38 Chapter 2 • FraCtions
Convert the following improper fractions to whole or mixed numbers.
Review exeRcises
For each of the following, identify the type of fraction and write it in word form.
2
SECTION I
2.
12
12
3.
15
9
4.
7
16
5. 2
1
8
1. 23
4
5
88
11
12.
6
1
2=
13
2
Convert the following mixed numbers to improper fractions.
35
9
12
1
48
13. 11
4
5=
59
5
14.
5
3=
3
use inspection or the greatest common divisor to reduce the following fractions
to lowest terms.
22.
24
32
24 ÷8
32
÷
8=
3
4
23.
14
112
14 ÷14
1
12
÷
14 =
1
8
24.
9
42
9÷3
42 ÷3=
3
14
25.
95
325
95 ÷5
325
÷
5=
19
65
8
23
150
306
Raise the following fractions to higher terms as indicated.
30.
2
3
to twenty-sevenths
2
3=
18
27
a27
÷3=9
9×2=18
b
31.
3
4
to forty-eighths
3
4=
36
48
a48 ÷4=12
12 ×3=36
b
32.
7
20
to eightieths
7
20
=
28
80
a80 ÷20 =4
4×7=28b
33.
32
32
a64 ÷32 =2
2×3=6b
5
3
b
5
3
15
6
13
3
to sixty-fourths
34.
1
to hundredths
35.
3
to ninety-eighths
85461_ch02_hr_031-063.indd 38 9/23/15 4:32 PM
seCtion i • Understanding and Working With FraCtions 39
40. What fraction represents the laptops in this group of computers?
41. What fraction represents the screwdrivers in this group of tools?
42. A wedding cake was cut into
40
slices. If
24
of the slices were eaten, what fraction represents the
eaten portion of the cake? Reduce your answer to lowest terms.
43. Jasmine Marley’s swimming pool holds
16,000
gallons of water, and her spa holds
2,000
gallons
of water. Of all the water in the pool and spa,
a. What fraction is the spa water?
b. What fraction is the pool water?
44. You work in the tool department at The Home Depot. Your manager asks you to set up a
point-of-purchase display for a set of
10
wrenches that are on sale this week. He asks you to
arrange them in order from smallest to largest on the display board. When you open the box, you
find the following sizes in inches:
9
32
,
5
8
,
5
16
,
1
2
,
3
16
,
3
4
,
7
8
,
5
32
,
1
4
,
3
8
.
a. Rearrange the wrenches by size from smallest to largest.
b. Next your manager tells you that the sale will be “
1/3
off” the regular price of
$57
and has asked you to calculate the sale price to be printed on the sign.
c. After the sale is over, your manager asks you for the sales figures on the wrench promotion.
If
150
sets were sold that week, what amount of revenue will you report?
d. If
$6,000
in sales was expected, what reduced fraction represents sales attained?
2,250
Lowe’s is number two with about
1,650
stores.
Courtesy of Bob Brechner
85461_ch02_hr_031-063.indd 39 9/23/15 4:32 PM
40 Chapter 2 • FraCtions
BUsiNess DecisiON: evalUatiNg the QUestiON
45. You are on an academic committee tasked to evaluate state employment math test questions. The
following question has come to the attention of the committee:
“Each of the four digits
2, 4, 6
, and
9
is placed in one of the boxes to
form a fraction. The numerator and the denominator are two-digit whole
numbers. What is the smallest value of all the common fractions that can
be formed? Express your answer as a reduced fraction.”
addition and sUbtraction of fractions
Adding and subtracting fractions occurs frequently in business. Quite often we must combine
or subtract quantities expressed as fractions. To add or subtract fractions, the denominators
determining the least common denominator
(lcd) of tWo or more fractions
The least common denominator (LCD) is the smallest number that is a multiple of each of the
given denominators. We can often find the LCD by inspection (i.e., mentally) just by using the
definition. For example, if we want to find the LCD of
1
4
and
1
6
, we think (or write out, if we wish):
Multiples of
4
are
4, 8, 12, 16, 20, 24
, and so on
4
1
2-6
least common denominator (LCD)
The smallest and, therefore, most efficient
common denominator in addition or
subtraction of fractions. The least common
denominator of the fractions
1
4 +
3
5
is
20
.
STEPS FoR DeteRMining the LeASt CoMMon DenoMinAtoR
oF tWo oR MoRe FRACtionS uSing pRiMe nuMbeRS
SteP 1. Write all the denominators in a row.
SteP 2. Find a prime number that divides evenly into any of the denominators. Write
2
SECTION II
Adapted from the NCTM Calendar, November 2004.
Some committee members contend this is not a valid question. Solve the problem and explain the
solution to prove (or disprove) the question’s validity.
85461_ch02_hr_031-063.indd 40 9/23/15 4:32 PM
46 Chapter 2 • FraCtions
Review exeRcises
Find the least common denominator for the following groups of fractions. For problems 1–3,
try finding the LCD by inspection (i.e., mentally) first, then use the prime-number method.
2
SECTION II
1.
4
5
,
2
3
,
8
15
3 5 3 15
5 5 1 5
1 1 1
Add the following fractions and reduce to lowest terms.
7.
5
6+
1
2
5
6
+ 3
6
8
6=1
2
6=1
1
3
2.
1
3
,
4
9
,
3
4
2 3 9 4
2 3 9 2
3 3 9 1
3.
5
6
,
11
12
,
1
4
,
1
2
2 6 12 4 2
2 3 6 2 1
3 3 3 1 1
17. Chet Murray ran 3
1
2
miles on Monday,
2
4
5
miles on Tuesday, and
4
1
8
miles on Wednesday. What
was Chet’s total mileage for the 3 days?
8.
1
3+
4
5
5
15
+ 12
15
17
15 =12
15
9.
5
8
+
13
16
10
16
+ 13
16
23
16 =17
1
6
10.
9
32 +
29
32
9+29
32 =38
32 =16
32 =13
16
85461_ch02_hr_031-063.indd 46 9/23/15 4:32 PM
1
18. Crate and Barrel shipped three packages to New York weighing 45
1
5
, 126
3
4
, and 88
3
8
pounds. What was the total weight of the shipment?
19. At the Fresh Market, you buy
6
3
10
pounds of yams and
4
1
3
pounds of corn. What is the total
weight of the purchase?
20. BrewMasters Coffee Co. purchased 12
1
2
tons of coffee beans in January,
1
5
4
5
tons in
February, and 34
7
tons in March. What was the total weight of the purchases?
Subtract the following fractions and reduce to lowest terms.
21.
5
6−
1
6
22.
3
5−
1
8
23.
3
4−
1
12
24.
3
4−
9
16
29. Casey McKee sold 18
4
5
of his 54
2
3
acres of land. How many acres does Casey have left?
30. A particular dress requires
3
1
4
yards of fabric for manufacturing. If the matching jacket requires
5
6
yard less fabric, how much fabric is needed for both pieces?
seCtion ii • addition and sUbtraCtion oF FraCtions 47
85461_ch02_hr_031-063.indd 47 9/23/15 4:32 PM
48 Chapter 2 • FraCtions
31. Robert Burkart bought a frozen, factory-processed turkey that included the giblets and neck.
The package weighed
2
2
3
4
pounds. Robert thawed the bird and then removed and weighed
the giblets and neck, which totaled 1
1
8
pounds. The liquid that he drained from the package
weighed
1
pound. How much did the turkey weigh going into the oven?
32. Brady White weighed 196
1
2
pounds when he decided to join a gym to lose some weight. At the
end of the first month, he weighed 191
3
8
pounds.
a. How much did he lose that month?
b. If his goal is 183
3
4
pounds, how much more does he have to lose?
33. Hot Shot Industries manufactures metal heat shields for light fixture assemblies. What is the
length,
x
, on the heat shield?
34. Tim Kenney, a painter, used
6
4
5
gallons of paint on the exterior of a house and 9
3
4
gallons on the
interior.
a. What is the total amount of paint used on the house?
b. If an additional 8
3
5
gallons was used on the garage, what is the total amount of paint used on
the house and garage?
c. Rounding your answer from part b up to the next whole gallon, calculate the total cost of the
paint if you paid
$23
for each gallon.
pounds perperson. The top
turkeyprocessorin the United
Richard Levine/Alamy
85461_ch02_hr_031-063.indd 48 9/23/15 4:32 PM
BUsiNess DecisiON: the ReD-eYe exPRess
35. You are an executive with the Varsity Corporation in Atlanta, Georgia. The company presi-
dent was scheduled to make an important sales presentation tomorrow afternoon in Seattle,
Washington, but has now asked you to take his place.
The trip consists of a 2
1
2
-hour flight from Atlanta to Dallas, a
1
1
4
-hour layover in Dallas, and
then a
3
3
4
-hour flight to Portland. There is a 1
1
2
-hour layover in Portland and then a
3
4
-hour flight
to Seattle. Seattle is on Pacific Time, which is 3 hours earlier than Eastern Time in Atlanta.
a. If you depart Atlanta tonight at 11:30 p.m. and all flights are on schedule, what time will you
arrive in Seattle?
b. If your return flight is scheduled to leave Seattle at 10:10 p.m. tomorrow night, with the same
flight times and layovers in reverse, what time are you scheduled to arrive in Atlanta?
c. If the leg from Dallas back to Atlanta is
2
3
of an hour longer than scheduled due to headwinds,
what time will you actually arrive?
STEPS FoR MuLtipLying FRACtionS
SteP 1. Multiply all the numerators to form the new numerator.
A procedure known as cancellation can serve as a useful shortcut when multiplying
fractions. Cancellation simplifies the numbers with which we are dealing and often leaves
cancellationWhen multiplying
fractions, cancellation is the process of
finding a common factor that divides
mUltiPlication and division of fractions
In addition and subtraction, we were concerned with common denominators; however, in
multiplication and division, common denominators are not required. This simplifies the
process considerably.
mUltiPlying fractions
and mixed nUmbers
2-9
2
SECTION III
seCtion iii • mULtipLiCation and division oF FraCtions 49
85461_ch02_hr_031-063.indd 49 9/23/15 4:32 PM
52 Chapter 2 • FraCtions
Review exeRcises
Multiply the following fractions and reduce to lowest terms. use cancellation whenever
possible.
SECTION III
2
9. 8
1
5 × 2
2
3
41
5 ×
8
3=
328
15 =21
13
15 11.
1
5×
1
5×
1
5=
1
125
EXAMPLE16
dividing
FrActionS
Divide the following fractions.
a.
4
5
÷
2
3
b.
6
3
8
÷2
1
2
c. 12
1
6
÷
3
SolutionStrategy
a.
4
5
÷
2
3
=
4
5
×
3
2
In this example, invert the divisor,
2
3
, to form its reciprocal,
3
2
, and change the sign from “÷” to “
×
.”
3
8
2
51
8
×
2
5
Next, invert the divisor,
5
2
, to its reciprocal,
2
5
, and change
thesign from “÷” to “
×
.”
5
1
8
4
× 2
1
5=51
20 =2 1
1
2
0
Now multiply in the usual way. Note that the
2
in the
numerator and the
8
in the denominator can be reduced
by the common factor
2
. The answer,
37
95
51
, is an improper
tryitexerciSe 16
Divide the following fractions and mixed numbers.
10. 1
2
×2
1
3
×4
1
5
×3
1
4
×5
1
1=1
1=
1
thousandths by
25
hundred-
thousandths and express
theresult in words.
Answer: one thousand, one hundred
85461_ch02_hr_031-063.indd 52 9/23/15 4:32 PM
13. A recent market research survey showed that
3
8
of the people interviewed preferred decaffeinated
coffee over regular.
a. What fraction of the people preferred regular coffee?
4,400
1
14. Wendy Wilson planned to bake a triple recipe of chocolate chip cookies for her office party. If
the recipe calls for 1
3
4
cups of flour, how many cups will she need?
15. A driveway requires
9
1
2
truckloads of gravel. If the truck holds
4
5
8
cubic yards of gravel, how
many total cubic yards of gravel are used for the driveway?
16. Melissa Silva borrowed
$4,200
from the bank. If she has already repaid
3
7
of the loan, what is the
remaining balance owed to the bank?
1
17. Amy Richards’ movie collection occupies
5
8
of her computer’s hard drive. Her photography takes
up
1
6
of the drive. The operating system, application software, and miscellaneous files take up
another
1
12
of the drive. If her hard drive’s capacity is
120
gigabytes, how many gigabytes of free
space remain on the hard drive?
18. Three partners share a business. Max owns
3
8
, Sherry owns
2
5
, and Duane owns the rest.
$150,000
Divide the following fractions and reduce to lowest terms.
19.
5
6
÷
3
8
20.
7
10
÷
1
5
21.
3
5
÷
2
7
25. 4
4
5
÷
7
8
1
1
5
26.
2
1
1
2
÷5
2
3
27.
1
8÷
18
19
of products and services people
want and at what price. By gathering
statistical data on competitors and
examining prices, sales, and methods
products.
According to the U.S. Bureau of
seCtion iii • mULtipLiCation and division oF FraCtions 53
85461_ch02_hr_031-063.indd 53 9/23/15 4:32 PM
54 Chapter 2 • FraCtions
31. Frontier Homes, Inc., a builder of custom homes, owns 126
1
2
acres of undeveloped land. If the
property is divided into
2
3
-acre pieces, how many homesites can be developed?
32. An automobile travels
365
miles on
1
6
2
3
gallons of gasoline.
a. How many miles per gallon does the car get on the trip?
876
33. Pier
1
Imports purchased
600
straw baskets from a wholesaler.
a. In the first week,
2
5
of the baskets are sold. How many are sold?
1
34. At the Cattleman’s Market, 3
1
2
pounds of hamburger meat are to be divided into
7
equal
packages. How many pounds of meat will each package contain?
518
1
36. The chef at the Sizzling Steakhouse has
140
pounds of sirloin steak on hand for Saturday night.
If each portion is
1
0
1
2
ounces, how many sirloin steak dinners can be served? Round to the
nearest whole dinner. (There are
16
ounces in a pound.)
37. Regal Reflective Signs makes speed limit signs for the state department of transportation. By law,
these signs must be displayed every
5
8
of a mile. How many signs will be required on a new high-
way that is 34
3
8
miles long?
840
1
b. What is the cost of wire per circuit board?
compiles the fuel economy data, and
the DOE publishes them in print and
on the Web at www.fueleconomy.gov.
85461_ch02_hr_031-063.indd 54 9/23/15 4:32 PM
4
39. At Celtex Manufacturing, a chemical etching process reduces
2
13
16
-inch copper plates by
35
64
of an
inch.
a. What is the thickness of each copper plate after the etching process?
BUsiNess DecisiON: DiNNeR sPecial
40. You are the owner of The Gourmet Diner. On Wednesday nights, you offer a special of “Buy
one dinner, get one free dinner—of equal or lesser value.” Michael and Wayne come in for the
special. Michael chooses chicken Parmesan for
$15
, and Wayne chooses a
$10
barbecue-combo
platter.
a. Excluding tax and tip, how much should each pay for his proportional share of the check?
seCtion iii • mULtipLiCation and division oF FraCtions 55
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