Math Rates

Vocabulary Rate—Ratio that compares quantities with different kinds of units. Ex.: 100 words 2 minutes Unit Rate— a Rate that has been simplified that has a denominator of 1. Ex.: 50 words 1 minute The units WORDS and MINUTES are different. The denominator is 1 unit.

COMMON UNIT RATES Ratio Unit Rate Name # of miles/1hour Miles per hour Abbreviation Name # of miles/1hour Miles per hour Mi/h or mph Speed # of miles/1 gallon Miles per gallon Mi/gal or mpg Gas Mileage # of dollars/1 pound Price per Pound Dollars/lb Unit Price # of dollars/1 hour Dollars per hour Dollars/h Hourly Wage

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? 1st write the rate as a fraction. 24 mi 3 hr Then divide the numerator by the denominator. The answer is 8 miles per hour.

Example #1 Gavin traveled 300 miles and used 15 gallons of gas. How many miles did he travel per gallon?

Example #2 Julia biked 40 miles in 5 hours. What should her average speed be in miles per hour?

Julia read 52 pages in 2 hours. Reading Julia read 52 pages in 2 hours. What is the average number of pages she read per hour?

Example Natalie swam 16 laps in 4 minutes. What is the average number of laps she swam per minute?

Running Alice ran 24 miles in 3 hours. What is her average speed in miles per hour?

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.

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 Price 3 books $19.35 5 books $32.25 7 books $38.50

Dish Detergent Prices The table shows the various sizes and prices of dish detergent. Which size is the better buy? Size Volume (fl oz) Price Mini 12 $1.20 Family 28 $2.24 Economy 40 $3.60

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

Let’s Go Shopping! The costs of different sizes of orange juice are shown below. Which container costs the least per ounce? Size Volume (fl oz) 16 oz $1.28 32 oz $1.92 64 oz $2.56 96 oz $3.36

Find each unit rate. Round to the nearest hundredth if necessary. 300 tickets in 6 days 220 miles in 8 gallons 228 feet in 24 seconds 440 miles in 8 hours