Deitz J.E., Southam J.L. Contemporary Business Mathematics for Colleges
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E (12 points) Complete each group of five multiplication problems and then add the five products. (1 point
for each correct answer)
51. 12 3 12.00 5 57. 21 3 7 3 16 5
52. 27 3 8.16 5 58. 13 3 101 3 22 5
53. 104 3 3.52 5 59. 33 3 14 3 7 5
54. 6 3 92.92 5 60. 99 3 11 3 100 5
55. 55 3 32.50 5 61. 3 3 88 3 100 5
56. Total 5 62. Total 5
Score for E (12)
F (24 points) Business Application.Complete the merchandise inventory TOTAL column. (1 point for each
correct total; 8 points for correct grand total)
MERCHANDISE INVENTORY
JUNE 30, 20xx
Stock Number Description Price # in Stock Total
G473-2 Linspire 4.5 $39.99 58
G763-4 Spysweeper $39.99 172
G865-A Encarta $49.95 98
G2238-1 Turbo Tax $34.99 225
G873-2 Ever Quest 2 $42.75 88
S876-3 Microsoft Word $98.77 178
S4433 Uninstaller 4 $32.59 85
S887-32 Doom 3 $45.79 110
S4536 Netscape Navigator $38.79 100
S1322 Norton Utilities 7.0 $67.85 68
S458-2 Quicken $27.75 205
S5382 City of Heros $95.69 80
E5673-E Typing Tutor $26.59 108
E82-18 Atari Atar $52.49 25
E2442 Adobe 6 $45.29 307
E3578-1 Perfect Spanish $44.79 80
TOTAL
Score for F (24)
$94,623.61
$ 3,583.20
$13,904.03
$ 1,312.25
$ 2,871.72
$ 7,655.20
$ 5,688.75
$ 4,613.80
$ 3,879.00
$ 5,036.90
$ 2,770.15
$17,581.06
$ 3,762.00
$ 7,872.75
$ 4,895.10
$ 6,878.28
$ 2,319.42
169,7723,075.42
26,4001,787.50
108,900557.52
3,234366.08
28,886220.32
2,352144.00
24 Part 1 Fundamental Review
Assignment 1.3 Continued
Chapter 1 Fundamental Processes 25
Assignment 1.4: Division
Name
Date Score
A (10 points) Divide the following problems mentally. ( point for each correct quotient)
1. 72 4 6 5 2. 75 4 5 5 3. 66 4 22 5
4. 110 4 5 5 5. 126 4 3 5 6. 189 4 21 5
7. 88 4 22 5 8. 144 4 12 5 9. 360 4 20 5
10. 135 4 9 5 11. 990 4 33 5 12. 361 4 19 5
13. 156 4 12 5 14. 900 4 15 5 15. 1,782 4 18 5
16. 84 4 12 5 17. 104 4 2 5 18. 357 4 17 5
19. 126 4 7 5 20. 315 4 15 5
Score for A (10)
B (10 points) Divide by shortcut methods. Express remainders in parentheses. (1 point for each correct
answer)
21. 1,818 4 333 5 22. 107,300 4 100 5 23. 97,600 4 100 5
24. 2,200 4 100 5 25. 7,800 4 20 5 26. 6,450 4 320 5
27. 9,005 4 100 5 28. 387 4 10 5 29. 7,600 4 1,000 5
30. 3,250,000 4 10,000 5
Score for B (10)
C (50 points) Divide. Show the remainder in parentheses after the whole number in the quotient.
(2 points for each correct answer)
31. 32. 33. 34.
35. 36. 37. 38.
39. 40. 41. 42.
43. 44. 45. 46.
47. 48. 49. 50.
51. 52. 53. 54.
55.
Score for C (50)
29q58,004,316
65q372,000 66q17,209 1,014q20,016 66q73,428
26q111,013 51q100 54q78,540 6q$13.20
13q$67,209 88q97,817 111q34,173 700q362,497
9q818,173 506q10,238 77q12,770 926q926,007
33q97,382 271q50,001 23q478 36q6,436
7q4,919
23q14,07613q2,79521q478
325
7 (600)38 (7)90 (5)
20 (50)39022
9761,0735 (153)
2118
21527
996013
193015
18124
94222
31512
1
2
22 (16) 215
612
702 (5)
2,950 (32)
90,908 (1)
$5,169 (12)
4,269 (19)
5,723 (5)
184 (137)
20 (118)
1,111 (49)
1 (49)
260 (49)
20 (18)
165 (65)
307 (96)
1,454 (24)
19 (750)
178 (28)
1,000 (7)
517 (597)
$2.20
1,112 (36)
2,000,148 (24)
4
Learning Objective
D (10 points) Divide and check the following problems. (2 points for each correct answer)
56. 57. 58. 59. 60.
Check:
33 3 3 3
55 5 5 5
Score for D (10)
E (20 points) Business Application. As an estimator for a printing company, you must estimate the paper
costs for printing jobs. Paper is priced by the ream, which is 500 pages. Compute the paper costs of the
jobs. (1 point for each correct computation)
No. of Booklets No. of Pages Total Pages Reams of Paper Cost per Ream Total Paper Cost
250 66 $2.00
120 150 $4.25
75 220 $4.83
110 250 $3.75
25 280 $3.15
30 250 $4.10
Total reams Total paper cost
Score for E (20)
$690.24186
61.50157,500
44.10147,000
206.255527,500
159.393316,500
153.003618,000
$66.003316,500
7112,2147,2841,3951,364
1 391 91 16
6722,2057,268
4221923122
16105794562
42
q
711
21
q
2,214 92
q
7,284 31
q
1,39522
q
1,364
26 Part 1 Fundamental Review
Assignment 1.4 Continued
62
45
79 (16)
105 (9)
16 (39)
Chapter 1 Fundamental Processes 27
Assignment 1.5: Estimating
Name
Date Score
A (60 points) Estimate an answer for each of the following problems. Show your rounding, dropping of
zeros with base product, and final estimate. (1 point for each correct answer)
Problem Round to Dropped Zeros and Base Product Estimated Answer
1. 1,095 3 427
2. 78,221 3 6,099
3. 34,007 3 80
4. 56 3 1,528
5. 18 3 2,855 3 93
6. 20 3 17 3 19
7. 2,997 3 13
8. 41 3 19 3 3
9. 212 3 101 3 99
10. 23 3 10,322
11. 777 3 777
12. 29,301 3 21
13. 72,111 3 108
14. 13 3 100 3 6
15. 99 3 99 3 99
16. 28 3 42
17. 111 3 39
18. 7 3 99
19. 204 3 17
20. 11 3 12 3 13
Score for A (60)
1,000
1 3 1 3 1 5 110 3 10 3 10
4,000
2 3 2 5 4200 3 20
700
7 3 1 5 77 3 100
4,000
1 3 4 5 4100 3 40
1,200
3 3 4 5 1230 3 40
1,000,000
1 3 1 3 1 5 1100 3 100 3 100
6,000
1 3 1 3 6 5 610 3 100 3 6
7,000,000
7 3 1 5 770,000 3 100
600,000
3 3 2 5 630,000 3 20
640,000
8 3 8 5 64800
3 800
200,000
2 3 1 5 220 3 10,000
2,000,000
2 3 1 3 1 5 2200 3 100 3 100
2,400
4 3 2 3 3 5 2440 3 20 3 3
30,000
3 3 1 5 33,000 3 10
8,000
2 3 2 3 2 5 820 3 20 3 20
5,400,000
2 3 3 3 9 5 5420 3 3,000 3 90
120,000
6 3 2 5 1260 3 2,000
2,400,000
3 3 8 5 2430,000 3 80
480,000,000
8 3 6 5 4880,000 3 6,000
400,000
1
3 4 5 41,000 3 400
5
Learning Objective
B (20 points) Estimate an answer for each of the following problems. Show your rounding, dropping of
zeros with base product, estimated answer, and real answer. (1 point for each correct answer)
Dropped Zeros
ProblemRound to and Base Product Estimated Answer Real Answer
21. 883 3 294
22. 42,100 3 412
23. 19,965 3 492
24. 89 3 33
25. 689 3 203
Score for B (20)
C (20 points) Estimate an answer for each of the following division problems. Show your rounding, drop-
ping of zeros, estimated answer, and real answer. (1 point for each correct answer)
ProblemRound to Drop Zeros Estimated Answer Real Answer
26. 123 4 41
27. 612 4 12
28. 4,836 4 78
29. 19,760 4 95
30. 21,390 4 690
Score for C (20)
3130
210 4 721,000 4 700
208200
200 4 120,000 4 100
6260
480 4 84,800 4 80
5160
60 4 1600 4 10
3
3
12 4 4
120 4 40
139,867
140,000
7 3 2 5 14700 3 200
2,9372,700
9 3 3 5 2790 3 30
9,822,78010,000,000
2 3 5 5 1020,000 3 500
17,345,20016,800,000
42 3 4 5 16842,000 3 400
259,602270,000
9 3 3 5 27900 3 300
28 Part 1 Fundamental Review
Assignment 1.5 Continued
Fractions
Chapter 2 Fractions 29
Learning Objectives
By studying this chapter and completing all assignments, you will be able to:
Learning Objective
Change improper fractions and mixed numbers.
Learning Objective
Change fractions to lower and higher terms.
Learning Objective
Add fractions and mixed numbers.
Learning Objective
Subtract fractions and mixed numbers.
Learning Objective
Multiply fractions, mixed numbers, and whole numbers.
Learning Objective
Divide fractions, mixed numbers, and whole numbers.
2
1
Learning Objective
2
Learning Objective
3
Learning Objective
4
Learning Objective
5
Learning Objective
6
Learning Objective
Fractions are a natural part of cultures around the world. Very young children who can-
not yet read learn simple fractions such as one half and one third when their parents
teach them about sharing a candy bar or a pizza. Before the development of inexpensive
handheld calculators, fractions were more important than they are today because they
permitted shortcuts in arithmetic. However, fractions are still important in some indus-
tries. Moreover, the rules of fractions will always remain very important in algebra and
higher mathematics.
30 Part 1 Fundamental Review
A restaurant cuts its medium-sized pizzas into six pieces. Each piece is “one sixth”of
the pizza. If you take two pieces of pizza, you have “two sixths” of the pizza. Using num-
bers, two sixths can be written as . If you buy two medium-sized pizzas and cut each
pizza into six pieces, you will have twelve pieces, or twelve sixths, written as . If you eat
one of the twelve slices of pizza, eleven pieces remain, or eleven sixths, written as .
In the three fractions , , and , the bottom number (6) is called the denominator.
The top numbers (2, 12, and 11) are called numerators. is called a proper fraction
because the numerator (2) is smaller than the denominator (6). and are called
improper fractions because the numerators are greater than, or equal to, the denominators.
Notice that represents one whole pizza plus of the second pizza. can be written
as which is called a mixed number because there is a whole number part (1) and a
proper fraction .
Figure 2-1 illustrates these concepts. Diagram b represents a proper fraction. Diagrams
a, c, and d all represent improper fractions. Diagram d also represents a mixed number.
(
5
6
)
1
5
6
11
6
5
6
11
6
11
6
12
6
2
6
11
6
12
6
2
6
11
6
12
6
2
6
Notation and Vocabulary of Fractions
Figure 2-1
Using simple arithmetic, we can change improper fractions to mixed numbers and mixed
numbers to improper fractions.
Changing Improper Fractions and
Mixed Numbers
Learning Objective
1
Learning Objective
Change improper fractions and
mixed numbers.
2.1 The line separating the numerator
and denominator is often called the
“fraction bar.”Encourage students to
write the fraction bar as a horizontal
line instead of a slanted line.Because
of printing fonts,even in this book
fractions are sometimes written with
a slanted line,such as 1/4.However,
when someone is writing by hand,
using a dull pencil,it is not uncommon
to confuse 2 1/4 with 21/4.
a. 1 whole pizza b. 2 pieces c. 2 whole pizzas d.1 piece missing 5
11
6
5 1
5
6
5
12
6
5
2
6
5
6
6
© KELLY CLINE/ISTOCKPHOTO
INTERNATIONAL
EXAMPLE B
Change to an improper fraction.
2 3 6 Thus,
Note: Refer to Point B in Figure 2-2 to see where these numbers appear on a ruler.
3
1
2
5
6 1 1
2
5
7
2
STEPS 2, 3STEP 1
3
1
2
Chapter 2 Fractions 31
to Change an Improper Fraction to a Mixed Number
1. Divide the numerator by the denominator.
2. The quotient is the whole-number part of the mixed number.
3. The remainder is the numerator of the fraction part.
4. The original denominator is the denominator of the fraction part.
STEPS
2.2 Remind students that 3 means
3 .
1
2
1
2
Figure 2-2
12
12
16
C
AB
6
8
=
3
4
=
1
11
8
=
3
8
3
222
7
2
=
1
2
3
12
16
D
6
8
=
3
4
=
4
to Change a Mixed Number to an Improper Fraction
1. Multiply the denominator of the fraction part by the whole number.
2. Add the numerator of the fraction part to the product of Step 1. The sum
is the numerator of the improper fraction.
3. The denominator of the fraction of the mixed number is the denomina-
tor of the improper fraction.
STEPS
EXAMPLE A
Change to a mixed number.
Thus, 1
8
3
Note: Refer to Point A in Figure 2-2 to see where these numbers appear on a ruler.
3
8
11
8
8q11
1 R3
11
8
STEPS 2, 3, & 4STEP 1
11
8
Read Point C on the ruler shown in Figure 2-2. Point C marks the distance of an inch,
but it could also be read as or of an inch. Thus , , and are three ways to write the
same value. We say that is in lower terms and is in higher terms because 8 is a
smaller denominator than 16. We also say that is in lowest terms because it cannot be
changed to any lower terms. When we change a fraction to lower terms, we say that we
are reducing the fraction to lower terms. If we change a mixed number such as to ,
we say that we have reduced the mixed number to its lowest terms. When we change
fractions to higher terms, we say that we are raising them to higher terms.
2
3
4
2
12
16
3
4
12
16
6
8
3
4
6
8
12
16
3
4
6
8
12
16
32 Part 1 Fundamental Review
Changing Fractions to Lower and Higher Terms
to Reduce a Fraction to Lowest Terms
1. Divide both the numerator and the denominator by a common divisor
greater than 1 to arrive at a reduced fraction.
2. If necessary, repeat Step 1 until the fraction cannot be reduced any
further.
Note: If a fraction’s numerator and denominator have no common divisor
greater than 1, the fraction is already in lowest terms.
STEPS
EXAMPLE C
Reduce to lowest terms.
or else
Note that dividing by 4 once is faster than dividing by 2 twice. Always use the greatest
common divisor that you can find.
12
16
5
12 4 4
16 4 4
5
3
4
12
16
5
12 4 2
16 4 2
5
6
8
5
6 4 2
8 4 2
5
3
4
12
16
2
Learning Objective
Change fractions to lower and
higher terms.
to Raise a Fraction to Higher Terms
1. Divide the new denominator by the old denominator. The quotient is the
common multiplier.
2. Multiply the old numerator by the common multiplier.
3. Multiply the old denominator by the common multiplier.
STEPS
EXAMPLE D
Raise to twenty-fourths.
24 4 6
So,
3
4
5
3 3 6
4 3 6
5
18
24
STEPS 2 & 3
3
4
5
?
24
STEP 1
3
4
Reducing and
Raising Fractions
Video
2.3 The word cancel often is used,as in
“cancel a common factor.”Emphasize
that the word cancel means to divide
out the common factor.The word can-
cel is not wrong,but some students
simply cross out common digits
without thinking.An interesting
example is .
If the two 6s are “crossed out,”the
result is ,which is correct nu-
merically.Naturally,however,that
method does not work with most
other fractions—such as ,for
instance .You can challenge
students to find other examples that
do work.
16
96
2
1
9
16
96
16
64
5
1
4
16
64
Fractions and mixed numbers are all numbers, so they can be added and subtracted just
like whole numbers. However, when you add fractions and/or mixed numbers, you must
first find a common denominator. This is a denominator shared by all of the fractions
and it also will be the denominator of the fraction part of the answer.
The smallest common denominator possible is called the least common denomina-
tor. If the least common denominator is not easily apparent, it may be quicker to use the
first common denominator that you can discover and then reduce the answer to lowest
terms. The product of all of the denominators always will be a common denominator,
but very often there will be a smaller common denominator.
Chapter 2 Fractions 33
Adding and
Subtracting
Fractions and
Mixed Numbers
Video
to Add Two or More Fractions and/or Mixed Numbers
1. If necessary, change the fraction parts to fractions with common denomi-
nators. The common denominator is the denominator in the fraction
part of the answer.
2. Add the numerators to make the numerator of the fraction part of the
answer. If there are any whole-number parts, add them to make the
whole-number part of the answer.
3. If necessary, change an improper fraction to a mixed number and men-
tally add any whole number parts.
4. Reduce the fraction part of the answer to lowest terms.
STEPS
EXAMPLE E EXAMPLE F
Add and . Add and .
The fractions already have a A common denominator is 6 4 24.
common denominator of 8.
38
24
5 1
14
24
5 1
7
12
6
10
8
5 6 1 1
2
8
5 7
1
4
3
4
5
3 3 6
4 3 6
5
18
24
4
3
8
5
6
5
5 3 4
6 3 4
5
20
24
2
7
8
3
4
5
6
4
3
8
2
7
8
2.4 If time permits,you can experi-
ment.Give each student two problems:
Solve the first one by using the com-
mon denominator that is the product
of all of the denominators and then
reducing the answer to lowest terms;
solve the second one by first finding
the least common denominator (no
credit for using any other denomina-
tor).Have the students time them-
selves.Students will probably not be
uniformly quicker with one method or
the other.As an alternative,you could
let half the class solve problem 1 and
the other half solve problem 2.
1.
A common denominator is
15 6 10.
2.
Find the least common denominator;
then add.
5
14
1
7
10
1
4
35
7
15
1
5
6
1
9
10
Adding Fractions and Mixed Numbers
Add fractions and mixed numbers.
3
Learning Objective
STEP 1
STEP 2 STEP 3 STEP 4 STEPS 2, 3, & 4