401019

12. Holt CA Course 1 5-3 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. Student Practice 3: Write the ratios of beans to water for 8 servings and for 35 servings. Ratio of beans to water, 8 servings: 4343 Ratio of beans to water, 35 servings: 13 9 4343 = 4 · 3 3 · 3 = 12 9 13 9 12 9 13 9 Write the ratio as a fraction. Write the ratios with a common denominator, such as 9. Servings of BeansCups of BeansCups of Water 843 35139 Since =, the two ratios are not proportional.

13. Holt CA Course 1 5-3 Identifying and Writing Proportions You can find an equivalent ratio by multiplying or dividing the numerator and the denominator of a ratio by the same number.

14. Holt CA Course 1 5-3 Identifying and Writing Proportions Teacher Example 4: Finding Equivalent Ratios and Writing Proportions Find a ratio equivalent to each ratio. Then use the ratios to find a proportion. A. 3535 3535 = 3 · 2 5 · 2 6 10 = Multiply both the numerator and denominator by any number, such as 2. 3535 = 6 10 Write a proportion. B. 28 16 28 16 = 28 ÷ 4 16 ÷ 4 28 16 = 7474 = 7474 Divide both the numerator and denominator by any number, such as 4. Write a proportion.

15. Holt CA Course 1 5-3 Identifying and Writing Proportions Student Practice 4: Find a ratio equivalent to each ratio. Then use the ratios to find a proportion. Possible Answers: A. 2323 2323 = 2 · 3 3 · 3 6969 = Multiply both the numerator and denominator by any number, such as 3. 2323 = 6969 Write a proportion. B. 16 12 16 12 = 16 ÷ 4 12 ÷ 4 16 12 = 4343 = 4343 Divide both the numerator and denominator by any number, such as 4. Write a proportion.