Unit 3. Day 7.

Today’s Lesson 1) Review Unit Rate 2) Using Unit Rate to compare. 3) Introduction to proportions

𝑚𝑖 𝑔𝑎𝑙 𝑔𝑎𝑙 𝑚𝑖 𝑜𝑟 𝑚 2 𝑔𝑎𝑙 𝑔𝑎𝑙 𝑚 2 𝑜𝑟 Example A*: A car uses 2 7 8 of a gallon to drive 40 1 4 miles. What is the mileage of the car? 𝑚𝑖 𝑔𝑎𝑙 𝑔𝑎𝑙 𝑚𝑖 𝑜𝑟 Example B*: Winston used 2 1 2 gallons of paint to cover a wall that is 12 1 4 square meters. How much area will one gallon of paint cover? 𝑚 2 𝑔𝑎𝑙 𝑔𝑎𝑙 𝑚 2 𝑜𝑟

𝑚𝑖 1 𝑔𝑎𝑙 40 1 4 161 4 𝑚𝑖 23 8 𝑔𝑎𝑙 𝑚𝑖 𝑔𝑎𝑙 𝑔𝑎𝑙 𝑚𝑖 𝑜𝑟 = 2 7 8 = = = = 14 Example A*: A car uses 2 7 8 of a gallon to drive 40 1 4 miles. What is the mileage of the car? 40 1 4 ÷ 23 8 161 4 𝑚𝑖 23 8 𝑔𝑎𝑙 𝑚𝑖 1 𝑔𝑎𝑙 𝑚𝑖 𝑔𝑎𝑙 𝑔𝑎𝑙 𝑚𝑖 𝑜𝑟 = 2 7 8 ÷ 23 8 161 4 ÷ 23 8 14 1 161 4 ∙ 8 23 1288 92 2∙2∙2∙7∙23 = = = = 14 14 = 2∙2∙23

Example B*: Winston used 2 1 2 gallons of paint to cover a wall that is 12 1 4 square meters. How much area will one gallon of paint cover? 12 1 4 ÷ 5 2 49 4 𝑚 2 5 2 𝑔𝑎𝑙 𝑚 2 1 𝑔𝑎𝑙 𝑚 2 𝑔𝑎𝑙 𝑔𝑎𝑙 𝑚 2 𝑜𝑟 = 2 1 2 ÷ 5 2 49 4 ÷ 5 2 49 10 49 4 ∙ 2 5 98 20 2∙7∙7 4 9 10 4 9 10 = = = = = 2∙2∙5

Today’s Lesson 1) Review Unit Rate 2) Using Unit Rate to compare. 3) Introduction to proportions

𝑎𝑐𝑟𝑒 1 ℎ𝑟 𝑎𝑐𝑟𝑒 1 ℎ𝑟 21 4 𝑎𝑐𝑟𝑒 7 2 ℎ𝑟 𝑎𝑐𝑟𝑒 ℎ𝑟 ℎ𝑟 𝑎𝑐𝑟𝑒 𝑜𝑟 = 𝑎𝑐𝑟𝑒 ℎ𝑟 = = Example C*: Richard Ritter, Ms. Ritter’s dad, hired two people to help him on the farm. Drew plowed 5.25 acres in 3 1 2 hours. Steven plowed 1 4 an acre in 8 minutes. Which is the better (more efficient) worker? 5 25 100 5 1 4 21 4 𝑎𝑐𝑟𝑒 7 2 ℎ𝑟 ÷ 7 2 5.25 𝑎𝑐𝑟𝑒 ℎ𝑟 ℎ𝑟 𝑎𝑐𝑟𝑒 𝑎𝑐𝑟𝑒 1 ℎ𝑟 𝑜𝑟 = 3 1 2 ÷ 7 2 1 4 ÷ 2 15 𝑎𝑐𝑟𝑒 ℎ𝑟 𝑎𝑐𝑟𝑒 1 ℎ𝑟 2 15 8 60 ÷ 2 15 1 4 ÷ 2 15 1 4 ∙ 15 2 2∙3∙7 3∙5 1 1 2 1 1 2 1 7 8 1 7 8 21 4 ÷ 7 2 21 4 ∙ 2 7 42 28 15 8 3 2 15 8 = = = = = = = = = = 2∙2∙2 2∙2∙7

Today’s Lesson 1) Review Unit Rate 2) Using Unit Rate to compare. 3) Introduction to proportions

8 Is this proportional? 𝑏𝑟𝑒𝑎𝑑 𝑝𝑒𝑟𝑠𝑜𝑛 8 12 Is this fair? 𝑏𝑟𝑒𝑎𝑑 𝑝𝑒𝑟𝑠𝑜𝑛 9 24 9 12 24 3 8 2 3 0. 375 𝑏𝑟𝑒𝑎𝑑 1 𝑝𝑒𝑟𝑠𝑜𝑛 0. 6 𝑏𝑟𝑒𝑎𝑑 1 𝑝𝑒𝑟𝑠𝑜𝑛

4 Is this proportional? 𝑏𝑟𝑒𝑎𝑑 𝑝𝑒𝑟𝑠𝑜𝑛 4 8 Is this fair? 𝑏𝑟𝑒𝑎𝑑 𝑝𝑒𝑟𝑠𝑜𝑛 15 30 15 8 30 1 2 1 2 0. 5 𝑏𝑟𝑒𝑎𝑑 1 𝑝𝑒𝑟𝑠𝑜𝑛 0.5 𝑏𝑟𝑒𝑎𝑑 1 𝑝𝑒𝑟𝑠𝑜𝑛

Is this proportional? ℎ𝑜𝑢𝑟𝑠 𝑝𝑎𝑖𝑛𝑡𝑖𝑛𝑔 9 ℎ𝑜𝑢𝑟𝑠 𝑝𝑎𝑖𝑛𝑡𝑖𝑛𝑔 ℎ𝑜𝑢𝑟𝑠 𝑝𝑎𝑖𝑛𝑡𝑖𝑛𝑔 15 Is this fair? ℎ𝑜𝑢𝑟𝑠 𝑝𝑎𝑖𝑛𝑡𝑖𝑛𝑔 3 5 3 1 3 1

Is this proportional? ℎ𝑜𝑢𝑟𝑠 𝑝𝑎𝑖𝑛𝑡𝑖𝑛𝑔 ℎ𝑜𝑢𝑟𝑠 𝑝𝑎𝑖𝑛𝑡𝑖𝑛𝑔 14 Is this fair? ℎ𝑜𝑢𝑟𝑠 𝑝𝑎𝑖𝑛𝑡𝑖𝑛𝑔 ℎ𝑜𝑢𝑟𝑠 𝑝𝑎𝑖𝑛𝑡𝑖𝑛𝑔 10 3 4 3. 3 1 3.5 1

3 𝑐𝑎𝑛𝑐𝑒𝑟 100 𝑝𝑒𝑜𝑝𝑙𝑒 = 30,000 𝑐𝑎𝑛𝑐𝑒𝑟 1,000,000 𝑝𝑒𝑜𝑝𝑙𝑒 $1 2 ℎ𝑜𝑢𝑟𝑠 $4 8 ℎ𝑜𝑢𝑟𝑠 A proportion is an stating that two ratios (or rates) are equivalent. equation = 1 4 = 2 8 $3 2 𝑠𝑜𝑑𝑎𝑠 = $9 6 𝑠𝑜𝑑𝑎𝑠 60 𝑚𝑖𝑙𝑒𝑠 60 𝑚𝑖𝑛 = 1 𝑚𝑖𝑙𝑒 1 𝑚𝑖𝑛 3 𝑐𝑎𝑛𝑐𝑒𝑟 100 𝑝𝑒𝑜𝑝𝑙𝑒 = 30,000 𝑐𝑎𝑛𝑐𝑒𝑟 1,000,000 𝑝𝑒𝑜𝑝𝑙𝑒