Power Point shared with permission from

Ms. GallacherJames 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:

903

Rate: 90 miles3 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 ratio903

can be simplified by dividing:903

= 301

Notes

Rate Movie

QuickTime™ and aSorenson Video 3 decompressorare needed to see this picture.

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 91.

468 students to 91 computers

468 students to 91 computers is approximately 5 students per computer.

468 students91 computers

455 students91 computers

5 students1 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 85.

583 soccer players to 85 soccer balls.

583 soccer players to 85 soccer balls is approximately 7 players per soccer ball.

583 players85 soccer balls

595 players85 soccer balls

7 players1 soccer ball

Divide to find players per soccer ball.

Practice

• Estimate each unit rate121 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 packagenumber of pens

=$1.955

= $0.39

price for packagenumber of pens

= $6.2015

$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?

$2.1924

= $0.09

= $3.7936

$0.11

The 24 oz jar for $2.19 has the lower unit price.

price for bottlenumber of ounces

price for bottlenumber of ounces

Divide the price by the number of ounces.

Lesson Quiz: Part I1. 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 IIFind each unit price. Then tell which has

the lower unit price.

5. A half dozen carnations for $4.75 or a

dozen for $9.24

6. 4 pens for $5.16 or a ten-pack for

$12.90.

a dozen

They cost the same.