Math Rates 1
Vocabulary Rate—Ratio that compares quantities with different kinds of units. Ex. : 100 words The units WORDS and MINUTES are 2 minutes different. Unit Rate— a Rate that has been simplified that has a denominator of 1. The denominator is 1 Ex. : 50 words unit. 1 minute 2
COMMON UNIT RATES Ratio # of miles/1 hour Unit Rate Miles per hour Abbreviation Name Mi/h or mph Speed # of miles/1 Miles per gallon Mi/gal or mpg Gas Mileage # of dollars/1 pound # of dollars/1 hour Price per Pound Dollars/lb Unit Price Dollars per hour Dollars/h Hourly Wage 3
Notes To find unit rate, you divide by the denominator. Ex. : Allie ran 24 miles in 3 hours. What is her average speed in miles per hour? 1 st write the rate as a fraction. 24 mi 3 hr Then divide the numerator by the denominator. The answer is 8 miles per hour. 4
Example #1 Gavin traveled 300 miles and used 15 gallons of gas. How many miles did he travel per gallon? 5
Example #2 Julia biked 40 miles in 5 hours. What should her average speed be in miles per hour? 6
Reading Julia read 52 pages in 2 hours. What is the average number of pages she read per hour? 7
Example Natalie swam 16 laps in 4 minutes. What is the average number of laps she swam per minute? 8
Running Alice ran 24 miles in 3 hours. What is her average speed in miles per hour? 9
How Much Does It Cost? Find the unit price per orange if it costs $2 for 6 oranges. Round to the nearest tenth if necessary. Find the unit price per can if it costs $3 for 6 cans of soda. Round to the nearest tenth if necessary. Find the unit price per cookie if it costs $3 for 12 cookies. Round to the nearest tenth if necessary. 10
Example Claire is a member of a book club at a book store. The store offers 3 book deals for members. Which deal is the best buy Deal 3 books 5 books 7 books Price $19. 35 $32. 25 $38. 50 11
Dish Detergent Prices The table shows the various sizes and prices of dish detergent. Size 12 $1. 20 Which size is the better buy? Family 28 $2. 24 Economy $3. 60 Volume Price (fl oz) Mini 40 12
Let’s Go Shopping! The costs of different sizes of peanut butter are shown below. Which jar costs the least per ounce? Size Price 12 oz $2. 49 40 oz $5. 30 80 oz $10. 89 13
Let’s Go Shopping! The costs of different sizes of orange juice are shown below. Size Volume (fl 16 oz $1. 28 Which container costs the least per ounce? 32 oz $1. 92 64 oz $2. 56 96 oz $3. 36 oz) 14
Find each unit rate. Round to the nearest hundredth if necessary. a. 300 tickets in 6 days b. 220 miles in 8 gallons c. 228 feet in 24 seconds d. 440 miles in 8 hours 15
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