LESSON

How do you use rates to compare quantities?

Rates7.2

Texas Essential Knowledge and Skills

The student is expected to:

Proportionality—6.4.D

Give examples of rates as the comparison by division oftwo quantities having different attributes, including ratesas quotients.

Mathematical Processes

6.1.G

Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

$6.50 per candle

A The cost of 3 candles is $19.50. What is the unit price?

ADDITIONAL EXAMPLE 1

1.5 meters per second

B Michael walks 30 meters in 20 seconds. How many meters does he walk per second?

458 miles per hour

C An airplane makes a 2,748-mile flight in6 hours. What is the airplane’s average rate of speed in miles per hour?

In a youth soccer league, each team will have 18 players and 3 coaches. This year 162 players signed up. How many coaches are needed?

27 coaches

ADDITIONAL EXAMPLE 2

7.2 LESSON QUIZ

The table shows the available sizes and prices of Henry’s favorite movie popcorn. Use the table to answer questions 1 and 2.

regular: 0.50; large: 0.47

1. What is the unit rate for each size?

6.4.D

The table shows the available sizes and prices of Henry’s favorite movie popcorn. Use the table to answer questions 1 and 2.

large

2. Which size is the better buy?

The table shows the available sizes and prices of Henry’s favorite movie popcorn. Use the table to answer questions 1 and 2.

$12

3. Rita charges $60 for 5 tutoring sessions. What is the cost per session?

The table shows the available sizes and prices of Henry’s favorite movie popcorn. Use the table to answer questions 1 and 2.

$0.30

4. A package of 12 pens costs $3.60. What is the cost per pen?

The table shows the available sizes and prices of Henry’s favorite movie popcorn. Use the table to answer questions 1 and 2.

0.62 mile

5. A train travels 40 miles in 65 minutes. To the nearest tenth of a mile, how far does the train travel per minute?

A carpenter installed 10 windows in 4 hours. A second carpenter installed 15 windows in5 hours. A third carpenter installed 50 windows in 20 hours.

• Draw a 4-column rate table to display this information. Include a column for Unit Rate on the table.

• Which carpenter is working at the fastest rate?

second carpenter; 3 windows per hour

• Who has the next fastest rate? Explain.

The first and the third carpenters are tied for the next fastest rate–2.5 windows per hour.

How do you use rates to compare quantities?

You use division to compare two quantities with different units.

Sample answer: