1. Review of Whole Numbers and Integers
CHAPTER 1
Review of Whole Numbers and Integers

2. Read and round integers.
1-1
Learning Outcomes
Read whole numbers.
Write whole numbers.
Round whole numbers.
Read and round integers.

3. Read whole numbers
Section 1-1
Place Value and Our Number System
Our system of numbers, the decimal number system uses 10 symbols called digits:
0,1, 2, 3, 4, 5, 6, 7, 8, and 9.
Place-value system: a number system that determines the value of a digit by its position in a number.

4. Each group is called a period.
HOW TO:
Read whole numbers
Section 1-1
Place Value and Our Number System
Beginning with the ones place on the right, the digits are grouped with three digits in each group.
For example: 286,418,917
Each group is called a period.

5. Understanding place value
HOW TO:
Understanding place value
Section 1-1
Place Value and Our Number System
Each period has a name
Every period has a ones place, a tens place, and a hundreds place.
In a number, the first period from the left may have fewer than three digits.
In many cultures, the periods are separated by commas.

6. Understanding place value
HOW TO:
Understanding place value
Section 1-1
Place Value and Our Number System
Identify the period name of the leftmost group.
Read the three digit number from left to right.
Name the period.
4,693,107 would read four million six hundred ninety-three thousand one hundred seven

7. 34, 000, 892 Do not read or name a period that is all zeros.
Exceptions…
Section 1-1
Place Value and Our Number System
Do not read or name a period that is all zeros.
34,000,892 would read thirty-four million, eight hundred ninety-two.
Do not name the units period (892).
34,
000,
892

8. When reading whole numbers, remember…
HOW TO:
When reading whole numbers, remember…
Section 1-1
Place Value and Our Number System
The period name will be read at each comma.
Period names are read in the singular:
(“thousand” not “thousands”).
Hundreds is not a period name.
Do not say the word “and” when reading whole numbers.
Calculator displays ordinarily do not show commas; insert them when writing the number.

9. Begin recording digits from left to right.
1-1-2
Write whole numbers
Section 1-1
Place Value and Our Number System
Begin recording digits from left to right.
Insert a comma at each period name.
Every period after the first period must have three digits.
Insert zeros as necessary.

10. Eight million, nine hundred three thousand, four hundred twenty-two…
An Example…
Section 1-1
Place Value and Our Number System
Eight million, nine hundred three thousand, four hundred twenty-two…
8, million
903, thousand (units)
…is written 8,903,422.

11. Rounding to a specific place: Identify the place.
1-1-3
Round whole numbers
Section 1-1
Place Value and Our Number System
Rounding to a specific place:
Identify the place.
“nearest hundred”, for example.
Look at the digit immediately to the right.
Is it 5 or higher? Round up.
Is it 4 or lower? Specified digit stays the same.
All digits to the right of the specified place become zeros.

12. Round to the nearest hundred: 4,856 10,527 234,567 8,648,078 4,900
Examples…
Section 1-1
Place Value and Our Number System
Round to the nearest hundred:
4,856
10,527
234,567
8,648,078
4,900
10,500
234,600
8,648,100

13. Read and round integers
1-1-4
Read and round integers
Section 1-1
Place Value and Our Number System
In the business world we sometimes want to express numbers that are smaller than 0.
These are referred to as negative numbers.
When the set of whole numbers is expanded to include negative numbers, this set is called the set of integers.

14. Read and round integers
HOW TO:
Read and round integers
Section 1-1
Place Value and Our Number System
When reading integers:
The rules are the same as for reading whole numbers.
State the word negative or minus to read a number less than zero.
When rounding integers:
The rules are the same as for rounding whole numbers.

15. Read the number for the U.S. national debt:
An Example…
Section 1-1
Place Value and Our Number System
Read the number for the U.S. national debt:
–$18,936,042,802,503
Negative eighteen trillion, nine hundred thirty-six billion, forty-two million, eight hundred two thousand, five hundred three dollars.

16. Round the previous example to the nearest trillion:
An Example…
Section 1-1
Place Value and Our Number System
Round the previous example to the nearest trillion:
–$18,936,042,802,503
The trillions digit is 8.
–$18,936,042,802,503
The digit to the right is 9.
9 is more than 5, so increase the 8, by 1, to get 9. Replace all digits to the right of 2 with zeros.
–$19,000,000,000,000
The answer is –$19 trillion.

17. Add and subtract whole numbers. Add and subtract integers.
1-2
Learning Outcomes
Add and subtract whole numbers.
Add and subtract integers.
Multiply integers.
Divide integers.
Apply the standard order of operations to a series of operations.

18. The numbers being added. Sum or total
Key Terms…
Section 1-2
Place Value and Our Number System
Addends
The numbers being added.
Sum or total
The answer or result of addition.

19. Add and subtract whole numbers
1-2-1
Add and subtract whole numbers
Section 1-2
Operations With Whole Numbers and Integers
To add whole numbers, write the numbers in a vertical column, aligning digits according to their place values.
Beginning with the ones column, add the place digits.
Add, if necessary, to the tens column.
Repeat the operation, adding to the hundreds column, if necessary, until you have reached the farthest column of digits to the left.

20. Answer: 64,948 Add An Example… Add the ones column.
Section 1-2
Operations with Whole Numbers and Integers
Add 1 1 2 2
Add the ones column.
Place 8 at the bottom of the ones column.
Carry the 2 to the tens column.
Place the 4 in the tens column.
Carry the 2.
Finish the operation. 1 3 6 7 8 5 4 2 9 + __ = 6 4 9 4 8
Answer: 64,948

21. Estimate: to find a reasonable approximate answer for a calculation.
HOW TO:
Estimating
Section 1-2
Operations with Whole Numbers and Integers
Estimate: to find a reasonable approximate answer for a calculation.
Use estimating as a quick tool when an exact number is not required.
Round whole numbers to the place desired for an estimate.

22. What was the week’s total to the nearest hundred?
An Example…
Section 1-2
Operations with Whole Numbers and Integers
Sales for last week’s concession stand.
Monday: $219
Tuesday: $877
Wednesday: $455
Thursday: $614
Friday: $980
What was the week’s total to the nearest hundred?
$200 + $900 + $500 + $600 + $1000
= $3,200

23. Subtract whole numbers
HOW TO:
Subtract whole numbers
Section 1-2
Operations with Whole Numbers and Integers
When subtracting whole numbers, the order of the numbers is important.
Therefore, subtraction is not commutative.
9 – 4 ≠ 4 – 9
Grouping in subtraction is important.
Subtraction is not associative.
(8 – 3) – 1 = 5 – 1 = 4 but
8 – (3 – 1) = 8 – 2 = 6
4 ≠ 6

24. Minuend Subtrahend Difference Borrow Key Terms…
Section 1-2
Operations with Whole Numbers and Integers
Minuend
The beginning amount or number that a second number is being subtracted from.
Subtrahend
The number being subtracted.
Difference
The answer or result of subtracting.
Borrow
Regroup digits in the minuend by borrowing 1 from the digit to the left of the specified place, and adding 10 to the specified place.

25. Subtract Answer: 695 An Example…
Section 1-2
Operations with Whole Numbers and Integers
Borrow 1 from the ten column, add 10 to the ones column.
Subtract 8 from 13.
Borrow 1 from the hundreds column, add 10 to the tens column.
Subtract 9 from 18.
Borrow 1 from the thousands column.
Subtract 5 from 11.
Subtract 1 2 9 3 - 5 8 = 1 2 9 3 11 1 18 18 8 1 6 9 5
Answer: 695

26. Using rounding in subtraction
HOW TO:
Using rounding in subtraction
Section 1-2
Operations with Whole Numbers and Integers
Subtract 128 from 1,345 by rounding each number to the nearest hundred to estimate the difference.
128 would become 100.
1,345 would become 1,300.
The estimated difference would be 1,200.

27. Add and subtract integers
1-2-2
Add and subtract integers
Section 1-2
Operations with Whole Numbers and Integers
To add two negative integers, add the numbers without regard to the signs.
Assign a negative to the sum.
Last year Murphy’s Used Car Co. lost $23,000. This year they lost another $16,000.
What is the total loss?
–$23,000 + (–$16,000) = –$39,000
The two-year loss is –$39,000.

28. Add and subtract integers
HOW TO:
Add and subtract integers
Section 1-2
Operations with Whole Numbers and Integers
To add a positive and a negative integer, subtract the numbers without regard to the signs.
Look at the numbers without the signs.
Choose the larger of these numbers;
Assign the sum the sign of the larger number.

29. Jeremy has a bank balance of $47, then writes a check for $89.
An Example…
Section 1-2
Operations with Whole Numbers and Integers
Jeremy has a bank balance of $47, then writes a check for $89.
What is the new balance, including a $30 overdraft fee?
$47 + (–$89) = –$42
–$42 + (–$30) = –$72
The final balance is –$72.

30. Numbers can be multiplied in any order without affecting the result
HOW TO:
Multiply integers
Section 1-2
Operations with Whole Numbers and Integers
Numbers can be multiplied in any order without affecting the result
Commutative property of multiplication.
8 × 12 = 12 × 8
96 = 96

31. The number being multiplied. Multiplier The number multiplied by.
Key Terms…
Section 1-2
Operations with Whole Numbers and Integers
Multiplicand
The number being multiplied.
Multiplier
The number multiplied by.
Factor
Each number involved in multiplication.

32. The answer or result of multiplication. Partial product
Key Terms…
Section 1-2
Operations with Whole Numbers and Integers
Product
The answer or result of multiplication.
Partial product
The product of one digit of the multiplier and the entire multiplicand.

33. Multiply Multiplicand Multiplier Partial product Partial product
An Example…
Section 1-2
Operations with Whole Numbers and Integers
Multiply 7 9 x 2 3 1 5 8 _
Multiplicand
Multiplier 1
Partial product
Partial product
PRODUCT

34. Examples to try without a calculator…
Section 1-2
Operations with Whole Numbers and Integers
418 × 107 = ?
Answer: 44,726
88 × 120 = ?
Answer: 10,560
348 × 27 = ?
Answer: 9,396

35. 1-2-3
Multiply integers
Section 1-2
Operations with Whole Numbers and Integers
To multiply a negative and a positive integer, multiply the two integers without regard to the signs.
Assign a negative sign to the product.
What is the total loss generated from selling 87 frames each for $2 below cost?
87 × (−$2) = −$174
The total loss is −$174.

36. What is the product of (−16)(−3)?
HOW TO:
Multiply integers
Section 1-2
Operations with Whole Numbers and Integers
To multiply two negative or two positive integers, multiply the two integers without regard to the signs.
The product is positive.
What is the product of (−16)(−3)?
16 × 3 = 48
The product is positive and is 48.

37. A $40 tip is shared equally among 5 servers.
1-2-4
Divide integers
Section 1-2
Operations with Whole Numbers and Integers
Division is used to find the number of equal parts into which a whole quantity can be separated.
A $40 tip is shared equally among 5 servers.
How much does each server receive?
$40 ÷ 5 servers = $8 each.

38. The number being divided or the total quantity. Divisor
Key Terms…
Section 1-2
Operations with Whole Numbers and Integers
Dividend
The number being divided or the total quantity.
Divisor
The number to divide by.
Quotient
The answer or result of the operation.
Whole-number part of the quotient
The quotient without regard to its remainder.

39. The quotient of the partial dividend and the divisor.
Key Terms…
Section 1-2
Operations with Whole Numbers and Integers
Remainder of quotient
A number that is smaller than the divisor that remains after division is complete.
Partial dividend
The part of the dividend that is being considered at a given step of the process.
Partial quotient
The quotient of the partial dividend and the divisor.

40. That amount may be expressed as… A remainder (R 2). A fraction.
HOW TO:
Remainders
Section 1-2
Operations with Whole Numbers and Integers
There will be a remainder if an amount is too small to be further divided by the divisor.
For example: 152 ÷ 3 = 50 R 2
That amount may be expressed as…
A remainder (R 2).
A fraction.
A decimal.

41. HOW TO:
Divide integers
Section 1-2
Operations with Whole Numbers and Integers
1235 ÷ 5 = ?
STEP 1
Beginning with its leftmost digit, identify the first group of digits of the dividend that is larger than or equal to the divisor.
Is it 1? No.
Is it 12? Yes.
5 goes into 12 two times. Place the 2 above the 2 in the dividend.
MORE

42. HOW TO:
Divide integers
Section 1-2
Operations with Whole Numbers and Integers
1235 ÷ 5 = ?
STEP 2
Multiply 2 by the divisor. Place 10 under the 12 and subtract. The result is 2.
STEP 3
Bring down the following digit which is 3, and divide 5 into 23.
STEP 4
The result is 4. Place the 4 directly above the 3 in the dividend.
MORE

43. HOW TO:
Divide integers
Section 1-2
Operations with Whole Numbers and Integers
1235 ÷ 5 = ?
STEP 5
Multiply 4 by the divisor. Place 20 under the 23 and subtract. The result is 3.
STEP 6
Bring down the last digit, which is 5, and divide 5 into 35. The result is 7.
STEP 7
Place 7 directly above the 5. You have finished and the answer is 247.

44. Examples to try without a calculator…
Section 1-2
Operations with Whole Numbers and Integers
Adams-Duke Realty Company estimates that its losses for the year will be $36,000,000.
What is the average loss per month?
Answer: −$3,000,000
Divide the following: 63,500,000 ÷ 1,000
(mentally eliminate the ending zeros from both numbers)
Answer: 63,500

45. Apply the standard order of operations to a series of operations
1-2-5
Section 1-2
Operations with Whole Numbers and Integers
STEP 1
Perform all operations that are inside grouping symbols, such as parentheses.
STEP 2
Perform all multiplications and divisions as they appear from left to right.
STEP 3
Perform all additions and subtractions as they appear from left to right.

46. 15 – (4 + 7) = ? Answer: 4 (75 + 50 + 35 + 90) ÷ 5 = ? Answer: 50
Examples to try…
Section 1-2
Operations with Whole Numbers and Integers
15 – (4 + 7) = ?
Answer: 4
( ) ÷ 5 = ?
Answer: 50
45 − 4 × 9 = ?
Answer: 9

47. Exercise Set

48. EXERCISE SET
2. An automobile manufacturer claims to create more than twenty thousand direct jobs. Use digits to write this number.

49. EXERCISE SET
4. By its own claim, HFS, Inc., is the world’s largest hotel franchising organization. It claims to have five thousand, four hundred hotels with four hundred ninety-five thousand rooms in over seventy countries, and more than twenty percent of the franchises are minority-owned. Use digits to write each of the numbers.

50. Write the word name for the number.
EXERCISE SET
Write the word name for the number.
6. LVMH had a gain of $30,860,000,000 in a recent year. Show how you would read this number.
8. Delta Airlines had an annual loss of −$8,922,000,000 in a recent year. Show how you would read this number.

51. Round to the specified place. 10. 9,374 (nearest thousand)
EXERCISE SET
Round to the specified place.
10. 9,374 (nearest thousand)
,218 (nearest ten-thousand)
14. A color video surveillance system with eight cameras is priced at $3,899. Round this price to the nearest thousand dollars.

52. Round to the specified place.
EXERCISE SET
Round to the specified place.
16. A black-and-white video surveillance system with eight cameras is priced at $2,499. What is the price to the nearest hundred dollars?

53. Round to the first digit. 18. 3,784,809
EXERCISE SET
Round to the first digit.
18. 3,784,809
20. 2,063,948

54. EXERCISE SET
Add.

55. EXERCISE SET
Mentally estimate the sum by rounding each number to the first digit. Then find the exact sum.
26. 74,374
82,849
72,494
+ 89,219

56. EXERCISE SET
Mentally estimate the sum in Exercise 28 by rounding each number to the nearest hundred. Then find the exact sum.
854
324
+ 687

57. EXERCISE SET
30. Kiesha had the following test scores: 92, 87, 96, 85, 72, 84, 57, 98. What is the student’s total number of points?

58. EXERCISE SET
32. A furniture manufacturing plant had the following labor-hours in one week: Monday, 483; Tuesday, 472; Wednesday, 497; Thursday, 486; Friday, 464; Saturday, 146; Sunday, 87. Find the total labor-hours worked during the week.

59. EXERCISE SET
Estimate the difference by rounding each number to the first digit. Then find the exact difference.
34.
9,748
5,676

60. EXERCISE SET
Estimate the difference by rounding each number to the first digit. Then find the exact difference.
36.
83,748,194
27,209,104

61. EXERCISE SET
Estimate the difference by rounding each number to the first digit. Then find the exact difference.
38.
12,748
 5,438

62. EXERCISE SET
40. Sam Andrews has 42 packages of hamburger buns on hand but expects to use 130 packages. How many must he order?
42. Frieda Salla had 148 tickets to sell for a baseball show. If she has sold 75 tickets, how many does she still have to sell?

63. Add or subtract the integers as indicated. 44. (32) + (27)
EXERCISE SET
Add or subtract the integers as indicated.
44. (32) + (27)
 (12)
(58)
– (21)

64. Multiply and check the product. 52. 5,931  835
EXERCISE SET
Multiply and check the product.
,931
 835

65. Multiply and check the product. 54. 33  500
EXERCISE SET
Multiply and check the product.
 500

66. Multiply and check the product. 56. 5,565  839
EXERCISE SET
Multiply and check the product.
,565
 839

67. Multiply and check the product. 58. 283  3,000
EXERCISE SET
Multiply and check the product.
 3,000

68. EXERCISE SET
Mentally estimate the product in Exercise 60 by rounding each number to the first digit. Then find the exact product.
60. 7,489
 34

69. EXERCISE SET
Mentally estimate the product in Exercise 62 by rounding each number to the first digit. Then find the exact product.
 576

70. EXERCISE SET
64. A day-care center has 28 children. If each child eats one piece of fruit each day, how many pieces of fruit are required for a week (five days)?

71. EXERCISE SET
66. Auto Zone has a special on fuel filters. Normally, the price of one filter is $15, but with this sale, you can purchase two filters for only $27. How much can you save by purchasing two filters at the sale price?

72. Divide and check the quotient. 68. 1,232  16
EXERCISE SET
Divide and check the quotient.
68. 1,232  16

73. EXERCISE SET
Estimate the quotient in Exercise 70 by rounding the divisor to the first digit. Then find the exact quotient. Write the exact answer with a whole-number remainder.
70.

74. EXERCISE SET
Divide.
,000 ÷ 3,000
,000 ÷ 5,000

75. The dealer can make 285 packages.
EXERCISE SET
76. A parts dealer has 3,420 bolts. The bolts are packaged with 12 in each package. How many packages can be made?
3,420 ÷ 12 = 285
The dealer can make 285 packages.
78. A stack of countertops measures 238 inches. If each countertop is 2 inches thick, how many are in the stack?
238 ÷ 2 = 119
The stack has 119 countertops.

76. EXERCISE SET
80. Carissa’s Fashions sold 138 jackets at a loss of $7 ($7) each. What was her total loss?
138($7) = $966 loss
82. Soledad’s Tamale Shop had an annual loss of −$10,152. What was her average quarterly loss for each of the four quarters in the year?
−$10,152 ÷ 4 = −$2,538

77. Perform the operations according to the standard order of operations.
EXERCISE SET
Perform the operations according to the standard order of operations.
 3  7
86. (–3)(–12) – 5
÷ 7

78. Practice Test

79. Write the word name for the number. 2. 12,056,039
PRACTICE TEST
Write the word name for the number.
2. 12,056,039
Round to the specified place.
,213 (first digit)

80. 6. Seventeen million, five hundred thousand, six hundred eight.
PRACTICE TEST
Write the number.
6. Seventeen million, five hundred thousand, six hundred eight.
8. CVS Caremark Drugs had revenues of $87,471,900,000 in a recent year. Show how you would read the revenue.

81. Estimate by rounding to hundreds. Then find the exact result.
PRACTICE TEST
Estimate by rounding to hundreds. Then find the exact result.
 346

82. PRACTICE TEST
Add.
12. –38 + (15)
Subtract.
14. –8 – 21

83. PRACTICE TEST
Estimate by rounding to the first digit. Then find the exact result. Write the exact answer for division with a whole-number remainder.
16.

84. PRACTICE TEST
18. A section of a warehouse is 31 feet high. Boxes that are each two feet high are to be stacked in the warehouse. How many boxes can be stacked one on top of the other?

85. PRACTICE TEST
20. Baker’s Department Store sold 23 pairs of ladies’ leather shoes. If the store’s original inventory was 43 pairs of the shoes, how many pairs remain in inventory?

86. PRACTICE TEST
22. A day-care center has 28 children. If each child eats two pieces of fruit each day, how many pieces of fruit are required for a week (five days)?

87. PRACTICE TEST
24. John Chang ordered 48 paperback novels for his bookstore. When he received the shipment, he learned that 11 were on back order. How many novels did he receive?

88. PRACTICE TEST
26. Ingram Micro in Santa Ana, California, recently had annual revenues of $34,362,200,000 and losses of $394,900,000. Find their annual expenses. (Expenses = Revenues  Profits)
Loss = negative profit
Expenses = $34,362,200,000  ( $394,900,000)
= $34,362,200,000 + (+ $394,900,000)
= $34,757,100,000

89. PRACTICE TEST
28. Hatcher’s Farm Supply posted a combined loss of $15,814 for January and February. If the loss for February was $7,928, use a signed number to express the loss for January.

90. PRACTICE TEST
30. Lifecycle Fitness Center had an annual loss of $26,136. What was the average loss for each of the twelve months?
$26,136  12 = $2,178

91. PRACTICE TEST
Perform the order of operations according to the standard order of operations.
32. ($68 + $52  $71 + $32)  9