warm up divide. round answers to the nearest tenth. 1. 2. 3. 4

Evaluating Algebraic Expressions

5-2 Rates and Unit Rates

Warm UpDivide. Round answers to the nearest tenth.

1. 2.

3. 4.

23.3 3.5

23.8 23.9

420 18

73 21

380 16

430 18



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.



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


5-2 Rates and Unit RatesAdditional Example 1: Finding Unit Rates

Geoff can type 30 words in half a minute. How many words can he type in 1 minute?

Write a rate.

=

Geoff can type 60 words in one minute.

Multiply to find words per minute.

60 words 1 minute

30 words minute

12

30 words • 2 minute • 212


5-2 Rates and Unit RatesAdditional Example 2A: Chemistry Application

Five cubic meters of copper has a mass of 44,800 kilograms. What is the density of copper?

Copper has a density of 8,960 kg/m3.

44,800 kg5 m3

Write the rate.

Divide to find kilograms per 1 m3.

44,800 kg ÷ 55 m3 ÷ 5

8,960 kg1 m3


5-2 Rates and Unit RatesAdditional Example 2B: Chemistry Application

A piece of gold with a volume of 0.5 cubic meters weighs 9650 kilograms. What is the density of gold?

Gold has a density of 19,300 kg/m3.

9650 kg0.5 m3

Write the rate.

Multiply to find kilograms per 1 m3.

9650 kg • 20.5 m3 • 2

19,300 kg1 m3



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.




Additional Example 3B: Estimating Unit Rates

Choose a number close to 313 that is divisible by 8.

313 feet in 8 seconds

313 feet to 8 seconds is approximately 40 feet per second.

313 feet8 seconds

320 feet8 seconds

40 feet1 second

Divide to find feet per second.



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.



Jamie can buy a 15 oz jar of peanut butter for $2.19 or a 20 oz jar for $2.78. Which jar has the lower unit price?

Additional Example 4B: Finding Unit Prices to Compare Costs

$2.1915

= $0.15

= $2.7820

$0.14

The 20 oz jar for $2.78 has the lower unit price.

price for jarnumber of ounces

price for jarnumber of ounces

Divide the price by the number of ounces.


5-2 Rates and Unit RatesLesson Review: 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?


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


5-2 Rates and Unit RatesLesson Review: 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.

warm up divide. round answers to the nearest tenth. 1. 2. 3. 4

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