Holt CA Course Identifying and Writing Proportions Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

Holt CA Course Identifying and Writing Proportions Warm Up Find the unit rate miles in 3 hours 2. 6 apples for $ cans for $ CDs for $43 6 mi/h $0.55 per apple $0.29 per can $8.60 per CD

Holt CA Course 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

Holt CA Course 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.

Holt CA Course Identifying and Writing Proportions 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

Holt CA Course 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 = If two ratios are equivalent, they are said to be proportional to each other, or in proportion. Reading Math

Holt CA Course Identifying and Writing Proportions Determine whether the ratios are proportional. Teacher Example 1: Comparing Ratios in Simplest Forms, ÷ ÷ 8 = ÷ 3 51 ÷ 3 = 8 17 Simplify Simplify Since =, the ratios are not proportional. 9 16

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

Holt CA Course Identifying and Writing Proportions Determine whether the ratios are proportional. Teacher Example 2: Comparing Ratios in Simplest Forms, ÷ 9 63 ÷ 9 = ÷ ÷ 15 = 10 7 Simplify Simplify Since =, the ratios are proportional. 10 7

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

Holt CA Course 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: = 3 · 19 6 · 19 = = 10 · 6 19 · 6 = 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

Holt CA Course 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: = 4 · 3 3 · 3 = Write the ratio as a fraction. Write the ratios with a common denominator, such as 9. Servings of BeansCups of BeansCups of Water Since =, the two ratios are not proportional.

Holt CA Course 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.

Holt CA Course 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 = 3 · 2 5 · = Multiply both the numerator and denominator by any number, such as = 6 10 Write a proportion. B = 28 ÷ 4 16 ÷ = 7474 = 7474 Divide both the numerator and denominator by any number, such as 4. Write a proportion.

Holt CA Course 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 = 2 · 3 3 · = Multiply both the numerator and denominator by any number, such as = 6969 Write a proportion. B = 16 ÷ 4 12 ÷ = 4343 = 4343 Divide both the numerator and denominator by any number, such as 4. Write a proportion.