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Chapter Four—Ratio and Proportion:
Solving and Applying Proportions (4-1)
WORD BANK:
ratio
proportion
rate
unit rate
dimensional analysis
extremes
means
cross products
similar figures
scale
scale factor
probability
outcome
event
sample space
experimental
theoretical
complement
odds
independent variable
dependent variable
A __________ is a comparison of two numbers by division.
If the two numbers represent quantities measured in different units, then the ratio is a
____________. A _____________ is a rate with a denominator of 1. Ex. 40 miles / 1
hour. When you convert from one unit to another, you do a ___________________
___________.
A ___________________ is an equation that states that two ratios are equal. a/b= c/d or
a:b=c:d. (Read as “a is to b as c is to d.”) The _______________ of the proportion are a
and d, while the ___________ of the proportion are b and c. The products ad and bc are
the _________________ of the proportion a/b= c/d; if a/b= c/d, then ad = bc.
___________ ___________have the same shape and proportions, but not necessarily
the same size. ___________ ____________ have congruent corresponding angles
and the ratios of their sides are proportionate.
A _________ ______________is an enlarged or reduced drawing that is similar to an
actual object or place. The ratio of a distance in the drawing to the corresponding actual
distance is the ______________ of the drawing.
The following problems are copied from Prentice Hall Algebra I:
Practice: (p. 185) Find each unit rate:
#1) $57 for 6 hours
#2) $2/5 lb
#4) 600 calories/1.5 h
#6) A 12-ounce bottle of juice costs $1.08. What is the cost per ounce?
Convert each measurement:
#12a) 120 cm = ________ m
b) 42 inches = _____________ feet
c) 12,000 mm = ________ km
d) 3 miles = ______________ feet
Chapter Four—Ratio and Proportion:
Solving and Applying Proportions (4-1)
Practice: (pp. 185 + 186) Solve each proportion:
#14) 5/6 = c/9
#26) q/42 = 15/7
#28) 7/n = 35/88
#29) 20/18 = 75/w
#31) Suppose you traveled 66 kilometers in 1.25 hours. Moving at the same rate
how many kilometers would you cover in 2 hours?
#50) You are riding a bike. It takes you 21 min to go 5 mi. If you continue
traveling at the same rate, how long will it take you to go 12 mi?
Solve each proportion:
#32) x+3/4 = 7/8
#34) 8/9 = w – 2/6
#36) 8/b+10 = 4/2b – 7
#37) k+5/10 = k – 12/9
Answers: 1) $9.50/h; 2) $0.40/lb; 4) 400 cal/h; 6) $0.09/0z; 12a) 1.2m; b) 3.5 feet; c) 0.012 km; d) 15,840 feet; 14) 7.5; 26)
90; 28) 17.6; 29) 67.5; 31) 105.6km; 50) 50.4 min; 32) 0.5; 34) 7 1/3; 36) 8; 37) 165.
Chapter Four—Proportions and Similar Figures:
Solving and Applying Proportions (4-2)
Practice: (pp.192+193) Find the missing lengths:
The scale of a map is 1 inch : 17.5 mi.
#11) 5 in. =
#12) 8.3 inch =
#13) 18.6 inch =
#14) 20 inch =
#16) The actual distance between two towns is 28km. Suppose you measure the
distance on your map and find that it is 3.5cm. What is the scale of your map?
Using each of the following scales, find the dimensions in a blueprint of an 8 ft-by-12 ft. room.
#18) 1 in. : 3 ft.
#20) 1 in. : 2.5 ft.
#21) Two rectangles are similar. One is 4 inch wide and 15 inch long. The other
is 9 inch wide. How long is second rectangle?
#29) Two rectangles are similar. One is 5cm by 12 cm. The longer side of the
second rectangle is 8cm greater than twice its shorter side. Find its length and
width.
Answers: 5) 80 inch; 7) 20.25 cm; 11) 87.5 mi; 12) 145.25 mi; 13) 325.5 mi; 14) 350 mi; 16) 1 cm : 8km; 18) 2 2/3 in. by 4
in. ; 20) 3.2 in. by 4.8 in.; 21) 33.75 in.; 29) 48 cm long by 20 cm wide
Chapter Four—Proportions and Similar Figures:
Solving and Applying Proportions (4-2)
Practice: (pp.193 +194) Find the missing lengths:
#32b) Two cubes have side lengths of 4cm and 8cm. How is the ratio of their
volumes (small : large) related to the ratio of their sides (small : large)?
c) If the ratio of the sides of the two cubes is 3 : 1, what is the ratio of their
volumes? Why?
#33) The perimeter of a triangle with sides a, b, and c is 24 cm. Side a is 2 cm
longer than side b. The ratio of the lengths of sides b and c is 3 : 5. What are the
lengths of the three sides of the triangle?
#34) The state of Alabama is about 335 mi long and 210 mi wide. What scale
would you use to draw a map of Alabama on an 8.5 in-by-11 in. paper to make
the map as large as possible?
Answers: 32b) 1 : 8, 1 : 2, The volume ratio is the cube of the side ratio. c) 27 : 33) a + 8, b = 6, c = 10; 34) about 1 in. :
24.7 mi.
Chapter Four—Proportions and Percent Equations:
Solving and Applying Proportions (4-3) and (4-4)
Finding the Percent:
What percent of 300 is 225? (answer: 75%)
Find 75% of 300. (answer: 225)
75% of what number is 225? (answer: 300)
OR:
is = %
of 100
A percent is a ratio that compares a number to 100. A percent of change is the ratio
(______________ / _______________). _______________ is the percent of increase.
_________________ is the percent of decrease.
You can find the percent of change by dividing the amount of change by the original
amount. OR: % of change = amount of change
original amount
Practice: (p 200+201)
#2) What percent of 80 is 20?
#3) 15 is what percent of 45?
#8) What is 80% of 20?
#12) 16% of 125 is what number?
#19) Theresa worked 18 hours at a day-care center. This is 60% of her school’s
requirement for community service. How many hours of community service does her
school require?
#49) Sales tax in Georgia is 5%, while in Florida its 7.2%. Jane, who lives in Florida,
plans to buy a car that costs $13,500. Her friend Julie lives in Georgia. She also plans to
buy a car for $13,500. How much more will Jane pay in sales tax?
#51) Juan earns a 5.5% commission on his bicycle sales. In September, he earned
$214.28 in commissions. What were his sales for the month?
#64) Pete chose a shirt from a sale rack. The ink on the price tag had smeared, and he
couldn’t read what the percent discount was. The original price was $35.00. When the
clerk rang up the sale, the price before tax was $22.75. What percent was taken off?
Answers: 2) 25%; 3) 33 1/3%; 8) 16; 12) 20; 19) 30 h; 49) $297.00; 51) $3896.00; 64) 35%
Chapter Four—Applying Ratios to Probability (4-5) and (4-6)
The ______________ of an event, or P(event), tells you how likely it is. An __________
is the result of a single trial. An _________ is any outcome or group of outcomes. The
___________ ___________ is all of the possible outcomes. The _____________
probability of an event= the number of favorable outcomes/ number of possible
outcomes. You can write the probability of an event as a fraction, decimal, or percent.
The probability of an event ranges from 0 to 1.
The _____________________ of an event consists of all the outcomes not in the event.
The more you do an experiment (like flipping a coin), the closer the ______________
probability will come to the theoretical probability. This is called the ________ ____
______________ ____________.
You can find the probability of any event or outcome by dividing the number of favorable
outcomes by the number of possible outcomes.
OR : P = #favorable events
total # of events
You can find the __________ of an event by dividing the # of favorable events by the #
of unfavorable events.
OR: ______= #favorable events
#unfavorable events
o
o
Probability of two independent events, where the events do not influence each
other: P(A and B) = P(A) * P(B) [with replacement].
Probability of two dependent events, where the events do influence each other:
P(A and B) = P(A) * P(B after A) [NO replacement].
Practice: (p.214+215)
#14) Suppose the probability that you will be picked for a committee at school is
20%. What is the complement?
#21a) A forest contains about 500 trees. You randomly pick 67 trees and find that
27 of them are oaks. What is the experimental probability that a tree in the forest
is an oak?
b) How many oak trees would you predict there are in the forest?
#34) The U.S. has a land area of about 3,536,278 mi2. The state of Illinois has an
area of about 57,918 mi2. What is the probability that a location picked at random
in the U.S. is in Illinois?
Answers: 14) 89%; 21a) about 40%; b) about 200 oak trees; 34) 1.6%
Chapter Four—Applying Ratios to Probability (4-5) and (4-6)
Practice: (p. 216+17; 223+24)
#51) Of 150 widgets inspected, 142 passed inspection. Out of 2855 widgets,
about how many would you predict would fail an inspection?
#54) An inspector for an office-supply company checked a batch of 350 staples. He
found that 18 of them were defective. What is the experimental probability of getting a
defective stapler in this batch? Production must be stopped when the percent of
defective staplers exceeds 4%. Should the inspector stop production? Explain.
# 45a) A two-digit number is formed by randomly selecting from the digits 1, 2, 3,
and 5. How big is the sample space? (How many possibilities are there?)
b) What is the probability that a two-digit number contains a 2 or a 5?
c) What is the probability that a two-digit number is prime?

What is the probability that a two-digit number contains a 2 and a 5?
#48) A standard domino set has 28 dominoes. Seven of these are called
“doubles” since they have the same number on both ends or are blank on both
ends. The first and second player each take a domino at random. What is the
probability that they will both draw a double?
#49) You have a bag of marbles with 3 green, 4 red, and 2 yellow. You select 2 marbles
at random, without replacing them. How does the probability that they will both be green
compare to the probability that they will both be red?
Answers: 51) 150; 54) P(defective stapler) = 18/350 or about 5.1%, production should be stopped because 5.1% > 4%. 45a)
12, the sample space is 16 because there are four possibilities for each of two outcomes( 4*4=16); b) 5/6; c) 1/3; 1/8; 48)
1
/18; 49) P(green, green) = 3/9 • 2/8 = 6/72 = 1/12, P(red, red) = 4/9 • 3/8 = 12/72 = 1/6, so P(r, r) is twice as likely as P(g, g).
Chapter Four—Ratio and Proportion:
Solving and Applying Proportions (4-1)
By the end of this unit you should be able to say: I can…
 Find and use ratios and unit rates.
 Write and solve proportions.
 Find, compute, and use percents.
 Solve a problem by making a table.
 Calculate probabilities.
 Find the complement of an event.
 Find unit rates.
 Compare prices using unit rates.
 Convert rates and units.
 Convert measurement units within and between systems.
 Solve a proportion for a variable.
 Find and use cross products of a proportion.
 Find the missing length of a side of a triangle, given the other 2 sides
and a triangle that is similar.
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
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Apply similarity to problems.
Find distances on a map using a scale.
Use a proportion to find a percent. (What percent of 40 is 10?)
Find the part of the whole. (What is 45% of 450?)
Find the whole given the percent. (75% of what number is 500?)
Remember equivalent fractions for common percents.
Find the percent of change.
Find markups or discounts.