FLC
Ch 6
Math 20 Arithmetic
Sec 6.1: Introduction to Ratios and Rates
Defn A ratio is a quotient that compares two quantities with the same type of units. A rate is a
quotient that compares two quantities with different units.
Ex
For every $20 Bob makes, he spends $10.
Notation
The ratio 10 to 9 can be expressed the following ways:
or
Ex 1
DO NOT WRITE RATIOS AS MIXED FRACTIONS. NOTE THAT THE ORDER MATTERS.
Express the given ratio as fraction reduced to lowest terms.
a)
b)
c)
d)
d)
e)
100 meters to 50 meters
The price of Kate’s favorite brand of lipstick increased from
$5.50 to $7.00. Find the ratio of the increase in price from the
original price.
Defn A ratio is a quotient that compares two quantities with the same type of units. A rate is a
quotient that compares two quantities with different units.
NOTE: “per” means “divide”
Ex 2
Write each rate as a fraction in lowest terms.
a)
b)
c)
$6 for 30 packages
500 miles in 10 hours
90 miles per 2.5 gallons
Note: We are finding the ____________ ____________.
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FLC
Ch 6
Defn
A unit rate is a rate whose denominator is 1.
Ex 3
Judah was paid 181 dollars for 8.75 hours of work. What is his hourly rate, rounded to the
nearest penny?
Ex 4
One automobile travels 297.6 miles on 10.7 gallons of gasoline. A second automobile travels
298.1 miles on 12.6 gallons of gasoline. Which automobile gets the better gas mileage?
Ex 5
Which tube of toothpaste is a better buy? You have a coupon for 85 cents off Brand C and a
coupon for 20 cents off Brand D.
Brand C Price
Brand C is $3.89 for 6 ounces
Brand D is $1.59 for 2.5 ounces
Brand D Price
Sec 6.2: Introduction to Proportion
Defn
A proportion is a statement that equates two ratios or rates.
Ex 6
Write each proportion.
a) $7 is to 3 cans as $28 is to 12 cans
b) 9 meters is to 16 meters as 18 meters is to 32 meters
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FLC
Ex 7
Ch 6
Determine whether each proportion is true or false by writing both ratios in lowest terms.
a)
b) PP
c) PP
d)
Alternative Method
Another way to determine whether a proportion is true or false is by using cross products. If the cross
products are equal, the proportion is true. Otherwise, it is false.
Product of Extremes and Means
In the proportion
the product of the means equals the product of the extremes. That is,
Ex 8
a)
Find the cross-products to see whether each proportion is true or false.
b) PP
c)
d)
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Ch 6
Ex 9
Solve each proportion. Provide only exact answers. Do not write answers as decimals.
(Fractions and mixed fractions are acceptable.)
a)
b)
c)
d)
e)
f)
g)
h)
i)
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FLC
Ch 6
Ex 10 (#48)
If 4 oranges cost $4.28, what will be the cost for 3 oranges (assuming an equal rate)?
Round your answer to the nearest penny. Also provide the exact answer.
Ex 11 (#50)
As proposed, the Shell Wind Energy project consists of 25 ridge-top turbines that can
generate up to 50 megawatts, or enough to supply electricity to about 1,000 homes. Estimate the
number of ridge-top turbines that would be need to supply electricity to about 70,000 homes, the
approximate number of properties in Humboldt County, CA.
Ex 12 (#52)
Alaska’s 26,000 square mile Tongass National Forest plan allows for timber sales of up to
267 million board-feet per year – enough for nearly 27,000 two-bedroom homes, but the demand for
timber is far short of that. Less than 25 million board-feet was logged in the forest in 2009. Forest
Service officials have said they hope to increase logging in the Tongass to about 100 million board-feet
per year.
i) Estimate the number of 2-bedroom homes that 25 million board-feet per year would build.
ii) How many 2-bedroom homes would 100 million board-feet of timber build?
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FLC
Ch 6
Ex 13 PP
A -cup serving of penne pasta has 210 calories and 2 grams of dietary fiber. How many
calories and grams of fiber will be in a 1-cup serving?
Sec 6.3: Unit Conversion: American System
In the U.S., we use the English system of measurement for many everyday activities. Examples of
English units are inches, feet, quarts, ounces, and pounds. However, the fields of science, medicine,
sports, and manufacturing use the metric system (meters, liters, and grams). Because the rest of the
world uses only the metric system, the U.S. businesses have been shifting to the metric system in order
to compete internationally.
English Measurement Relationships
Length
Weight
1 foot (ft) = 12 inches (in)
1 yard (yd) = 3 feet (ft)
1 mile (mi) = 5280 feet (ft)
1 pound (lb) = 16 ounces (oz)
1 ton (T) = 2000 pounds (lb)
Volume/Capacity
Time
1 cup (c) = 8 fluid ounces (fl oz)
1 pint (pt) = 2 cups (c)
1 quart (qt) = 2 pints (pt)
1 gallon (gal) = 4 quarts (qt)
1 minute (min) = 60 seconds (s)
1 hour (hr) = 60 minutes (min)
1 day = 24 hours (hr)
1 week (wk) = 7 days (day)
1 year (yr) = 365 days (day)
Converting Among Measurement Units
1) Multiply when converting from a __________ unit to a ___________ unit. ex
2) Divide when converting from a __________ unit to a ___________ unit.
Ex 14
Complete each conversion.
a)
b)
126 feet to yards
4.9 miles to feet
c)
198,550 inches to miles
correct to the nearest tenth of a mile
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Ch 6
d)
e)
f)
5.3 tons to ounces
20,000 pounds to tons
g)
h)
i)
2.9375 pints to fluid ounces
5.7 gallons to pints
3 gallons to cups
j)
k)
l)
6.6 years to hours
4,672,133 seconds to days
45 seconds to minutes
pounds to ounces
Ex 15 Change 99 miles per hour to feet per second. Provide the exact answer (exam). Next, round
your answer to the nearest foot per second.
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Ch 6
Ex 16 PP
Change 388 feet per second to miles per hour. Provide the exact answer (exam). Next,
round your answer to the nearest mile per hour.
Ex 17 The amount of time it takes Earth to rotate once around on its axis is one day. How many
seconds it that?
Sec 6.4: Unit Conversion: Metric System
The metric system of units is the standard system of units preferred by scientists. It is based on the base
ten number system and its decimal format is more user-friendly.
Move LEFT
Prefix
kilo-
Meaning 1000
Symbol
k
Move RIGHT
hecto-
deka-
Basic Unit deci- centi- milli-
100
10
1
h
da or D
m, g, or L
d
c
m
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FLC
Ch 6
Ex 18
What is the meaning of the prefix kilo? Centi? The abbreviation km? g?
Ex 19
Convert each.
a)
b)
c)
d)
12 m to cm
4.9 km to m
516 mg to cg
16.6 L to cL
e)
f)
g)
h)
i)
j)
k)
j)
k)
l)
m)
n)
o)
p)
q)
r)
s)
t)
u)
v)
̅
̅
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FLC
Ch 6
Sec 6.5: American Units to Metric Units and Vice-Versa
U.S. to Metric
Units of length
1 mile
1.6093 kilometers
1 kilometer
1 yard
0.9144 meter
1 meter
3.2808 feet
1 foot
0.3048 meter
1 meter
1.09 yards
1 inch
Units of volume
Units of weight
Metric to U.S.
0.6214 mile
2.54 centimeters* 1 centimeter
1 fluid ounce
0.030 liter
1 liter
0.3937 inch
33.8 fluid ounces
1 pint
0.473 liter
1 quart
0.946 liter
1 liter
1.06 quarts
1 gallon
3.785 liters
1 liter
0.264 gallon
0.454 kilogram
1 kilogram
28.35 grams
1 gram
1 pound
1 ounce
1 liter
2.1 pints
2.2 pounds
0.035 ounce
*Exact value
Ex 20 Use the conversion 1 yd = 0.9144 m to convert 1522 centimeters to yards, rounded to the
nearest tenth of a centimeter.
Ex 21 PP
Use the conversion 1 in = 2.54 cm to convert 19 centimeters to inches, rounded to the
nearest tenth of a centimeter.
Ex 22 Use the conversion 1 m = 3.2808 ft to convert 251 inches to meters, rounded to the nearest
tenth of an inch.
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FLC
Ch 6
Ex 23 Use the conversion 1 kg = 2.2 lb to convert 17.7 kg to pounds, rounded to the nearest tenth of a
pound.
Ex 24 Use the conversion 1 kg = 2.2 lb to convert 82 pounds to kilograms, rounded to the nearest
tenth of a kilogram.
Ex 25 Use the conversion 1 qt = 0.946 L to convert 22 quarts to liters, rounded to the nearest tenth of
a liter.
Ex 26
hour.
Change 63 kilometers per hour to miles per hour. Round your answer to the nearest mile per
Ex 27 Blizzard condition winds in the Artic blew 80 miles per hour. Find the wind speed to the nearest
kilometer per hour.
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