Unit Rates, and Proportions
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. The scale used to create a blueprint of a new house is 0.25 inches = 1 foot. If the dimensions of the
master bedroom are 4 inches by 3.25 inches on the drawing, what is the actual area of the room?
a. 52 square feet
c. 256 square feet
b. 208 square feet
d. 13 square feet
____
2. The Great Pyramid of Giza originally had a height of about 150 meters. If a scale model of the
pyramid is built as shown below, what will be the height of the model? Round your answer to the
nearest tenth if necessary.
Scale: 1 cm = 4.25 m
a. 35.3 centimeters
b. 637.5 centimeters
____
c. 29.6 centimeters
d. 48 centimeters
3. The amount of fencing running around the perimeter of Lin’s vegetable garden is 24 yards. If he
doubles the dimensions of the garden, how much fencing will be required?
5 yd
7 yd
a. 48 feet
b. 45 feet
____
c. 96 feet
d. 72 feet
4. If the model car below was built using the scale 1 inch = 1.5 feet, what is the length of the actual
car?
10 in.
a. 12 feet
c. 6.7 feet
b. 17.5 feet
____
d. 15 feet
5. The distance between two state parks on a map is about 4.5 centimeters. Use the scale shown in
the table to find the actual distance between the two parks. Round your answer to the nearest tenth
of a kilometer if necessary.
Map Scale
Actual
Map Distance
Distance
1 centimeter
3 kilometers
a. 20.8 kilometers
b. 1.5 kilometers
____
c. 13.5 kilometers
d. 10.4 kilometers
6. Sumio plans to have a screened-in patio built on the back of his home. The patio floor plan will have
the dimensions shown in the scale drawing below. If the scale of the drawing is 0.5 inches = 1 foot,
what are the actual dimensions of the patio?
8 in.
11 in.
a. 22 feet by 22 feet
b. 16 feet by 12 feet
____
c. 22 feet by 16 feet
d. 25 feet by 19 feet
7. Lisa is drawing a map of her backyard. She plans to use the scale
inch : 4 feet. If the actual
distance between the tree house and the swing set is 32 feet, what should the distance on the scale
drawing be? Round your answer to the nearest tenth of an inch if necessary.
a. 4.8 inches
c. 4 inches
b. 2 inches
d. 256 inches
____
8. The Eiffel Tower in France was built for the Paris Exposition of 1889. The structure stands at a
height of about 986 feet. If a scale model of the tower is created using the scale 1 inch : 75 feet,
how tall will the model be? Round your answer to the nearest tenth of an inch if necessary.
a. 13.1 inches
c. 18.1 inches
b. 6.6 inches
d. 8.8 inches
____
9. Mi-Yung is driving across the United States. If Mi-Yung’s map is 12 inches across, and the
United States is 3,000 miles across, what is the scale of the map?
a. 1 inch = 12 miles
c. 1 inch = 0 miles
b. 1 inch = 3,000 miles
d. 1 inch = 250 miles
____ 10. A circular above ground swimming pool has a circumference of approximately 73 feet. If the
dimensions of the pool are doubled, what will the new circumference be?
C = 73 ft
a. 584 feet
b. 292 feet
c. 110 feet
d. 146 feet
____ 11. Carl took a 4-inch by 6-inch picture for his photography class. He wants to enlarge the picture and
frame it for his wall. The larger picture will be similar to the smaller picture. What scale factor should
he use if the dimensions of the frame are 6 inches by 9 inches?
a. 1.5
c. 2
3
b. 3.5
d. 2
____ 12. Rectangle ABCD is similar to Rectangle WXYZ. What is the length, in units, of
D
8 units
Z
A
12 units
W
4 units
C
B
Y
a. 9 units
b. 6 units
X
c. 8 units
d. 7 units
____ 13. The two quadrilaterals shown below are similar figures. What is the value of x?
9 mm
6 mm
9 mm
a. 20.3 millimeters
b. 15.1 millimeters
Solve the proportion.
____ 14.
x
c. 13.5 millimeters
d. 6 millimeters
?
a. 74.4
b. 76.4
c. 67.9
d. 8
Numeric Response
15. The floor plan for a detached garage is shown in the scale drawing below. If the scale of the
drawing is 0.5 inches = 1 foot, what is the actual area of the garage in square feet?
17 in.
14 in.
16. The actual distance between two cities is 42 miles. About how far apart would these cities appear
on a map that has the scale shown in the table? Round your answer to the nearest tenth of an inch.
Map Scale
Map
Actual
Distance
Distance
3.5 inches
15 miles
? inches
42 miles
17. Carlton used a ruler to measure the distance between two towns on a map and found them to be
about 5.5 centimeters apart from each other. If the map has the scale shown below, about how
many kilometers apart are the two towns?
Scale
cm = 4 km
18. The developer of a golf course is hiring a graphic design company to create a scale drawing of the
course’s layout to print on the score cards. How many inches long will the seventh hole appear to
be on the score card if the actual length of the hole is 380 yards? Round your answer to the nearest
tenth of an inch, if necessary.
Twin Meadows Golf Course
Scorecard Scale
1 inch
200 yards
19. A dress originally designed for girls is being duplicated in a smaller version to be worn by a new line
of children’s dolls. The scale for the doll dresses will be 1 inch = 10 inches. The length of the
original dress is shown in the figure below.
50 in.
What will be the length of the doll dress, in inches? Round the answer to the nearest tenth, if
necessary.
20. Members of the Performing Arts Club are selling tickets for the spring play at Middleton
High School. After 55 minutes, they have sold 33 tickets to students and faculty members. At this
rate, how many tickets will be sold by the end of the 7-hour school day?
Short Answer
L1ii Identify if the following are unit rates(U), ratios(R), or neither(N):
21.
.
22. ___ You run 1400 steps in 2 miles
23. L4ii A map has a scale of 1inch is 11 km. The distance between two towns is 60km. How far is it
on the map?
.
24. 7.RP.1 L5 One lakefront property with 100 feet of shoreline is worth $120,000. Assuming that this rate is
the same per foot of shoreline how much would a property of 80 feet of shoreline be worth?
.
25. L3 Measuring out 3 cm on a map of Mississippi gives you 200 miles in real life. Using proportional
reasoning predict how many miles 5.1 inches on the map will actually represent. Show all work!
.
12 cm
26. An artist is creating a new metal sculpture. The sculptor needs a piece shaped like the one shown
in the scale drawing below.
2.5 cm 4.5 cm 2.5 cm
1 cm = 4 meters
If the piece is cut out of a rectangular piece of metal, what area (in square meters) must the metal
have prior to cutting? Round your answer to the nearest tenth of a meter if necessary.
27. This is a map of Louisiana. ESTIMATE the land area of this state. Explain the method you used.
= 1,000 square miles
28. Sue’s car has a highway fuel efficiency rating of 28 miles per gallon. At this rate, how many highway
miles should she expect to be able to drive on 8 gallons of gasoline? Show your work.
Find the value of the variable that makes the ratios equivalent.
29.
Solve the proportion.
30.
Unit Rates, and Proportions
Answer Section
MULTIPLE CHOICE
1. ANS: B
Set up and solve a proportion to find the actual length of the room and another proportion to find the
actual width of the room. Then calculate the area of the bedroom.
The actual area of the master bedroom is
square feet.
Feedback
A
B
C
D
What are the actual dimensions of the master bedroom?
Correct!
Set up two proportions to find the actual dimensions of the room. Then find its
area.
Is this the area of the drawing or the actual area of the room?
PTS: 1
DIF: Bloom’s Level: Application | Webb’s Level: Level 1
REF: Workplace
OBJ: Solve problems involving scale drawings of geometric figures, including computing actual lengths and
areas from a scale drawing and reproducing a scale drawing at a different scale.
NAT: 7: 7.G.1
STA: 7: 7.G.1
TOP: Geometry
KEY: scale drawing | proportion
MSC: MA-09-00169
2. ANS: A
Set up and solve a proportion.
Feedback
A
B
C
D
Correct!
Did you switch the numerator and denominator in one of your ratios?
What two ratios are equal in the problem statement? Use these to set up a
proportion.
Set up a proportion to solve the problem.
PTS: 1
DIF: Bloom’s Level: Application | Webb’s Level: Level 1
REF: Science
OBJ: Solve problems involving scale drawings of geometric figures, including computing actual lengths and
areas from a scale drawing and reproducing a scale drawing at a different scale.
NAT: 7: 7.G.1
STA: 7: 7.G.1
TOP: Geometry
KEY: proportion | scale drawing
MSC: MA-09-00193
3. ANS: A
The new perimeter becomes
feet.
Feedback
A
B
C
D
Correct!
What is the perimeter of the larger garden?
What will the new dimensions of the vegetable garden be?
Find the perimeter of the garden with twice the width and twice the length.
PTS: 1
DIF: Bloom’s Level: Application | Webb’s Level: Level 1
REF: Workplace
OBJ: Solve problems involving scale drawings of geometric figures, including computing actual lengths and
areas from a scale drawing and reproducing a scale drawing at a different scale.
NAT: 7: 7.G.1
STA: 7: 7.G.1
TOP: Geometry
KEY: area | rectangle | scale | dimensions
MSC: MA-08-00125
4. ANS: D
Set up a proportion and solve.
Feedback
A
B
C
D
How can you use the information given to set up a proportion?
Set up a proportion using the information in the problem statement.
Be careful when setting up your proportion.
Correct!
PTS: 1
DIF: Bloom’s Level: Application | Webb’s Level: Level 1
REF: Workplace
OBJ: Solve problems involving scale drawings of geometric figures, including computing actual lengths and
areas from a scale drawing and reproducing a scale drawing at a different scale.
NAT: 7: 7.G.1
STA: 7: 7.G.1
TOP: Geometry
KEY: proportion | scale model | scale
MSC: MA-08-00127
5. ANS: C
Set up a proportion and solve.
Feedback
A
B
C
D
Set up a proportion using the information in the problem statement.
Make sure you set up your proportion correctly.
Correct!
How can you use the information given to set up a proportion?
PTS: 1
DIF: Bloom’s Level: Application | Webb’s Level: Level 1
REF: Social Studies
OBJ: Solve problems involving scale drawings of geometric figures, including computing actual lengths and
areas from a scale drawing and reproducing a scale drawing at a different scale.
NAT: 7: 7.G.1
STA: 7: 7.G.1
TOP: Geometry
KEY: proportion | scale | distance | maps
MSC: MA-08-00128
6. ANS: C
Set up and solve a proportion for the length and a proportion for the width.
The actual dimensions of the patio are 22 feet by 16 feet.
Feedback
A
B
C
D
Will the length and width of the patio be the same?
How can you set up two different proportions to find the length and width of the
patio?
Correct!
Set up a proportion to find each dimension of the patio.
PTS: 1
DIF: Bloom’s Level: Application | Webb’s Level: Level 1
REF: Workplace
OBJ: Solve problems involving scale drawings of geometric figures, including computing actual lengths and
areas from a scale drawing and reproducing a scale drawing at a different scale.
NAT: 7: 7.G.1
STA: 7: 7.G.1
TOP: Geometry
KEY: scale drawing | proportion | dimensions | scale
MSC: MA-08-00129
7. ANS: C
Set up and solve a proportion.
Feedback
A
B
C
D
How can you use the information given to set up a proportion?
What is the scale of the drawing?
Correct!
Be careful when setting up your proportion. Make sure the ratios are
proportional.
PTS: 1
DIF: Bloom’s Level: Application | Webb’s Level: Level 1
REF: Workplace
OBJ: Solve problems involving scale drawings of geometric figures, including computing actual lengths and
areas from a scale drawing and reproducing a scale drawing at a different scale.
NAT: 7: 7.G.1
STA: 7: 7.G.1
TOP: Geometry
KEY: proportion | scale drawing | scale
MSC: MA-08-00130
8. ANS: A
Set up and solve a proportion.
Feedback
A
B
C
D
Correct!
Be careful when solving your proportion.
Are there two equivalent ratios that you can compare in a proportion?
What two ratios are equal in the problem statement? Use these to set up a
proportion.
PTS: 1
DIF: Bloom’s Level: Application | Webb’s Level: Level 1
REF: Social Studies
OBJ: Solve problems involving scale drawings of geometric figures, including computing actual lengths and
areas from a scale drawing and reproducing a scale drawing at a different scale.
NAT: 7: 7.G.1
STA: 7: 7.G.1
TOP: Geometry
KEY: proportion | scale model | scale
MSC: MA-08-00132
9. ANS: D
If the map width is 12 inches and the United States is 3,000 miles wide, then the scale is
1 inch =
miles.
Feedback
A
B
C
D
The width of the United States should be divided by some number.
Divide the distance across the United States by the width of the map.
Check your division.
Correct!
PTS: 1
DIF: Bloom’s Level: Application | Webb’s Level: Level 1
REF: Social Studies
OBJ: Solve problems involving scale drawings of geometric figures, including computing actual lengths and
areas from a scale drawing and reproducing a scale drawing at a different scale.
NAT: 7: 7.G.1
STA: 7: 7.G.1
TOP: Geometry
KEY: maps | scale | distance
MSC: MA-08-00150
10. ANS: D
The circumference of a circle is given by the formula
. If the diameter is doubled, the new
circumference becomes
, or twice the original circumference. So the new
circumference of the pool will be about 146 feet.
Feedback
A
B
C
D
How is the expression for the circumference of a circle changed when the
diameter is doubled?
How many dimensions are being scaled?
What is the formula for the circumference of a circle?
Correct!
PTS: 1
DIF: Bloom’s Level: Application | Webb’s Level: Level 1
REF: Workplace
OBJ: Solve problems involving scale drawings of geometric figures, including computing actual lengths and
areas from a scale drawing and reproducing a scale drawing at a different scale.
NAT: 7: 7.G.1
STA: 7: 7.G.1
TOP: Geometry
KEY: circle | dimensions | scale | circumference
MSC: MA-08-00122
11. ANS: A
Divide the dimensions of the frame by the corresponding dimensions of the picture to find the scale
factor.
Feedback
A
B
C
D
Correct!
Divide the dimensions of the frame by the corresponding dimensions of the
picture.
Is the print a reduction or an enlargement?
How do the dimensions of the frame compare to the dimensions of the picture?
PTS: 1
DIF: Bloom’s Level: Application | Webb’s Level: Level 1
REF: The Arts
OBJ: Solve problems involving scale drawings of geometric figures, including computing actual lengths and
areas from a scale drawing and reproducing a scale drawing at a different scale.
NAT: 7: 7.G.1
STA: 7: 7.G.1
TOP: Geometry
KEY: similar figures | scale
MSC: MA-06-00240
12. ANS: B
Divide the length of
by
to find how many times larger Rectangle WXYZ is than ABCD.
Multiply the length of
by 1.5 to find the length of
.
Feedback
A
B
C
D
What number can you multiply by the sides of the smaller rectangle to find the
sides of the larger rectangle?
Correct!
How many times larger is Rectangle WXYZ?
What scale factor was used to create the larger rectangle?
PTS: 1
DIF: Bloom’s Level: Application | Webb’s Level: Level 1
REF: Mathematics
OBJ: Solve problems involving scale drawings of geometric figures, including computing actual lengths and
areas from a scale drawing and reproducing a scale drawing at a different scale.
NAT: 7: 7.G.1
STA: 7: 7.G.1
TOP: Geometry
KEY: similar figures | rectangle
MSC: MA-06-00247
13. ANS: C
Set up a proportion using the corresponding sides of the similar figures.
Feedback
A
B
C
D
Set up a proportion using two equal ratios from the similar figures.
What are two equal ratios in the similar figures?
Correct!
Be careful when setting up your proportion.
PTS:
REF:
NAT:
KEY:
14. ANS:
LOC:
KEY:
1
DIF: Bloom’s Level: Application | Webb’s Level: Level 1
Mathematics OBJ: Represent proportional relationships by equations.
7: 7.RP.2.c
STA: 7: 7.RP.2.c
TOP: Ratios and Proportional Relationships
similarity | similar figures | proportion | ratioMSC:
MA-07-00238
A
PTS: 1
DIF: Level B
REF: MLC30385
NCTM 6-8.NOP.3.d
TOP: Lesson 7.2 Writing and Solving Proportions
solve | proportion
MSC: Knowledge NOT: 978-0-618-73965-3
NUMERIC RESPONSE
15. ANS: 952
PTS: 1
DIF: Bloom’s Level: Application | Webb’s Level: Level 1
REF: Workplace
OBJ: Solve problems involving scale drawings of geometric figures, including computing actual lengths and
areas from a scale drawing and reproducing a scale drawing at a different scale.
NAT: 7: 7.G.1
STA: 7: 7.G.1
TOP: Geometry
KEY: proportion | scale drawing
MSC: MA-09-00251
16. ANS: 9.8
PTS: 1
DIF: Bloom’s Level: Application | Webb’s Level: Level 2
REF: Workplace
OBJ: Solve problems involving scale drawings of geometric figures, including computing actual lengths and
areas from a scale drawing and reproducing a scale drawing at a different scale.
NAT: 7: 7.G.1
STA: 7: 7.G.1
TOP: Geometry
KEY: scale drawing | proportion
MSC: MA-09-00253
17. ANS: 44
PTS: 1
DIF: Bloom’s Level: Application | Webb’s Level: Level 1
REF: Workplace
OBJ: Solve problems involving scale drawings of geometric figures, including computing actual lengths and
areas from a scale drawing and reproducing a scale drawing at a different scale.
NAT: 7: 7.G.1
STA: 7: 7.G.1
TOP: Geometry
KEY: scale drawing | proportion | scale | maps
MSC: MA-08-00161
18. ANS: 1.9
PTS: 1
DIF: Bloom’s Level: Application | Webb’s Level: Level 1
REF: Health/Physical Education
OBJ: Solve problems involving scale drawings of geometric figures, including computing actual lengths and
areas from a scale drawing and reproducing a scale drawing at a different scale.
NAT: 7: 7.G.1
STA: 7: 7.G.1
TOP: Geometry
KEY: proportion | scale drawing | scale
MSC: MA-07-00230
19. ANS: 5
PTS: 1
DIF: Bloom’s Level: Application | Webb’s Level: Level 1
REF: Workplace
OBJ: Solve problems involving scale drawings of geometric figures, including computing actual lengths and
areas from a scale drawing and reproducing a scale drawing at a different scale.
NAT: 7: 7.G.1
STA: 7: 7.G.1
TOP: Geometry
KEY: scale
MSC: MA-07-00209
20. ANS: 252
PTS:
REF:
NAT:
KEY:
1
DIF: Bloom’s Level: Application | Webb’s Level: Level 1
The Arts
OBJ: Represent proportional relationships by equations.
7: 7.RP.2.c
STA: 7: 7.RP.2.c
TOP: Ratios and Proportional Relationships
conversion | rate | problem solving MSC: MA-09-00270
SHORT ANSWER
21. ANS:
no
PTS: 1
22. ANS:
U
PTS: 1
23. ANS:
kjh
PTS: 1
24. ANS:
$80
PTS: 1
25. ANS:
25.2 miles
PTS: 1
26. ANS:
Note: The following is only a sample answer. All reasonable answers should be accepted.
1,824 square meters
PTS: 1
DIF: Bloom’s Level: Application | Webb’s Level: Level 1
REF: Science
OBJ: Solve problems involving scale drawings of geometric figures, including computing actual lengths and
areas from a scale drawing and reproducing a scale drawing at a different scale.
NAT: 7: 7.G.1
STA: 7: 7.G.1
TOP: Geometry
KEY: scale drawing | area | model
MSC: MA-08-00202
27. ANS:
Note: The following is only a sample answer. All reasonable answers should be accepted.
approximately 38.5,000 to 48.5,000 square miles
The area of Louisiana is approximately 43.5,000 square miles. First, count 27 squares that were
completely covered by land. Then count 33 squares that were partly or mostly covered by land.
Divide 33 by 2 (16.5) because on average these squares were only half covered. Add 27 and 16.5
together for a total of 43.5 squares, which is equal to 43,500 square miles.
PTS: 1
DIF: Bloom’s Level: Application | Webb’s Level: Level 3
REF: Social Studies
OBJ: Solve problems involving scale drawings of geometric figures, including computing actual lengths and
areas from a scale drawing and reproducing a scale drawing at a different scale.
NAT: 7: 7.G.1
STA: 7: 7.G.1
TOP: Geometry
KEY: estimation | area
MSC: MA-05-00074
28. ANS:
Note: The following is only a sample answer. All reasonable answers should be accepted.
224 miles
Multiply the fuel efficiency (in miles per gallon) by the number of gallons.
PTS: 1
DIF: Bloom’s Level: Application | Webb’s Level: Level 1
REF: Workplace
OBJ: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other
quantities measured in like or different units.
NAT: 7: 7.RP.1
STA: 7: 7.RP.1
TOP: Ratios and Proportional Relationships
KEY: rate | problem solving
MSC: MA-08-00224
29. ANS:
PTS: 1
DIF: Level B
REF: MLC30383 LOC: NCTM 6-8.NOP.3.d
TOP: Lesson 7.1 Ratios and Rates
KEY: solve | proportion | cross product
MSC: Knowledge NOT: 978-0-618-73965-3
30. ANS:
25
PTS: 1
DIF: Level A
LOC: NCTM 6-8.NOP.3.d
KEY: solve | proportion
REF: MLC10434 NAT: NT.CCSS.MTH.10.8.8.EE.5
TOP: Lesson 7.2 Writing and Solving Proportions
MSC: Knowledge NOT: 978-0-618-73965-3