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## California Standards

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**California**Standards MG1.3 Use measures expressed as rates (e.g., speed, density)**Notes**A rate is a comparison of two quantities measured in different units. 90 3 Ratio: Read as “90 miles per 3 hours.” 90 miles 3 hours Rate:**90**3 The ratio can be simplified by dividing: Notes Unit rates are rates in which the second quantity is 1. 90 3 30 1 = 30 miles, 1 hour unit rate: or 30 mi/h**30 words minute**1 2 30 words • 2 minute • 2 1 2 Additional Example 1: Finding Unit Rates Geoff can type 30 words in half a minute. How many words can he type in 1 minute? Notes Write a rate. Multiply to find words per minute. 60 words 1 minute = Geoff can type 60 words in one minute.**Check It Out! Example 1**Face Penelope can type 90 words in 2 minutes. How many words can she type in 1 minute? 90 words 2 minutes Write a rate. Divide to find words per minute. 90 words ÷ 2 2 minutes ÷ 2 45 words 1 minute = Penelope can type 45 words in one minute.**Additional Example 2A: Chemistry Application**Five cubic meters of copper has a mass of 44,800 kilograms. What is the density of copper? 44,800 kg 5 m3 Write the rate. 44,800 kg ÷ 5 5 m3 ÷ 5 Divide to find kilograms per 1 m3. 8,960 kg 1 m3 Copper has a density of 8,960 kg/m3.**Additional Example 2B: Chemistry Application**A piece of gold with a volume of 0.5 cubic meters weighs 9650 kilograms. What is the density of gold? 9650 kg 0.5 m3 Write the rate. 9650 kg • 2 0.5 m3 • 2 Multiply to find kilograms per 1 m3. 19,300 kg 1 m3 Gold has a density of 19,300 kg/m3.**455 students**91 computers 468 students 91 computers 5 students 1 computer Additional Example 3A: Estimating Unit Rates Notes Estimate each unit rate. 468 students to 91 computers Choose a number close to 468 that is divisible by 91. Divide to find students per computer. 468 students to 91 computers is approximately 5 students per computer.**320 feet**8 seconds 313 feet 8 seconds 40 feet 1 second Additional Example 3B: Estimating Unit Rates Estimate each unit rate. 313 feet in 8 seconds Choose a number close to 313 that is divisible by 8. Divide to find feet per second. 313 feet to 8 seconds is approximately 40 feet per second.**595 players**85 soccer balls 583 players 85 soccer balls 7 players 1 soccer ball Check It Out! Example 3A Estimate each unit rate. 583 soccer players to 85 soccer balls. Choose a number close to 583 that is divisible by 85. Divide to find players per soccer ball. 583 soccer players to 85 soccer balls is approximately 7 players per soccer ball.**270 yards**3 hours 271 yards 3 hours 90 yards 1 hour Check It Out! Example 3B Estimate each unit rate. 271 yards in 3 hours Choose a number close to 271 that is divisible by 3. Divide to find yards per hour. 271 yards to 3 hours is approximately 90 yards per hour.**Additional Example 4A: Finding Unit Prices to Compare Costs**Pens can be purchased in a 5-pack for $1.95 or a 15-pack for $6.20. Which pack has the lower unit price? Divide the price by the number of pens. price for package number of pens $1.95 5 = = $0.39 price for package number of pens $6.20 15 = $0.41 The 5-pack for $1.95 has the lower unit price.**price for jar**number of ounces price for jar number of ounces Additional Example 4B: Finding Unit Prices to Compare Costs Jamie can buy a 15 oz jar of peanut butter for $2.19 or a 20 oz jar for $2.78. Which jar has the lower unit price? Divide the price by the number of ounces. $2.19 15 = $0.15 $2.78 20 = $0.14 The 20 oz jar for $2.78 has the lower unit price.**Check It Out! Example 4A**Golf balls can be purchased in a 3-pack for $4.95 or a 12-pack for $18.95. Which pack has the lower unit price? Divide the price by the number of balls. price for package number of balls $4.95 3 = $1.65 price for package number of balls $18.95 12 = $1.58 The 12-pack for $18.95 has the lower unit price.**price for bottle**number of ounces price for bottle number of ounces Check It Out! Example 4B John can buy a 24 oz bottle of ketchup for $2.19 or a 36 oz bottle for $3.79. Which bottle has the lower unit price? Divide the price by the number of ounces. $2.19 24 = $0.09 $3.79 36 = $0.11 The 24 oz jar for $2.19 has the lower unit price.