Power Point shared with permission from Ms. Gallacher James Workman Middle School of Technology and the Arts A note from Ms. Gallacher:

California Standards MG1.3 Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., person-days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer. Unit 9: Rates Objective: Finding Unit Rates Finding Unit Prices to Compare Costs

Ratio: 90 3 Rate: 90 miles 3 hours Read as “90 miles per 3 hours.” A rate is a comparison of two quantities measured in different units. Notes

Unit rates are rates in which the second quantity is 1. unit rate: 30 miles, 1 hour or 30 mi/h The ratio 90 3 can be simplified by dividing: 90 3 = 30 1 Notes

Rate Movie

Check It Out! Example 1 Penelope can type 90 words in 2 minutes. How many words can she type in 1 minute? 90 words 2 minutes Write a rate. = Penelope can type 45 words in one minute. 90 words ÷ 2 2 minutes ÷ 2 Divide to find words per minute. 45 words 1 minute

Estimate each unit rate. Example 2: Estimating Unit Rates Choose a number close to 468 that is divisible by students to 91 computers 468 students to 91 computers is approximately 5 students per computer.  468 students 91 computers 455 students 91 computers  5 students 1 computer Divide to find students per computer.

Estimate each unit rate. Check It Out! Example 3 Choose a number close to 583 that is divisible by soccer players to 85 soccer balls. 583 soccer players to 85 soccer balls is approximately 7 players per soccer ball.  583 players 85 soccer balls 595 players 85 soccer balls  7 players 1 soccer ball Divide to find players per soccer ball.

Practice Estimate each unit rate  121 students in 3 buses  $31.50 for 4 hours

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

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? Example 5: Finding Unit Prices to Compare Costs Divide the price by the number of pens. price for package number of pens = $ =$0.39 price for package number of pens = $  $0.41 The 5-pack for $1.95 has the lower unit price.

Check It Out! Example 6 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?  $ = $0.09 = $  $0.11 The 24 oz jar for $2.19 has the lower unit price. price for bottle number of ounces price for bottle number of ounces Divide the price by the number of ounces.

Lesson Quiz: Part I 1. Meka can make 6 bracelets per half hour. How many bracelets can she make per hour? 2. Sam counted 157 blue jays in the park. There are 5 bird feeders in the park. Approximately how many birds are there for each bird feeder? Estimate each unit rate. 3. $2.22 for 6 stamps 4. 8 heartbeats in 6 seconds $0.37 per stamp ≈ 150/5 ≈ 30 birds per bird feeder  1.3 beats/s 12

Lesson Quiz: Part II Find each unit price. Then tell which has the lower unit price. 5. A half dozen carnations for $4.75 or a dozen for $ pens for $5.16 or a ten-pack for $ a dozen They cost the same.