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

Vocabulary

Rate

Unit Rate

Unit Price

Estimate

Ratio: 903

Rate: 90 miles3 hours

...as a ratio like this,

A rate is a comparison of two quantities measured in different units.

For example, the phrase “90 miles per 3 hours” can be written...

...or as a rate, like this

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 also be simplified by dividing:

903

= 301

Class Example

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

Write as 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

Partner Practice

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

Individual Practice

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

To estimate is to find a value that is close to the actual value, but not necessarily the true value.

Estimate the unit rate.

Partner Practice

313 Is not divisible by 8, so 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.

Estimate each unit rate.

Individual Practice

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.

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?

Class Practice

Set up proportions for both situations.price for package

number of pens =$1.95

5= $0.39

price for packagenumber of pens

= $6.2015

$0.41

The 5-pack for $1.95 has the lower unit price.

Divide the price by the number of pens.

Compare to determine your answer.

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?

Partner Practice

$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