(7) Lesson 1.3 - Convert Unit Rates

1. Course 2, Lesson 1-3
Simplify.
1. 2. 3.
4. On her last science test, Maria answered of the
questions incorrectly. Write as a fraction in
simplest form.
5. Jasmine is making a quilt. She bought yards of
fabric. Her total cost was $26. What was the cost per
yard?
9
3
4
11
12
2
4
5
1
2
1
5 %
3
1
5 %
3
1
4
3

2. Course 2, Lesson 1-3
Answers:
1. 12
2.
3.
4.
5. $6
11
24
3
1
5
4
75

3. HOW can you show that
two objects are proportional?
Ratios and Proportional Relationships
Course 2, Lesson 1-3

4. Ratios and Proportional Relationships
Course 2, Lesson 1-3 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council
of Chief State School Officers. All rights reserved.
• 7.RP.2
Recognize and represent proportional relationships between quantities.
• 7.RP.3
Use proportional relationships to solve multistep ratio and percent
problems. Examples: simple interest, tax, markups and markdowns,
gratuities and commissions, fees, percent increase and decrease, percent
error.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
5 Use appropriate tools strategically.

5. • To convert one rate to an
equivalent rate by
multiplying by a unit ratio
or its reciprocal.
Ratios and Proportional Relationships
Course 2, Lesson 1-3

6. Ratios and Proportional Relationships
Course 2, Lesson 1-3
• unit ratio
• dimensional analysis
12 inches
1 foot
16 ounces
1 pound
10 ft10 ft =
1 s
12 in.
•
1 s 1 ft
10•12 in. 120 in.
= =
1 s•1 1 s

7. Use 1 foot = 12 inches. Multiply by .1
Need Another Example?
2 Divide out common units.
Simplify.3
4 Simplify.
5
Step-by-Step Example
1. A remote control car travels at a rate of 10 feet
per second. How many inches per second is this?
So, 10 feet per second equals 120 inches per second.

8. Answer
Need Another Example?
Convert 15 yards per hour to inches per hour.
540 inches per hour

9. 1
Need Another Example?
2 Multiply by .
Divide out common units.3
4 Simplify.
Simplify.5
6
Step-by-Step Example
2. A swordfish can swim at a rate of 60 miles
per hour. How many feet per hour is this?
You can use 1 mile = 5,280 feet to convert the rates.
A swordfish can swim at a rate of 316,800 feet per hour.

10. Answer
Need Another Example?
The Shinkansen passenger train of Japan
travels at a rate of 300 kilometers per hour.
How many meters per hour is this speed?
300,000 m/h

11. 1
Need Another Example?
2 Multiply by and .
Divide out common units.3
4 Simplify.
Simplify.5
6
Step-by-Step Example
3. Marvin walks at a speed of 7 feet per second.
How many feet per hour is this?
You can use 60 seconds = 1 minute and you can use
60 minutes = 1 hour to convert the rates.
Marvin walks 25,200 feet in 1 hour.

12. Answer
Need Another Example?
Kelley runs at a speed of 9 miles per hour.
How many miles per second is her speed?
0.0025 mi/s

13. 1
Need Another Example?
2
Multiply by distance and time unit ratios.
Divide out common units.3
4 Simplify.
Simplify.5
6 Simplify.
Step-by-Step Example
4. The average speed of one team in a relay race is about 10
miles per hour. What is this speed in feet per second?
We can use 1 mile = 5,280 feet, 1 hour = 60 minutes, and
1 minute = 60 seconds to convert the rates.
7 The relay team runs at an average speed of 14.7 feet
per second.

14. Answer
Need Another Example?
A car travels at an average speed of 60 miles
per hour on a trip. What is the car’s speed in
feet per second?
88 ft/s

15. How did what you learned
today help you answer the
HOW can you show that
two objects are proportional?
Course 2, Lesson 1-3
Ratios and Proportional Relationships

16. How did what you learned
today help you answer the
HOW can you show that
two objects are proportional?
Course 2, Lesson 1-3
Ratios and Proportional Relationships
Sample answers:
• By finding unit ratios for customary and metric units of
measure
• By using dimensional analysis when converting rates

17. Explain how your
knowledge of unit rates
helped you to convert rates
using dimensional analysis.
Ratios and Proportional RelationshipsRatios and Proportional Relationships
Course 2, Lesson 1-3