Study Guide and Review
Complete each sentence with the correct term. Choose from the list below.
congruent
constant of
proportionality
corresponding parts
cross products
dilation
dimensional analysis
indirect measurement
inverse proportion
nonproportional
proportion
proportional
rate
ratio
scale
scale drawing
scale factor
scale model
similar figures
unit rate
A statement of equality of two ratios or rates is called a(n) ___________.
A statement of equality of two ratios or rates is called a proportion.
proportion
A(n) _______ is a ratio of two measurements having different units.
A rate is a ratio of two measurements having different units.
rate
Proportional relationships can be described by using the equation y = kx, where k is the ___________________.
Proportional relationships can be described by using the equation y = kx, where k is the constant of
proportionality.
constant of proportionality
The ratio of the length on a scale drawing to the corresponding length on the real object is called the
_______________.
The ratio of the length on a scale drawing to the corresponding length on the real object is called the scale factor.
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scale factor
Page 1
Proportional relationships can be described by using the equation y = kx, where k is the constant of
proportionality.
Study Guide and Review
constant of proportionality
The ratio of the length on a scale drawing to the corresponding length on the real object is called the
_______________.
The ratio of the length on a scale drawing to the corresponding length on the real object is called the scale factor.
scale factor
Figures that have the same shape but not necessarily the same size are called _____________.
Figures that have the same shape but not necessarily the same size are called similar figures.
similar figures
A(n) _______ is a comparison of two quantities by division.
A ratio is a comparison of two quantities by division.
ratio
The process of including units of measurement as factors when computing is called ______________.
The process of including units of measurement as factors when computing is called dimensional analysis.
dimensional analysis
Two quantities are _____________ if they have a constant ratio or rate.
Two quantities are proportional if they have a constant ratio or rate.
proportional
Express each ratio as a fraction in simplest form.
10 girls out of 24 students
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6 red cars to 4 blue cars
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Two quantities are proportional if they have a constant ratio or rate.
Study Guide and Review
proportional
Express each ratio as a fraction in simplest form.
10 girls out of 24 students
6 red cars to 4 blue cars
10 yards to 8 inches
Convert 10 yards to inches. Three are 36 inches in 1 yard.
18 ounces to 3 cups
Convert 3 cups to ounces. Three are 8 ounces in 1 cup.
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Study Guide and Review
18 ounces to 3 cups
Convert 3 cups to ounces. Three are 8 ounces in 1 cup.
BASEBALL Jean got 12 hits out of 16 times at bat. Express this rate as a fraction in simplest form. Explain its
meaning.
For every 4 times at bat, Jean got 3 hits or on
; For every 4 times at bat, Jean got 3 hits or on
Express each rate as a unit rate. Round to the nearest tenth, if necessary.
$25.97 for 8 boxes
The unit rate is $3.25 per box.
$3.25 per box
400 meters in 5 minutes
The unit rate is 80 meters per minute.
80 meters per minute
$175 for 4 concert tickets
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The unit rate is 80 meters per minute.
Study Guide and Review
80 meters per minute
$175 for 4 concert tickets
The unit rate is $43.75 per ticket.
$43.75 per ticket
125 miles in 200 minutes
The unit rate is 0.6 mile per minute.
0.6 mile per minute
SHOPPING An eight pack of juice boxes costs $4.79, and a twelve pack of juice boxes costs $6.59. Which is a
better buy? Explain.
The eight pack costs $0.60 per juice box.
The twelve pack of juice boxes costs $0.55 per juice box.
The twelve pack is a better buy because the cost per juice box is less.
12 juice boxes for $6.59; Sample answer: The eight pack of juice boxes costs $0.60 per juice box and the twelve
pack of juice boxes costs $0.55 per juice box.
Complete each conversion. Round to the nearest hundredth.
17.78
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Study
Guide and Review
17.78
21.88
739.35
1.06
8.51
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Study Guide and Review
8.51
340.2
PLANES A plane is flying at a speed of 425 miles per hour. How far will the plane travel in 0.75 hour?
The plane will travel 318.75 miles.
318.75 mi
WATER A swimming pool is being drained at a rate of 50 gallons per hour. How many milliliters per second is this?
The pool is being drained at a rate of about 52.6 milliliters per second.
52.6 milliliters per second
Determine whether the set of numbers in each table is proportional. Explain.
Write the rate of boxes to pens in simplest form.
Each rate is equal to
. So, the number of boxes is proportional to the number of pens.
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The pool is being drained at a rate of about 52.6 milliliters per second.
Study Guide and Review
52.6 milliliters per second
Determine whether the set of numbers in each table is proportional. Explain.
Write the rate of boxes to pens in simplest form.
Each rate is equal to
. So, the number of boxes is proportional to the number of pens.
Yes; each rate is equal to
.
Write the rate of number of people to brownies eaten in simplest form.
The rates are not equal. So, the number of people is not proportional to the brownies eaten.
No; the rates are not equal.
FESTIVALS A customer at the ring toss booth gets 8 rings for $2. Write an equation relating the cost to the
number of rings. At this same rate, how much would a customer pay for 11 rings? for 20 rings?
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the constant
ofbyproportionality.
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The rates are not equal. So, the number of people is not proportional to the brownies eaten.
Study Guide and Review
No; the rates are not equal.
FESTIVALS A customer at the ring toss booth gets 8 rings for $2. Write an equation relating the cost to the
number of rings. At this same rate, how much would a customer pay for 11 rings? for 20 rings?
Find the constant of proportionality.
The cost is $0.25 times the number of rings, r. The equation is c = 0.25r.
To find the cost of 11 rings, substitute 11 for r.
11 rings cost $2.75.
To find the cost of 20 rings, substitute 20 for r.
20 rings cost $5.
c = 0.25r, 11 rings cost $2.75; 20 rings cost $5
Solve each proportion.
12
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Study
12 Guide and Review
7.2
14
7
REAL ESTATE A homeowner whose house is assessed for $120,000 pays $1800 in taxes. At the same rate, what
is the tax on a house assessed at $135,000?
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Let Manual
t represent
the tax
on a house
assessed at $135,000.
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Study Guide and Review
7
REAL ESTATE A homeowner whose house is assessed for $120,000 pays $1800 in taxes. At the same rate, what
is the tax on a house assessed at $135,000?
Let t represent the tax on a house assessed at $135,000.
The tax on a house assessed at $135,000 is $2025.
$2025
On the scale drawing of a museum, the scale is 0.5 inch = 10 feet. Find the actual length of each gallery.
Let x = the actual length of the Modern Art gallery.
The actual length of the Modern Art gallery is 120 feet.
120 ft
Let x = the actual length of the Renaissance gallery.
The actual length of the Renaissance gallery is 85 feet.
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85 ft
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The actual length of the Modern Art gallery is 120 feet.
Study
and Review
120Guide
ft
Let x = the actual length of the Renaissance gallery.
The actual length of the Renaissance gallery is 85 feet.
85 ft
Let x = the actual length of the Egypt gallery.
The actual length of the Egypt gallery is 150 feet.
150 ft
MAPS The length of a highway is 900 miles. If 0.5 inch on a map represents 50 miles, what is the length of the
highway on the map?
Let x = the length of the highway on the map.
The length of the highway on the map is 9 inches.
9 in.
TheManual
figures
are similar.
Determine
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each missing measure.
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The length of the highway on the map is 9 inches.
Study Guide and Review
9 in.
The figures are similar. Determine each missing measure.
Since
ABC ~
The length of
WXY, the corresponding sides are proportional.
is 7.2 in.
7.2 in.
Since Figure EFGH ~ RUST, the corresponding sides are proportional.
The length of
is 8 cm.
8 cm
MOSAIC A mosaic is created using rectangular blocks. Block A has a length of 5 centimeters and a width of 2.5
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and has a length of 7 centimeters. What is the width of block B?
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centimeters.
Block by
B is
similar to block A
The length of
is 8 cm.
Study Guide and Review
8 cm
MOSAIC A mosaic is created using rectangular blocks. Block A has a length of 5 centimeters and a width of 2.5
centimeters. Block B is similar to block A and has a length of 7 centimeters. What is the width of block B?
Since Block A ~ Block B, the length and width are proportional.
The width of Block B is 3.5 cm.
3.5 cm
HISTORY The largest known pyramid is the Pyramid of Khufu. At a certain time of day, a vertical yard stick casts
a shadow 1.5 feet long, and the pyramid casts a shadow 241 feet long. How tall is the pyramid?
The pyramid is 482 feet tall.
482 ft
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