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# California Standards

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1. California Standards MG1.3 Use measures expressed as rates (e.g., speed, density)

2. 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:

3. 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

4. 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.

5. 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.

6. 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.

7. 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.

8. 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.

9. 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.

10. 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.

11. 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.

12. Unit price is a unit rate used to compare price per item.

13. 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.

14. 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.

15. 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.

16. 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.