(7) Lesson 1.4 - Proportional and Nonproportional Relationships

1. Course 2, Lesson 1-4
Convert each rate. Round to the nearest hundredth if necessary.
1. 24 mi/h = ft/min
2. 3 gal/s = qt/min
3. 10 lb/in. = oz/ft
4. The average U.S. highway speed limit is 65 miles per hour. What is
this speed in feet per minute?
5. Suppose the Postal Service charges $10.30 per pound on a
package shipped to England. What is this rate in dollars per ounce?
6. What conversion factor is needed to convert 16 grams per
centimeter into grams per meter?

2. Course 2, Lesson 1-4
ANSWERS
1. 2,112
2. 720
3. 1,920
4. 5,720
5. $0.64/oz
6. 100 cm/1 m

3. HOW can you show that
two objects are proportional?
Ratios and Proportional Relationships
Course 2, Lesson 1-4

4. Ratios and Proportional Relationships
Course 2, Lesson 1-4 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.2a
Decide whether two quantities are in a proportional relationship, e.g., by
testing for equivalent ratios in a table or graphing on a coordinate plane and
observing whether the graph is a straight line through the origin.
• 7.RP.2b
Identify the constant of proportionality (unit rate) in tables, graphs,
equations, diagrams, and verbal descriptions of proportional relationships.

5. Ratios and Proportional Relationships
Course 2, Lesson 1-4 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council
of Chief State School Officers. All rights reserved.
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.

6. • To identify proportional relationships
• To use equivalent ratios
Ratios and Proportional Relationships
Course 2, Lesson 1-4

7. Ratios and Proportional Relationships
Course 2, Lesson 1-4
• proportional
• nonproportional
• equivalent ratios

8. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
1. Andrew earns $18 per hour for mowing lawns. Is the amount of money he
earns proportional to the number of hours he spends mowing? Explain.
Find the amount of money he earns for working a different
number of hours. Make a table to show these amounts.
For each number of hours worked, write the relationship of the
amount he earned and hour as a ratio in simplest form.
All of the ratios between the two quantities can be simplified to 18.
The amount of money he earns is proportional to the number
of hours he spends mowing.

9. Answer
Need Another Example?
Anna walks 6 miles per day. Is the number of miles she walks
proportional to the number of days she walks? Explain.
Yes; The ratio of number of miles walked to the
number of days is constant. The ratio is or 6.
Since the ratio is constant, the number of miles
walked is proportional to the number of days.

10. 1
Need Another Example?
2
3
Step-by-Step Example
2. Uptown Tickets charges $7 per baseball game ticket plus a $3
processing fee per order. Is the cost of an order proportional to
the number of tickets ordered? Explain.
For each number of tickets, write the relationship of the cost
and number of tickets as a ratio in simplest form.
Since the ratios of the two quantities are not the same, the cost
of an order is not proportional to the number of tickets ordered.

11. Answer
Need Another Example?
A cleaning service charges $45 for the first hour and
$30 for each additional hour. Is the fee proportional to
the number of hours worked? Make a table of values
to explain your reasoning.
No; the ratio of the fee to 1 hour of work is or
45, and the ratio of the fee to 2 hours of work is
or 37 , so the fee is not proportional to the
hours worked.

12. 1
Need Another Example?
2
3
4
Step-by-Step Example
3. You can use the recipe shown to
make a fruit punch. Is the amount
of sugar used proportional to the
amount of mix used? Explain.
Find the amount of sugar and mix needed for
different numbers of batches. Make a table to
help you solve.
For each number of cups of sugar, write the relationship of the cups and
number of envelopes of mix as a ratio in simplest form.
All of the ratios between the two quantities can be simplified to 0.5.
The amount of mix used is proportional to the amount of sugar used.

13. Answer
Need Another Example?
A recipe for jelly frosting calls for cup of jelly
and 1 egg white. Is the number of egg whites
used proportional to the cups of jelly used? Make
a table of values to explain your reasoning.
Yes; the ratios between the two quantities are all
equal to , so the amount of jelly used is
proportional to the number of egg whites used.

14. 1
Need Another Example?
2
3
Step-by-Step Example
4. The tables shown represent the number of pages Martin
and Gabriel read over time. Which situation represents a
proportional relationship between the time spent reading
and the number of pages read? Explain.
Write the ratios for each time period in simplest form.
All of the ratios between Martin’s quantities are . So, Martin’s
reading rate represents a proportional relationship.

15. Answer
Need Another Example?
Which situation represents a proportional
relationship between the time spent typing
and the number of words typed? Explain.
Emilio’s typing rate represents a proportional
relationship because all of the ratios simplify to .

16. How did what you learned
today help you answer the
HOW can you show that
two objects are proportional?
Course 2, Lesson 1-4
Ratios and Proportional Relationships

17. How did what you learned
today help you answer the
HOW can you show that
two objects are proportional?
Course 2, Lesson 1-4
Ratios and Proportional Relationships
Sample answers:
• Two quantities are proportional when the ratios are
constant.
• Two quantities are nonproportional when they do not
have a constant ratio.

18. Compare and
contrast proportional
and nonproportional
relationships.
Ratios and Proportional RelationshipsRatios and Proportional Relationships
Course 2, Lesson 1-4