2. Warm Up Write each fraction in lowest terms. 7 8 3 8 1 8 3 8 14 16 1. 9 72 3. 24 64 2. 45 120 4.
3. 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). California Standards
5. A ratio is a comparison of two quantities. Ratios can be written in several ways. 7 to 5, 7:5, and name the same ratio. 7 5
6. Additional Example 1: Writing Ratios in Simplest Form Write the ratio 15 bikes to 9 skateboards in simplest form. 15 9 5 3 The ratio of bikes to skateboards is , 5:3, or 5 to 3. = Write the ratio as a fraction. = = Simplify. 5 3 15 ÷ 3 9 ÷ 3 bikes skateboards
7. Check It Out! Example 1 Write the ratio 24 shirts to 9 jeans in simplest form. 24 9 8 3 The ratio of shirts to jeans is , 8:3, or 8 to 3. = Write the ratio as a fraction. = = Simplify. 8 3 shirts jeans 24 ÷ 3 9 ÷ 3
8. When simplifying ratios based on measurements, write the quantities with the same units, if possible.
9. Write the ratio 3 yards to 12 feet in simplest form. First convert yards to feet. 9 feet 12 feet There are 3 feet in each yard. Additional Example 2: Writing Ratios Based on Measurement 3 yards = 3 ● 3 feet = 9 feet Multiply. Now write the ratio. Simplify. = 3 yards 12 feet 3 4 = 9 ÷ 3 12 ÷ 3 = The ratio is , 3:4, or 3 to 4. 3 4
10. Write the ratio 36 inches to 4 feet in simplest form. First convert feet to inches. 36 inches 48 inches There are 12 inches in each foot. Check It Out! Example 2 4 feet = 4 ● 12 inches = 48 inches Multiply. Now write the ratio. Simplify. = 36 inches 4 feet 3 4 = 36 ÷ 12 48 ÷ 12 = The ratio is , 3:4, or 3 to 4. 3 4
11. 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.
12. Additional Example 3: Determining Whether Two Ratios Are Equivalent Simplify to tell whether the ratios are equivalent. 1 9 1 9 4 5 3 4 12 15 B. and 27 36 3 27 A. and 2 18 Since , the ratios are equivalent. 1 9 = 1 9 = 3 ÷ 3 27 ÷ 3 3 27 = = 2 ÷ 2 18 ÷ 2 2 18 = = 12 ÷ 3 15 ÷ 3 12 15 = = 27 ÷ 9 36 ÷ 9 27 36 = Since , the ratios are not equivalent. 4 5 3 4
13. Check It Out! Example 3 Simplify to tell whether the ratios are equivalent. 1 5 1 5 2 7 4 9 14 49 B. and 16 36 Since , the ratios are equivalent. 1 5 = 1 5 = 3 ÷ 3 15 ÷ 3 3 15 = = 9 ÷ 9 45 ÷ 9 9 45 = = 14 ÷ 7 49 ÷ 7 14 49 = = 16 ÷ 4 36 ÷ 4 16 36 = Since , the ratios are not equivalent. 2 7 4 9 3 15 A. and 9 45
14. Additional Example 4: Earth Science Application At 4°C, four cubic feet of silver has the same 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? Divide. Simplify. 4 ÷ 2 42 ÷ 2 ? = 20 ÷ 10 210 ÷ 10 2 21 = 2 21 4 42 ? = 20 210 Since , 210 cubic feet of water would have the same mass at 4°C as 20 cubic feet of silver. 2 21 = 2 21 ft 3 silver ft 3 water
15. Check It Out! Example 4 At 4°C, two cubic feet of silver has the same 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? Divide. Simplify. ? = 10 ÷ 5 105 ÷ 5 2 21 2 21 = 2 21 2 21 ? = 10 105 Since , 105 cubic feet of water would have the same mass at 4°C as 10 cubic feet of silver. 2 21 = 2 21 ft 3 silver ft 3 water
16. Lesson Quiz: Part I Write each ratio in simplest form. 1. 22 tigers to 44 lions 2. 5 feet to 14 inches Find two ratios that are equivalent to each given ratio. 4 15 3. 8 21 4. 8 30 12 45 Possible answer: , 16 42 24 63 Possible answer: , 1 2 30 7
17. Lesson Quiz: Part II 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? Simplify to tell whether the ratios are equivalent. and and 8 64 16 128 and ; yes, both equal 1 8 8 5 8 5 = ; yes 16 10 5. 36 24 6. 32 20 28 18 3 2 14 9 ; no
