1
Summary
DEFINITION /PROCEDURE
EXAMPLE
REFERENCE
The Decimal Place-Value System
Digits Digits are the basic symbols of the system.
Place Value The value of a digit in a number depends on its
position or place.
Section 1.1
0, 1, 2, 3, 4, 5, 6, 7, 8, and 9
are digits.
p. 3
7,352,589
Ones
Tens
Hundreds
Thousands
Ten thousands
Hundred thousands
The value of a number is the sum of each digit multiplied by
its place value.
Millions
p. 4
2345 (2 1000) (3 100)
(4 10) (5 1)
p. 4
Addition
Addends The numbers that are being added.
Sum The result of the addition.
Section 1.2
5
8
13
Addends
Sum
p. 12
The Properties of Addition
The Commutative Property The order in which you add two
whole numbers does not affect the sum.
5445
The Associative Property The way in which you group whole
numbers in addition does not affect the final sum.
(2 7) 8 2 (7 8)
The Additive Identity The sum of 0 and any whole number
is just that whole number.
60066
© 2001 McGraw-Hill Companies
Subtraction
Minuend The number we are subtracting from.
Subtrahend The number that is being subtracted.
Difference The result of the subtraction.
p. 13
p. 14
p. 14
Section 1.3
15
9
6
Minuend
Subtrahend
Difference
p. 29
Continued
117
118
CHAPTER 1
OPERATIONS ON WHOLE NUMBERS
DEFINITION /PROCEDURE
EXAMPLE
REFERENCE
Rounding, Estimation, and Order
Step 1
To round a whole number to a certain decimal place,
look at the digit to the right of that place.
Step 2
a. If that digit is 5 or more, that digit and all digits to
the right become 0. The digit in the place you are
rounding to is increased by 1.
b. If that digit is less than 5, that digit and all digits to
the right become 0. The digit in the place you are
rounding to remains the same.
Order on the Whole Numbers
For the numbers a and b, we can write
1. a b (read “a is less than b”) when a is to the left of b on
the number line.
2. a b (read “a is greater than b”) when a is to the right of b
Section 1.4
To the nearest hundred, 43,578 is
rounded to 43,600.
To the nearest thousand, 273,212
is rounded to 273,000.
p. 44
8 12
8
9
10
11
12
p. 47
15
p. 47
15 10
on the number line.
10
11
12
13
14
Multiplication
7 9 63
Product
p. 53
Factors
The Properties of Multiplication
The Commutative Property Multiplication, like addition, is
a commutative operation. The order in which you multiply two
whole numbers does not affect the product.
The Distributive Property To multiply a factor by a sum of
numbers, multiply the factor by each number inside the
parentheses. Then add the products.
The Associative Property Multiplication is an associative
operation. The way in which you group numbers in
multiplication does not affect the final product.
7997
p. 53
2 (3 7) (2 3) (2 7)
p. 55
(3 5) 6 3 (5 6)
p. 59
Division
Divisor The number we are dividing by.
Dividend The number being divided.
Quotient The result of the division.
Remainder The number “left over” after the division.
Dividend Divisor Quotient Remainder
Section 1.6
Divisor
5
7B38
35
3
Quotient
Dividend
Remainder
38 7 5 3
p. 71
p. 73
© 2001 McGraw-Hill Companies
Factors The numbers being multiplied.
Product The result of the multiplication.
Section 1.5
SUMMARY
DEFINITION /PROCEDURE
EXAMPLE
119
REFERENCE
Division
Section 1.6
The Role of 0 in Division
Zero divided by any whole number (except 0) is 0.
Division by 0 is undefined.
070
p. 74
7 0 is undefined.
p. 74
Exponential Notation and the Order of Operations
Section 1.7
Using Exponents
Base The number that is raised to a power.
Exponent The exponent is written to the right and above the
base. The exponent tells the number of times the base is to be
used as a factor.
Exponent
53 5 5 5 125
Base
Three
factors
This is read “5 to the third
power” or “5 cubed.”
p. 91
The Order of Operations
Mixed operations in an expression should be done in the
following order:
Step 1
Do any operations inside parentheses.
4 (2 3)2 7
Step 2
Evaluate any exponents.
4 52 7
Step 3
Do all multiplication and division in order from left
to right.
4 25 7
Step 4
Do all addition and subtraction in order from left to
right.
93
100 7
Remember Please Excuse My Dear Aunt Sally
p. 94
Solving Geometric Applications
Section 1.8
Measuring Perimeter
The perimeter is the total distance around the outside edge of a
shape. The perimeter of a rectangle is P 2 L 2 W.
6 ft
2 ft
2 ft
6 ft
© 2001 McGraw-Hill Companies
P 2 6 ft 2 2 ft
12 ft 4 ft
16 ft
Finding the Area of a Rectangle
The area of a rectangle is found using the formula A L W.
p. 103
6 ft
2 ft
A L W 6 ft 2 ft 12 ft2
p. 107
Continued
CHAPTER 1
OPERATIONS ON WHOLE NUMBERS
DEFINITION /PROCEDURE
EXAMPLE
REFERENCE
Solving Geometric Applications
Section 1.8
Finding the Volume of a Rectangular Solid
The volume is found by multiplying length width height.
2 ft
2 ft
3 ft
VLWH
3 ft 2 ft 2 ft
12 ft3
p. 109
© 2001 McGraw-Hill Companies
120
Summary Exercises
You should now be reviewing the material in Chapter 1. The following exercises will help in that process. Work all the
exercises carefully. References are provided to the section for each exercise. If you have difficulty with an exercise, go
back and review the related material.
[1.1]
In exercises 1 and 2, give the place value of each of the indicated digits.
1. 6 in the number 5674
2. 5 in the number 543,400
In exercises 3 and 4, give word names for each of the following numerals.
4. 200,305
3. 27,428
Write each of the following as a number.
5. Thirty-seven thousand, five hundred eighty-three
6. Three hundred thousand, four hundred
In exercises 7 and 8, name the property of addition that is illustrated.
7. 4 9 9 4
[1.2]
© 2001 McGraw-Hill Companies
9.
8. (4 5) 9 4 (5 9)
In exercises 9 to 13, perform the indicated operations.
784
385
247
10.
2570
498
21,456
28
11.
367
289
1463
2682
12.
6389
1567
315
113,602
13. Find the value for the following:
(a) 34 decreased by 7
(b) 7 more than 4
(c) the product of 9 and 5, divided by 3
121
122
CHAPTER 1
OPERATIONS ON WHOLE NUMBERS
Solve the following applications.
14. Passenger count. An airline had 173, 212, 185, 197, and 202 passengers on five morning flights between Washington,
D.C., and New York. What was the total number of passengers?
15. Salaries. The Future Stars summer camp employs five junior counselors. Their weekly salaries last week were $108,
$135, $81, $135, and $81. What was the total salary for the junior counselors?
[1.3]
16.
In exercises 16 to 20, perform the indicated operations.
5325
847
17.
38,400
19,600
18.
86,000
2169
19.
2682
108
20. Find the difference of 7342 and 5579.
Solve the following applications.
21. Credit card payments. Chuck owes $795 on a credit card after a trip. He makes payments of $75, $125, and $90.
Interest of $31 is charged. How much remains to be paid on the account?
22. Total Cost. Juan bought a new car for $16,785. The manufacturer offers a cash rebate of $987. What was the cost
after rebate?
[1.4]
In exercises 23 to 25, round the numbers to the indicated place.
23. 6975 to the nearest hundred
24. 15,897 to the nearest thousand
In exercises 26 and 27, complete the statements by using the symbol or .
26. 60 ____________ 70
[1.5]
27. 38 ____________ 35
In exercises 28 to 30, name the property of multiplication that is illustrated.
28. 7 8 8 7
30. (8 9) 4 8 (9 4)
29. 3 (4 7) 3 4 3 7
© 2001 McGraw-Hill Companies
25. 548,239 to the nearest ten thousand
SUMMARY EXERCISES 123
In exercises 31 to 33, perform the indicated operations.
31.
32.
58
32
25
43
33.
378
409
Solve the following application.
34. Costs. You wish to carpet a room that is 5 yards by 7 yards. The carpet costs $18 per square yard. What will be the
total cost of the materials?
5 yds.
7 yds
In exercise 35, perform the indicated operation.
35.
129
240
Estimate the product by rounding each factor to the nearest hundred.
36.
1217
494
[1.6]
In exercises 37 and 38, divide if possible.
37. 0 8
38. 5 0
In exercises 39 to 42, divide.
39. 8B2469
40. 39B2157
41. 64B31,809
42. 362B86,915
Solve the following application.
43. Mileage. Hasina’s odometer read 25,235 miles (mi) at the beginning of a trip and 26,215 mi at the end. If she used 35
© 2001 McGraw-Hill Companies
gallons (gal) of gas for the trip, what was her mileage (mi/gal)?
124
OPERATIONS ON WHOLE NUMBERS
CHAPTER 1
Estimate the following.
44. 356 divided by 37
[1.7]
45. 2125 divided by 123
In exercises 46 to 55, evaluate the expressions.
46. 5 23
47. (5 2)3
48. 4 8 3
49. 48 (23 4)
50. (4 8) 3
51. 4 3 8 3
52. 8 4 2 2 1
53. 63 2 3 54 (12 2 4)
54. (3 4)2 100 5 6
55. (16 2) 8 (6 3 2)
Find the perimeter of the following figures.
56.
57.
5 ft
2 ft
2 in.
2 ft
3 in.
1 in.
1 in.
1 in.
2 ft
4 in.
2 ft
4 in.
5 ft
6 in.
Find the area of the given figures.
58.
59.
6 in.
3 in.
2 ft
2 ft
3 in.
6 in.
6 ft
4 ft
5 ft
Find the volume of the given figure.
60.
6 in.
© 2001 McGraw-Hill Companies
3 in.
8 in.