SOL 7.4, 8.3a 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.

Objective: Finding Unit Rates Finding Unit Prices to Compare Costs

Rate Movie

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 ratio 903

can be simplified by dividing:

903

= 301

Notes

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.

Additional Example 3A: 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 3A

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.

Pactice

• 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?

Additional Example 4A: 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 4B

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 I

1. Meka can make 6 bracelets per half hour. How many bracelets can she make per hour?

2. A penny has a mass of 2.5 g and a volume of approximately 0.360 cm3. What is the approximate density of a penny?

Estimate each unit rate.

3. $2.22 for 6 stamps

4. 8 heartbeats in 6 seconds

$0.37 per stamp

≈ 6.94 g/cm3

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 $9.24

6. 4 pens for $5.16 or a ten-pack for $12.90.

a dozen

They cost the same.