Deitz J.E., Southam J.L. Contemporary Business Mathematics for Colleges
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ESTIMATING WHEN MULTIPLYING
Is estimating important? Ye s, it is! In using a calculator to make computations, you may
possibly omit keystrokes, accidentally repeat keystrokes, or incorrectly shift or omit decimal
points. There is a great deal of difference between 3 times $14.87 and 3 times $1,487.
When working with calculations in any manner—such as entering items into a spread-
sheet, a cash register, or a calculator—you should always have a mental estimate of the
final product.
Mentally estimating an answer provides a good method for checking whether your
product is a reasonable answer.
14 Part 1 Fundamental Review
Estimating
5
Learning Objective
Estimate answers before doing
calculations.
1.4 Emphasize that students should
round numbers to zeros and mentally
arrive at an approximate answer in all
business calculations.
Estimating
Answers
Video
to Estimate a Multiplication Answer
1. Round both the multiplicand and multiplier to the nearest 10 for two-
digit numbers, the nearest 100 for three-digit numbers, the nearest 1,000
for four-digit numbers, etc.
2. Drop the zeros to the right of the nonzero numbers.
3. Mentally multiply the nonzero numbers to determine the base product.
4. Reinsert all zeros dropped in Step 2.
STEPS
EXAMPLE DD
Reinsert Zeros
Drop Base Estimated Real
Problem Round to Zeros Product Answer Answer
68 3 21 70 3 20 7 3 2 14 1,400 1,428
693 3 1,957 700 3 2,000 7 3 2 14 1,400,000 1,356,201
7,869 3 43,242 8,000 3 40,000 8 3 4 32 320,000,000 340,271,298
9 3 511,739 9 3 500,000 9 3 5 45 4,500,000 4,605,651
31 3 22 3 71 30 3 20 3 70 3 3 2 3 7 42 42,000 48,422
891 3 39 3 104 900 3 40 3 100 9 3 4 3 1 36 3,600,000 3,613,896
ESTIMATING WHEN DIVIDING
Before doing long division problems, estimate a whole-number answer. The process of
mentally estimating whole-number answers helps to avoid major and embarrassing errors.
to Estimate a Long Division Answer
1. Round both the divisor and the dividend to the nearest 10 for two-digit
numbers, the nearest 100 for three-digit numbers, the nearest 1,000 for
four-digit numbers, etc.
2. Drop the number of zeros common to both.
3. Mentally divide the remaining divisor into the remaining dividend.
STEPS
EXAMPLE EE
Estimated Real
Pr
oblem Round to Drop Zeros Answer Answer
77 4 39 80 4 40 8 4 4 2 1.97
196 4 63 200 4 60 20 4 6 3* 3.11*
2,891 4 114 3,000 4 100 30 4 1 30 25.36
592 4 29 600 4 30 60 4 3 20 20.41
18,476 4 384 20,000 4 400 200 4 4 50 48.11
917 4 186 900 4 200 9 4 2 4* 4.93*
21,716,412 4 40,796 20,000,000 4 40,000 2,000 4 4 500 532.32
99,624 4 476 100,000 4 500 1,000 4 5 200 209.29
29,200 4 316 30,000 4 300 300 4 3 100 92.41
Chapter 1 Fundamental Processes 15
✔
CONCEPT CHECK 1.5
ESTIMATING MULTIPLICATION ANSWERS
Reinsert Zeros
Drop Base Estimated Real
Pr
oblem Round to
Zeros Product Answer Answer
47 3 31 50 3 30 5 3 3 15 1,500 1,457
498 3 221 500 3 200 5 3 2 10 100,000 110,058
ESTIMATING DIVISION ANSWERS
Estimated Real
Problem Round to Drop Zeros Answer Answer
88 4 29 90 4 30 9 4 3 3 3.03
9,811 4 394 10,000 4 400 100 4 4 25 24.90
COMPLETE ASSIGNMENT 1.5.
*Because 20 4 6 and 9 4 2 would result in remainders, we can reasonably assume that the real number
will be larger.
addend dividend multiplicand remainder
credit balance divisor multiplier subtrahend
cross-checking factors product sum
difference minuend quotient
Chapter Terms for Review
Try Microsoft
®
Excel
Tr y working the problems using the Microsoft Excel templates found on your student
CD. Solutions for the problems are also shown on the CD.
16 Part 1 Fundamental Review
THE BOTTOM LINE
Summary of chapter learning objectives:
Learning Objective
1.1
Use shortcuts to add rapidly and accurately.
Example
Add the following, using the technique indicated.
Number Repeated Counting
combinations digits by tens
1. 8 2. 18 3. 52 4. 23
262 58 41
343 57 37
227 52 56
1
5 1 80 1 51 1 42
Add and then check by adding both vertically and horizontally.
5. 22 1 54 1 63 1 37 5
27 1 82 1 44 1 19 5
83 1 39 1 72 1 12 5
91
1 71 1 21 1 84 5
__ 1 __ 1 __ 1 __ 5
Answers: 1. 20 2. 230 3. 270 4. 199 5. 821 6. 94 7. 118 8. 35 9. 518 10. 32,461 11. 43,700
12. 8,790 13. 8,850 14. 42,300
1.2
Use shortcuts to subtract rapidly and accurately.
Subtract the following and then check by addition.
6. 228 7. 335
2
134 1134 2217 1217
Subtract horizontally and check.
8. 53 9. 245 2 130 5
2
18 118 432 2 212 5
381 2 270 5
183
2 111 5
25
1.3
Use shortcuts to multiply rapidly and accurately.
Multiply. Multiplying by numbers ending in zero
10. 227 11. 437 12. 879
3
143 3100 310
Multiplying by 25 Multiplying by 50
13. 354 14. 846
3
25 350
THE BOTTOM LINE
Chapter 1 Fundamental Processes 17
Summary of chapter learning objectives:
Learning Objective
1.4
Use shortcuts to divide rapidly and
accurately.
Example
Divide and check the Dividing by numbers
answer by multiplication. ending in 0
15. 16. 8,430 4 10 5
27 17. 127,400 4 100 5
3
Dividing when both divisor and dividend end with zeros
18. 7,400 4 200 5
19. 53,200 4 400 5
20. 140,000 4 2,000 5
27q1,512
Answers: 15. 56 16. 843 17. 1,274 18. 37 19. 133 20. 70 21. 50 3 30; 5 3 3 5 15; 1,500; 1,457
22. 500 3 200; 5 3 2 5 10; 100,000; 110,058 23. 90 4 30; 9 4 3; 3; 3.03
24. 10,000 4 400; 100 4 4; 25; 24.90
1.5
Estimate answers before doing calculations.
Estimate these multiplication answers. Show your rounding, dropping of
zeros with base product, estimated answer, and real answer.
Dropped
Zeros
Round and Base Estimated Real
Problem to Product Answer Answer
21. 47 3 31
22. 498 3 221
Estimate these division answers. Show your rounding, dropping of zeros,
estimated answer, and real answer.
Round Drop Estimated Real
Problem to Zeros Answer Answer
23. 88 4 29
24. 9,811 4 394
SELF-CHECK
Review Problems for Chapter 1
18 Part 1 Fundamental Review
1 8 1 9 1 3 1 12 1 6 5
2 32 1 47 1 36 1 12 5
17 1 22 1 17 1 11 5
14 1 98 1 47 1 81 5
77 1 62 1 21 1 44 5
5
3 9,078
26,382
4 717 4 14 5
5 98 3 13 5
6 789 4 36 5
7 842 4 200 5
8 974 4 12 5
9 5
10 2,006 3 304 5
11 395 4 79 5
12 800 4 25 5
13 4,000,000 4 400 5
14 $370 2 $148 5
$422 2 $109 5
$982 2 $777 5
$ 2 $ 5
15 1,472
1328
16 704 3 1,002 5
17 704 4 25 5
18 16,000 4 25 5
19 6,000,006 4 300 5
20 77,777 4 707 5
27q876
Estimate answers for each of the following.
Answers to the Self-Check can be found in Appendix B at the back of the text.
21 78 3 29 5
22 103 3 19 5
23 397 3 200 5
24 3,982 3 99 5
25 1,503 3 600 5
26 396 4 79 5
27 892 4 29 5
28 9,891 4 480 5
29 3,111 4 59 5
30 6,219 4 3,114 5
Chapter 1 Fundamental Processes 19
Assignment 1.1: Addition
Name
Date Score
A (10 points) Add the following.Where possible, use combinations of 10. (1 point for each correct answer)
1. 17 2. 41 3. 19 4. 34 5. 97 6. 50 7. 72 8. 82 9. 38 10. 63
43 29 54 33 44 54 99 43 39 37
35 17 14 43 33 54 99 47 22 44
42 36 81 37 76 47 89 93 45 36
43 44 28 36 32 59 47 58 47 24
37 15 11 34 72 54 63 34 25 21
23 56 43 32 34 55 40 22 13 19
58 62 51 38 76 55 62 46 29 25
0
12 066 076 032 027 035 068 073 079 075
Score for A (10)
B (10 points) Add the following. (1 point for each correct answer)
11. 209 12. 782 13. 127 14. 920 15. 347 16. 852 17. 251 18. 885 19. 275 20. 773
301 280 145 751 399 428 271 115 342 417
116 438 665 359 354 112 244 316 342 200
214 473 818 822 334 238 234 584 898 416
0
375 0 655 0 682 0 807 0 192 0 959 0 589 0 736 0 505 0 204
Score for B (10)
C (10 points) Add the following. (1 point for each correct answer)
21.
248.28 22. 201.22 23. 234.81 24. 238.69 25. 326.52
820.14 513.14 371.60 982.30 217.38
306.80 250.54 271.37 376.48 267.34
0,
521.98 2,647.55 0,408.55 0,728.90 118.66
26. 703.91 27. 126.92 28. 442.71 29. 535.13 30. 233.48
422.38 32.15 71.93 44.78 607.22
721.05 873.19 416.90 208.17 211.25
0,
446.21 0,872.52 0,236.19 6,481.29 0,211.25
Score for C (10)
310 366 377 319 491 463 639 498 337 344
1,215 2,628 2,437 3,659 1,626 2,589 1,589 2,636 2,362 2,010
1,897.20 3,612.45 1,286.33 2,326.37 929.90
2,293.55 1,904.78 1,167.73 7,269.37 1,263.20
1
Learning Objective
D (10 points) Add the following. Use the count-by-10s-and-add-the-1s method. (1 point for each
correct answer)
31. 10.76 32. 20.43 33. 33.79 34. 45.86 35. 33.27 36. 11.43 37. 88.71 38. 94.32 39. 55.93 40. 22.79
31.43 82.76 42.56 22.18 98.21 27.43 56.32 74.23 10.70 43.28
88.33 30.42 12.70 33.81 90.01 11.51 83.70 21.44 30.46 12.48
33.08 64.22 21.20 10.04 11.33 21.48 44.12 63.01 47.05 53.20
0
12.33 0
56.03 022.19 080.31 033.04 11.80 23.51 034.20 080.11 030.22
Score for D (10)
E (30 points) Business Application.The following is the first part of a weekly sales summary—the Weekly
Sales Report for the computer department. Complete the totals, both horizontal and vertical, and verify
your addition by comparing the vertical and horizontal grand totals. (2 points for each column/row; 4
points for grand total)
DEPARTMENT SALES REPORT
Week of December 11–17, 20XX
Department: COMPUTERS
SALESPERSON SUN MON TUE WED THU FRI SAT TOTAL
Whalen $3,443 — — $8,643 $3,176 $7,885 $9,378
Tsao — $8,772 — $9,483 $7,339 $8,113 $9,771
Culver $8,722 $2,443 $3,114 $5,729 $6,193 — —
Hernandez $6,117 $8,783 — — $5,685 $9,473 $11,492
Ingake — $3,114 $8,492 $7,652 $3,994 $14,119 $12,378
Greenberg — — $5,141 $2,739 $8,941 $2,836 $10,242
Total
Score for E (30)
F (30 points) Business Application. The following is the second part of the weekly sales summary—the
Consolidated Sales Report for the entire store. Fill in the figures from the Department Sales Report and
complete the totals, both horizontal and vertical.Verify your addition by comparing the horizontal and
vertical grand totals. (2 points for each column/row; 2 points for grand total)
STORE SALES REPORT
Week of December 11–17, 20XX
DEPARTMENT SUN MON TUE WED THU FRI SAT TOTAL
Home Audio 3,465 1,147 1,523 2,403 1,773 2,873 3,432
Auto Audio 1,278 1,785 1,713 2,117 2,563 3,499 9,971
Video/TV 15,230 12,377 10,429 9,384 8,773 11,245 13,486
Computers 18,282 23,112 16,747 34,246 35,328 42,426 53,261
Telecomm 849 722 531 733 1,012 1,239 1,375
Games 882 248 379 287 415 978 1,015
Repairs 732 892 384 658 981 1,043 1,774
Total
Score for F (30)
20 Part 1 Fundamental Review
Assignment 1.1 Continued
175.93 253.86 132.44 192.20 265.86 83.65 296.36 287.20 224.25 161.97
$18,282 $23,112 $16,747 $34,246 $35,328 $42,426 $53,261 $223,402
$32,525
$43,478
$26,201
$41,550
$49,749
$29,899
16,616
22,926
80,924
223,402
6,461
4,204
6,464
40,718 40,283 31,706 49,828 50,845 63,303 84,314 360,997
Chapter 1 Fundamental Processes 21
Assignment 1.2: Subtraction
Name
Date Score
A (18 points) Subtract the following. (1 point for each correct answer)
1. 77 2. 90 3. 72 4. 63 5. 84 6. 38 7. 92 8. 83 9. 30
2
16 217 225 229 248 249 216 265 214
10. 39 11. 20 12. 13 13. 73 14. 63 15. 68 16. 99 17. 57 18. 27
2
36 213 226 214 219 239 227 243 239
Score for A (18)
B (12 points) Subtract the following.Then check your subtraction by adding the subtrahend and the
difference and comparing your total to the minuend. (2 points for each correct answer)
19. 584 20. 963 21. 103 22. 714 23. 616 24. 9,999
2
173 2874 2310 230 2333 23,264
Score for B (12)
C (6 points) Subtract the following. (1 point for each correct answer)
25. $97.17 26. $0.79 27. $71.69 28. $43.21 29. $80.41 30. $99.32
2
23.19 20.88 210.87 247.18 241.80 218.66
Score for C (6)
D (9 points) Subtract the following. (1 points for each correct answer)
31. $2,011.11 32. $964.38 33. $9,011.09 34. $7,430.29 35. $3,385.03 36. $1,029.27
2
3,400.07 2201.83 2795.08 22,597.73 2233.42 0289.27
Score for D (9)
E (15 points) Subtract the following. Sometimes a double subtraction is necessary.The following prob-
lems are of this type. (3 points for each correct final answer)
37. $477.09 38. $11,739.93 39. $734.12 40. $745.89 41. $1,837,042.03
0
2564.27 23,142.18 2672.18 2250.15
00
26,218.18
02124.13 21,694.25 213.14 2224.13 00239,917.16
Score for E (15)
1
2
61 73 47 34 36 (11) 76 18 16
3 7 (13) 59 44 29 72 14 (12)
2411 2089 0(207) 0684 2283 26,735
584 963 103 714 616 9,999
$73.98 ($0.09) $60.82 ($3.97) $38.61 $80.66
($1,388.96) $762.55 $8,216.01 $4,832.56 $3,151.61 $940.00
($87.18) 8,597.75 61.94 495.74 1,830,823.85
($211.31) $6,903.50 $48.80 $271.61 $1,790,906.69
2
Learning Objective
F (20 points) Business Application.In many cases, multiple subtractions are required to complete a
business transaction. (1 point for each intermediate answer; 2 points for each final answer)
WINTER CATALOG CLEARANCE SALE ON SOFTWARE AND GAMES
10% REDUCTIONS ON CATALOG ORDERS
10% PREFERRED CUSTOMER DISCOUNTS
MAIL-IN REBATE OFFERS
Item Sierra Half-Life The Sims 2 Grand Theft Auto Street Legal Zoo Tycoon
List price $43.95 $45.70 $42.25 $49.95 $53.75
Less 10% catalog rate 24.40 24.57 24.23 25.00 25.38
Less 10% preferred 23.96 24.11 23.80 24.50 24.84
customer rate
Mail2in rebate 27.50 26.25 27.50 26.75 25.75
Your price
Score for F (20)
G (20 points) Business Application. Maintaining a budget involves both addition and subtraction. Keeping
a budget sometimes involves a continuous record of cash income and expenses. Study the example and
then complete the balances. (2 points for each balance)
Date Subtract Add
2/1/98 To Expenses Income Balance
$1,475.38
2/2/98 Salary income $700.00 2,175.38
2/3/98 Hinson Real Estate $550.00 1,625.38
2/5/98 PG&E 23.22
2/6/98 Pacific Bell 18.76
2/6/98 Macy’s 43.22
2/10/98 Chevron 15.75
2/16/98 Salary income $700.00
2/17/98 Fitness USA 25.00
2/18/98 John Simms, D.D.S. 30.00
2/23/98 Prudential Insurance 17.73
2/25/98 Visa 85.42
2/27/98 General Motors Finance 257.87
Score for G (20)
22 Part 1 Fundamental Review
Assignment 1.2 Continued
39.55 41.13 38.02 44.95 48.37
35.59 37.02 34.22 40.45 43.53
$28.09 $30.77 $26.72 $33.70 $37.78
1,602.16
1,583.40
1,540.18
1,524.43
2,224.43
2,199.43
2,169.43
2,151.70
2,066.28
1,808.41
Chapter 1 Fundamental Processes 23
Assignment 1.3: Multiplication
Name
Date Score
A (12 points) Multiply the following. ( point for each correct answer)
1. 2 3 13 5 2. 7 3 17 5 3. 14 3 52 5 4. 22 3 22 5
5. 9 3 10 5 6. 5 3 15 5 7. 15 3 16 5 8. 60 3 7 5
9. 8 3 9 5 10. 6 3 12 5 11. 12 3 12 5 12. 55 3 9 5
13. 6 3 8 5 14. 8 3 12 5 15. 4 3 20 5 16. 62 3 70 5
17. 6 3 6 5 18. 7 3 22 5 19. 8 3 11 5 20. 14 3 700 5
21. 2 3 14 5 22. 9 3 22 5 23. 8 3 17 5 24. 70 3 70 5
Score for A (12)
B (24 points) Find the products. (2 points for each correct answer)
25. 1,728 26. 3,026 27. 38,246 28. 5,017 29. 3,600 30. 8,179
0
,3.42 0003.372 00,03.8,297 0003.201 0003.300 0,03.81
31. 8,222 32. 67,406 33. 1,236 34. 27,000 35. 8,125 36. 4,007
0
003.509 00,03.3,006 0,3.444 00003.420 0003.279 0003.308
Score for B (24)
C (10 points) Multiply by using shortcuts. (2 points for each correct answer)
37. 3,684 38. 4,999 39. 6,642 40. 3,212 41. 1,500
0
03.50 00,3.50 003.25 003.50 0,3.25
Score for C (10)
D (18 points) Multiply the three factors. (2 points for each final product)
42. 33 3 32 3 31 5 43. 51 3 9 3 60 5 44. 45 3 45 3 45 5
45. 14 3 100 3 7 5 46. 915 3 40 3 20 5 47. 10 3 10 3 10 5
48. 30 3 30 3 30 5 49. 17 3 34 3 1,013 5 50. 1,500 3 9 3 3 5
Score for D (18)
40,500585,51427,000
1,000732,0009,800
91,12527,54032,736
4,90013619828
9,8008815436
4,340809648
4951447272
4202407590
48472811926
1
2
72,576 1,125,672 317,327,062 1,008,417 1,080,000 662,499
4,184,998 202,622,436 548,784 11,340,000 2,266,875 1,234,156
184,200 249,950 166,050 160,600 37,500
3
Learning Objective