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5-1 Ratios Preview Evaluating Algebraic Expressions Warm Up California Standards Lesson Presentation 5-1 Ratios Evaluating Algebraic Expressions Warm Up Write each fraction in lowest terms. 1. 14 7 2. 24 3 16 8 64 8 3. 9 1 4. 45 3 72 8 120 8 5-1 Ratios Evaluating Algebraic Expressions California Standards Preparation for MG1.1 Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters). 5-1 Ratios Vocabulary Evaluating Algebraic Expressions ratio equivalent ratios 5-1 Ratios Evaluating Algebraic Expressions A ratio is a comparison of two quantities. Ratios can be written in several ways. 7 to 5, 7:5, and 7 name the same ratio. 5 5-1 Ratios Additional Example 1: Writing Ratios in Simplest Form Evaluating Algebraic Expressions Write the ratio 15 bikes to 9 skateboards in simplest form. bikes = 15 Write the ratio skateboards 9 as a fraction. 15 ÷ 3 = = 5 Simplify. 9÷3 3 5 The ratio of bikes to skateboards is , 5:3, or 5 to 3. 3 5-1 Ratios Check It Out! Example 1 Evaluating Algebraic Expressions Write the ratio 24 shirts to 9 jeans in simplest form. shirts = 24 Write the ratio as jeans 9 a fraction. 24 ÷ 3 = = 8 Simplify. 9÷3 3 8 The ratio of shirts to jeans is , 8:3, or 8 to 3. 3 5-1 Ratios Evaluating Algebraic Expressions When simplifying ratios based on measurements, write the quantities with the same units, if possible. 5-1 Ratios Additional Example 2: Writing Ratios Based on Measurement Evaluating yards to 12 feet in simplest Write the ratio 3 Algebraic Expressions form. First convert yards to feet. 3 yards = 3 ● 3 feet There are 3 feet in each yard. = 9 feet Multiply. Now write the ratio. 3 yards = 9 feet 9÷3=3 = Simplify. 12 feet 12 feet 12 ÷ 3 4 The ratio is 3 , 3:4, or 3 to 4. 4 5-1 Ratios Check It Out! Example 2 Write the ratio 36 inches to 4 feet in Evaluating Algebraic Expressions simplest form. First convert feet to inches. 4 feet = 4 ● 12 inches There are 12 inches in each foot. = 48 inches Multiply. Now write the ratio. 36 inches = 36 inches = 36 ÷ 12 = 3 Simplify. 4 feet 48 inches 48 ÷ 12 4 The ratio is 3 , 3:4, or 3 to 4. 4 5-1 Ratios Evaluating Algebraic Expressions Ratios that make the same comparison are equivalent ratios. Equivalent ratios represent the same point on the number line. To check whether two ratios are equivalent, you can write both in simplest form. 5-1 Ratios Additional Example 3: Determining Whether Two Ratios Are Equivalent Evaluating Algebraic Expressions Simplify to tell whether the ratios are equivalent. A. 3 and 2 3 3 ÷ 3 =1 1= 1 = Since , 27 18 27 27 ÷ 3 9 9 9 the ratios are 2 2 ÷ 2 =1 = equivalent. 18 18 ÷ 2 9 B. 12 and 27 12 = 12 ÷ 3 = 4 Since 4 3 , 15 36 15 15 ÷ 3 5 5 4 the ratios are not 27 = 27 ÷ 9 3 equivalent. 36 36 ÷ 9 = 4 5-1 Ratios Check It Out! Example 3 Simplify to tell whether the ratios are Evaluating Algebraic Expressions equivalent. A. 3 and 9 3 3÷3= 1 1= 1 = Since , 15 45 15 15 ÷ 3 5 5 5 the ratios are 9 9÷9= 1 = equivalent. 45 45 ÷ 9 5 14 = 14 ÷ 7 2 B. 14 and 16 Since 2 4 , 49 49 ÷ 7 = 7 7 9 49 36 the ratios are not 16 = 16 ÷ 4 4 equivalent. 36 36 ÷ 4 = 9 5-1 Ratios Additional Example 4: Earth Science Application At 4°C, four cubic feet of silver has the same Evaluating Algebraic Expressions mass as 42 cubic feet of water. At 4°C, would 20 cubic feet of silver have the same mass as 210 cubic feet of water? Since 2 = 2 , 4 ? 20 ft3 silver 21 21 = 42 210 ft3 water 210 cubic feet of water 4÷2 would have the same = 20 ÷ 10 Divide. ? 42 ÷ 2 210 ÷ 10 mass at 4°C as 20 cubic feet of silver. 2 = 2 21 21 Simplify. 5-1 Ratios Check It Out! Example 4 At 4°C, two cubic feet of silver has the same Evaluating Algebraic Expressions mass as 21 cubic feet of water. At 4°C, would 105 cubic feet of water have the same mass as 10 cubic feet of silver? 2 = 10 ? ft3 silver Since 2 = 2 , 21 105 ft3 water 21 21 2 = 10 ÷ 5 ? 105 cubic feet of water Divide. would have the same 21 105 ÷ 5 mass at 4°C as 10 cubic 2 = 2 Simplify. feet of silver. 21 21 5-1 Ratios Lesson Quiz: Part I Write each ratio in simplest form. Evaluating Algebraic Expressions 1 1. 22 tigers to 44 lions 2 2. 5 feet to 14 inches 30 7 Find two ratios that are equivalent to each given ratio. 3. 4 Possible answer: 8 , 12 15 30 45 4. 8 Possible answer: 16 , 24 21 42 63 5-1 Ratios Lesson Quiz: Part II Simplify to tell whether the ratios are Evaluating Algebraic Expressions equivalent. 5. 16 and 32 8 = 8; yes 10 20 5 5 6. 36 and 28 3 14 ; no 24 18 2 9 7. Kate poured 8 oz of juice from a 64 oz bottle. Brian poured 16 oz of juice from a 128 oz bottle. Are the ratios of poured juice to starting amount of juice equivalent? 8 and 16 ; yes, both equal 1 64 128 8

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