power point shared with permission from ms. gallacher james workman middle school of technology and...

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.