Unit 2, Lesson 2 Advanced

Rates and Unit Rates

Assignment: pp. 294-295, #10-19, 30-35.

 

Advanced Homework Answers pp. 290-291

14. 8/3 20. 11/12 26. yes

15. 1/5 21. 3/16 27. yes

16. 18/19 22. 16/3 28. no

17. 15/7 23. 5/1 31. yes 18. 4/1 24. 9/26 40. A

19. 11/30 25. 3/8 41. G

Rates• A ratio that compares 2 quantities

with unrelated units is called a RATE.

• Unrelated units cannot be converted to one another.

• miles and hoursmoney and weekswords and minutes

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

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!

READING Julia 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.

Simplify.

Write the rate as a fraction.

Top divided by bottom.

Answer: The average number of pages Julia reads, or unit rate, is 26 pages per hour.

SKATING Kyle 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

Write 440 miles in 8 hours as a unit rate in miles per hour.

ANSWER: The unit rate is 55 miles per hour.

Write 455 miles in 7 hours as a unit rate in miles per hour.

Answer: 65 mph (miles per hour)

READING Yi-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.

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

Find the unit price per can if it costs $3 for 6 cans of soda. Round to the nearest cent if necessary.

Answer: The unit price is $0.50 per can.

Simplify.

Write the rate as a fraction.

Top divided by bottom.

You are looking for cost per can, so put money on thetop and cans on the bottom. (Money is always on top!)

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

Unit Rates• To find the best buy, find the

unit rate of each part, then choose the lowest.

• Money ALWAYS goes on the top!

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.

The costs of different sizes of orange juice are shown in the table. Which container is the best buy? (costs the least per ounce)

Amount Total Cost16 oz $1.2832 oz $1.9264 oz $2.5696 oz $3.36

BEWARE!!: The chart lists ounces first, but you are looking for cost per ounce, so money goes in first.

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.

16-ounce container

32-ounce container

64-ounce container

96-ounce container

The costs of different sizes of bottles of laundry detergent are shown below. Which bottle is the best buy?

Amount Total Cost16 oz $3.1232 oz $5.0464 oz $7.0496 oz $11.52

Answer: 64-ounce bottle

SHOPPING Alex 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.

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.

Almonds:

Jellybeans:

SHOPPING Cameron 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

Ratios vs. Rates• Ratios have 2 numbers.

• They are fractions.

• Unit rates have 1 number.

• They aren’t fractions.

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.

Ratios vs. Rates

• Ratios have no labels.

• Unit rates are labeled and have per, each, every or a in the label.

Advanced Homework Answers pp. 294-295

10. 60 mi per hour 18. 12-oz bag11. 152 customers per day 19. bottle of 15012. 30 people per class 30. B13. $1.48 per lb 31. I14. 14¢ per oz 32. 11/1215. 270 calories per serving

33. 6/1

16. 3.08 m per sec 34. 3/517. 32 mpg 35. 10/7