5-2 Identifying and Writing Proportions Warm Up Problem of the Day Course 2 Warm Up Problem of the Day Lesson Presentation

Identifying and Writing Proportions Course 2 5-2 Identifying and Writing Proportions Warm Up Write each fraction in simplest terms. 6 18 1 3 9 21 3 7 1. 2. 20 25 4 5 21 36 7 12 3. 4. 12 18 2 3 5.

Identifying and Writing Proportions Course 2 5-2 Identifying and Writing Proportions Problem of the Day Bob made a square table top with 100 white square tiles. He painted the tiles along the edge of the table red. How many tiles are red? 36

Identifying and Writing Proportions Course 2 5-2 Identifying and Writing Proportions Learn to find equivalent ratios and to identify proportions.

Vocabulary 5-2 Identifying and Writing Proportions equivalent ratios Course 2 5-2 Identifying and Writing Proportions Vocabulary equivalent ratios proportion

Identifying and Writing Proportions Course 2 5-2 Identifying and Writing Proportions Students in Mr. Howell’s math class 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.

Identifying and Writing Proportions Course 2 5-2 Identifying and Writing Proportions 10 6 25 15 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. 5 3

Identifying and Writing Proportions Course 2 5-2 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 = Read the proportion by saying “ten is to six as twenty-five is to fifteen.” Reading Math 10 6 = 25 15

Identifying and Writing Proportions Course 2 5-2 Identifying and Writing Proportions If two ratios are equivalent, they are said to be proportional to each other, or in proportion.

Additional Example 1A: Comparing Ratios in Simplest Forms Course 2 5-2 Identifying and Writing Proportions Additional Example 1A: Comparing Ratios in Simplest Forms Determine whether the ratios are proportional. A. , 24 51 72 128 Simplify . 24 51 24 ÷ 3 51 ÷ 3 = 8 17 72 ÷ 8 128 ÷ 8 = 9 16 Simplify . 72 128 8 17 Since = , the ratios are not proportional. 9 16

Additional Example 1B: Comparing Ratios in Simplest Forms Course 2 5-2 Identifying and Writing Proportions Additional Example 1B: Comparing Ratios in Simplest Forms Determine whether the ratios are proportional. B. , 150 105 90 63 Simplify . 150 105 150 ÷ 15 105 ÷ 15 = 10 7 90 ÷ 9 63 ÷ 9 = 10 7 Simplify . 90 63 10 7 Since = , the ratios are proportional.

Identifying and Writing Proportions Course 2 5-2 Identifying and Writing Proportions Try This: Example 1A Determine whether the ratios are proportional. A. , 54 63 72 144 Simplify . 54 63 54 ÷ 9 63 ÷ 9 = 6 7 72 ÷ 72 144 ÷ 72 = 1 2 Simplify . 72 144 6 7 Since = , the ratios are not proportional. 1 2

Identifying and Writing Proportions Course 2 5-2 Identifying and Writing Proportions Try This: Example 1B Determine whether the ratios are proportional. B. , 135 75 81 45 Simplify . 135 75 135 ÷ 15 75 ÷ 15 = 9 5 81 ÷ 9 45 ÷ 9 = 9 5 Simplify . 81 45 9 5 Since = , the ratios are proportional.

Additional Example 2: Comparing Ratios Using a Common Denominator Course 2 5-2 Identifying and Writing Proportions Additional Example 2: Comparing Ratios Using a Common Denominator Use the data in the table to determine whether the ratios of rice to water are proportional for both servings of rice. Servings of Rice Cups of Rice Cups of Water 12 3 6 40 10 19 Write the ratios of rice to water for 12 servings and for 40 servings. 3 6 Ratio of rice to water, 12 servings: Write the ratio as a fraction. 10 19 Ratio of rice to water, 40 servings: Write the ratio as a fraction 3 6 3 · 19 6 · 19 57 114 = = Write the ratios with a common denominator, such as 114. 10 19 10 · 6 19 · 6 60 114 = = 57 114 60 114 Since = , the two ratios are not proportional.

Identifying and Writing Proportions Course 2 5-2 Identifying and Writing Proportions Try This: Example 2 Use the data in the table to determine whether the ratios of beans to water are proportional for both servings of beans. Servings of Beans Cups of Beans Cups of Water 8 4 3 35 13 9 Write the ratios of beans to water for 8 servings and for 35 servings. 4 3 Ratio of beans to water, 8 servings: Write the ratio as a fraction. 13 9 Ratio of beans to water, 35 servings: Write the ratio as a fraction 4 3 4 · 9 3 · 9 36 27 = = Write the ratios with a common denominator, such as 27. 13 9 13 · 3 9 · 3 39 27 = = 36 27 39 27 Since = , the two ratios are not proportional.

Identifying and Writing Proportions Course 2 5-2 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.

Insert Lesson Title Here Course 2 5-2 Identifying and Writing Proportions Insert Lesson Title Here Additional Example 3: Finding Equivalent Ratios and Writing Proportions Find a ratio equivalent to each ratio. Then use the ratios to find a proportion. 3 5 A. 3 5 3 · 2 5 · 2 6 10 = = Multiply both the numerator and denominator by any number such as 2. 3 5 6 10 = Write a proportion. B. 28 16 28 16 28 ÷ 4 16 ÷ 4 Divide both the numerator and denominator by any number such as 4. 7 4 = = 28 16 7 4 = Write a proportion.

Insert Lesson Title Here Course 2 5-2 Identifying and Writing Proportions Insert Lesson Title Here Try This: Example 3 Find a ratio equivalent to each ratio. Then use the ratios to find a proportion. 2 3 A. 2 3 2 · 3 3 · 3 6 9 Multiply both the numerator and denominator by any number such as 3. = = 2 3 6 9 = Write a proportion. B. 16 12 Divide both the numerator and denominator by any number such as 4. 16 12 16 ÷ 4 12 ÷ 4 4 3 = = 16 12 = 4 3 Write a proportion.

Identifying and Writing Proportions Insert Lesson Title Here Course 2 5-2 Identifying and Writing Proportions Insert Lesson Title Here Lesson Quiz Determine whether the rates are proportional by writing them in simplest form and comparing them. 9 30 12 40 12 21 10 15 1. , 2. , , ; proportional 3 10 , ; not proportional 4 7 2 3 Determine if the ratios are proportional by finding a common denominator. 3 8 , 2 5 3 7 9 21 3. 4. , , ; not proportional 15 40 16 , ; proportional 9 21

Identifying and Writing Proportions Insert Lesson Title Here Course 2 5-2 Identifying and Writing Proportions Insert Lesson Title Here Lesson Quiz 5. In a local pre-school, there are 5 children for every teacher. Write an equivalent ratio to show how many children there would be if there were 4 teachers. 20 51 4 ,