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Unit 2, Lesson 2 Advanced Rates and Unit Rates

Unit 2, Lesson 2 Advanced Rates and Unit Rates. Assignment: pp. 294-295, #10-19, 30-35. Advanced Homework Answers pp. 290-291. Rates. A ratio that compares 2 quantities with unrelated units is called a RATE. Unrelated units cannot be converted to one another. miles and hours

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Unit 2, Lesson 2 Advanced Rates and Unit Rates

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  1. Unit 2, Lesson 2 AdvancedRates and Unit Rates Assignment: pp. 294-295, #10-19, 30-35.

  2. Advanced Homework Answers pp. 290-291

  3. Rates • A ratio that compares 2 quantities with unrelated units is called a RATE. • Unrelated units cannot be converted to one another. • miles and hours money and weeks words and minutes

  4. Unit Rates • A UNIT RATE is a rate with a denominator of 1. • Unit rates usually have the words ‘per’, ‘each or every’ or ‘a’. • 60 miles PER hour • $100 EACH week • 60 words A minute

  5. Unit Rates • To find a unit rate, write the rate, then top ÷ bottom. • Unit rates are not fractions. (the 1 on the bottom goes away) • Unit rates are labeled. • This is different than ratios!

  6. Write the rate as a fraction. Simplify. Example 2-1a7 READINGJulia read 52 pages in 2 hours. What is the average number of pages she read per hour? Write the rate as a fraction. Then find an equivalent rate with a denominator of 1. Top divided by bottom. Answer: The average number of pages Julia reads, or unit rate, is 26 pages per hour.

  7. Example 2-1b7 SKATINGKyle skated 16 laps around the ice rink in 4 minutes. What is the average number of laps he skated per minute? Answer: 4 laps per minute

  8. Example 2-2a7 Write 440 miles in 8 hours as a unit rate in miles per hour. ANSWER: The unit rate is 55 miles per hour.

  9. Example 2-2d7 Write 455 miles in 7 hours as a unit rate in miles per hour. Answer: 65 mph (miles per hour)

  10. Example 1-3a READINGYi-Mei reads 141 pages in 3 hours. How many pages does she read per hour? Answer: Yi-Mei reads an average of 47 pages per hour.

  11. Example 1-3b TRAVEL On a trip from Columbus, Ohio, to Myrtle Beach, South Carolina, Lee drove 864 miles in 14 hours. What was Lee’s average speed in miles per hour? Answer: about 62 miles per hour

  12. Write the rate as a fraction. Simplify. Example 2-3a7 Find the unit price per can if it costs $3 for 6 cans of soda. Round to the nearest cent if necessary. You are looking for cost per can, so put money on the top and cans on the bottom. (Money is always on top!) Top divided by bottom. Answer: The unit price is $0.50 per can.

  13. Example 2-3b7 Find the unit price per cookie if it costs $3 for one dozen cookies. Round to the nearest hundredth if necessary. Answer: $0.25 per cookie

  14. Unit Rates • To find the best buy, find the unit rate of each part, then choose the lowest. • Money ALWAYS goes on the top!

  15. Unit Rates • You may have to go to 3 (or more) decimal places in order to determine the lowest price, even though we only write money with 2.

  16. Example 2-4a7 The costs of different sizes of orange juice are shown in the table. Which container is the best buy? (costs the least per ounce) BEWARE!!: The chart lists ounces first, but you are looking for cost per ounce, so money goes in first.

  17. 16-ounce container 32-ounce container 64-ounce container 96-ounce container Example 2-4b7 Find the unit price, or the cost per ounce, of each size of orange juice. Divide the price by the number of ounces. Answer: The 96-ounce container of orange juice costs the least per ounce.

  18. Example 2-4c7 The costs of different sizes of bottles of laundry detergent are shown below. Which bottle is the best buy? Answer: 64-ounce bottle

  19. Example 1-4a SHOPPINGAlex spends $12.50 for 2 pounds of almonds and $23.85 for 5 pounds of jellybeans. Which item costs less per pound? By how much? For each item, write a rate that compares the cost of the item to the number of pounds. Then find the unit rates. Almonds: Jellybeans: Answer: The almonds cost $6.25 per pound and the jellybeans cost $4.77 per pound. So, the jellybeans cost $6.25 – $4.77 or $1.48 per pound less than the almonds.

  20. Example 1-4b SHOPPINGCameron spends $22.50 for 2 pounds of macadamia nuts and $31.05 for 3 pounds of cashews. Which item costs less per pound? By how much? Answer: cashews by $0.90

  21. Ratios vs. Rates • Ratios have 2 numbers. • They are fractions. • Unit rates have 1 number. • They aren’t fractions.

  22. Ratios vs. Rates • The units in ratios must be converted so they are the same. • Rates have units that are unrelated, so they can’t be converted.

  23. Ratios vs. Rates • Ratios have no labels. • Unit rates are labeled and have per, each, every or a in the label.

  24. End of Slide Show

  25. Advanced Homework Answers pp. 294-295

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