CHAPTER
1
Solutions Key
Foundations of Algebra
b. 63(12) = 756 bottles;
63(25) = 1575 bottles;
63(50) = 3150 bottles
4a. 63s
ARE YOU READY? PAGE 3
1. E; a result of subtraction
2. B; a number that is multiplied by another number to
form a product
THINK AND DISCUSS
1. addition - increase by, sum of;
subtraction - decreased by, difference of;
multiplication - multiplied by, product of;
division - divided by, quotient of
3. A; the distance around a figure
4. D; the number of square units a figure covers
5. 23 + 6 = 29
6. 156 ÷ 12 = 13
7. 18 × 96 = 1728
8. 85 - 62 = 23
10. 0.32 - 0.18 = 0.14
2. Both types of expressions may contain numbers and
operation. Algebraic expressions may also contain
variables.
11. 29.34 + 0.27 = 29.61
12. 4 - 1.82 = 2.18
3.
13. 0.7 × 0.6 = 0.42
14. 2.5 × 0.1 = 0.25
9. 2.18 + 6.9
Words
Algebra
Addition
3 more than x
x+3
1 less than y
y -1
15. 1.5 × 1.5 = 2.25
16. 3.04 × 0.12 = 0.3648
Subtraction
Multiplication
The product of 2 and n
2n
17. 6.15 ÷ 3 = 2.05
18. 8.64 ÷ 2 = 4.32
Division
The quotient of x and 4
x÷4
19. 7.2 ÷ 0.4 = 18
20. 92.7 ÷ 0.3 = 309
21.
__3 × __1
5
2
3×1
= _____
5×2
3
= ___
10
4
7 × __
23. __
7
8
7×4
= _____
8×7
28
1
= ___ = __
56
2
2 = __
4
2 + __
25. __
5
5
5
1
1 + __
27. __
2
4
3
2 + __
1 = __
= __
4
4
4
EXERCISES
1
2 ÷ __
22. __
3
6
6
2 × __
= __
3
1
2×6
= _____
3×1
12 = 4
= ___
3
2
24. 4 ÷ __
3
3
= 4 × __
2
12 = 6
= ___
2
3 __
2 = __
1
__
26. - 1 = __
8
8
8
4
4
2
__
__
28. 3
9
6
4
= __ - __
9
9
GUIDED PRACTICE
1. variable
2–9. Possible answers given
2. 5 less than n; n decreased by 5
3. the quotient of f and 3; f divided by 3
4. c increased by 15; the sum of c and 15
5. 9 decreased by y; y less than 9
6. one-twelfth x; the quotient of x and 12
7. the sum of t and 12; t increased by 12
8. the product of 8 and x; 8 groups of x
9. x decreased by 3; the difference of x and 3
10. 45h
12. a - c
=3-2=1
14. b ÷ c
4÷2=2
1-1 VARIABLES AND EXPRESSIONS,
PAGES 6-11
16a. 0.5d
CHECK IT OUT!
11. w + 4
13. ab
3 · 4 = 12
15. ac
3·2=6
b. 0.5d
0.5(2) = 1
0.5(4) = 2
0.5(10) = 5
1. Possible answers given
PRACTICE AND PROBLEM SOLVING
a. 4 decreased by n; n less than 4
17. the product of 5 and p; 5 groups of p
b. the sum of 9 and q; q added to 9
18. 4 decreased by y; the difference of 4 and y
c. the quotient of t and 5; t divided by 5
19. the sum of 3 and x; 3 increased by x
d. the product of 3 and h; 3 times h.
2a. 65t
c. 32d
b. p - n
=9-2=7
20. the product of 3 and y; 3 times y
b. m + 5
21. negative 3 times s; the product of negative 3 and s
3a. mn
=3·2=6
22. the quotient of r and 5; one-fifth r
c. p ÷ m
=9÷3=3
23. 14 decreased by t; the difference of 14 and t
24. the sum of x and 0.5; x increased by 0.5
1
Holt McDougal Algebra 1
25. t + 20
26. 8n
27. 6 - 5 = 1
28. 5 + 3 = 8
29. 6 ÷ 3 = 2
30. 5 · 6 = 30
42a. Let p represent the weight of an object on Earth in
pounds; 0.38p
b. p = 120 + 44 = 164
0.38p = 0.38(164) = 62.31 lbs
31a. h - 40
43a. 47.84 + m
b. h - 40
(40) - 40 = 0
(44) - 40 = 0
(48) - 40 = 0
(52) - 40 = 0
b. 58.53 - s
44. Both algebraic and numerical expressions contain
numbers and operations, but algebraic expressions
also contain variables.
34. 17 - b; possible answer: Sarah started with
17 apples, but lost b of them.
Verbal
Algebraic
x = 12
x = 14
x reduced
x-5
12 - 5 = 7 14 - 5 = 9
by 5
45. 7 more than
x+7
12 + 7 = 19 14 + 7 = 21
x
x
14
12
=7
=6
46. The quotient
of x and 2
2
2
2
47. The sum of
x+3
12 + 3 = 15 14 + 3 = 17
x and 3
35. y + 10; possible answer; April had y CDs and then
got 10 more.
TEST PREP
36a. air pressure
48. C; b fewer than 3.
32. To evaluate an expression is to find its value. To do
this, substitute values for the variables and perform
all the indicated operations.
33. 2x; possible answer: Jim has twice as many aunts
as Carly, who has x aunts.
_
c. 14.7 + 0.445d
= 14.7 + 0.445(8)
= 14.7 + 3.56
= 18.26 psi
51. 2ab = 2(6)(3)
= 36
41.
52. 2x + y = 2(4) + (5)
= 8 + 5 = 13
53. 3x ÷ 6y = 3(6) ÷ 6(3)
=1
A = 9(8) = 72 in 2
A = 9(11) = 99 in 2
c. A = · w or w
40.
49. F; 12 - 5
CHALLENGE AND EXTEND
38a. P = 2 + 2w
39.
__
50. B; Sarah has driven the difference of 25 and x.
b. depth below the water in feet.
37. A = · w
A = 9w
2
A = 9(1) = 9 in
A = 9(9) = 81 in 2
__
54. Let h represent the number of hours used in a
month when h is more than 20 hours.
9.95 + 0.50(h - 20)
= 9.95 + 0.50(35 - 20)
= 9.95 + 0.50(15) = $17.45
b. P = 2 + 2w
= 2(14) + 2(8)
= 28 + 16
= 44 cm
d. A = w
= (8)(14)
= 112 cm 2
x
1
2
3
4
x + 12
(1) + 12 = 13
(2) + 12 = 14
(3) + 12 = 15
(4) + 12 = 16
x
1
5
10
15
10x
10(1) = 10
10(5) = 50
10(10) = 100
10(15) = 150
x
12
20
26
30
x÷2
(12) ÷ 2 = 6
(20) ÷ 2 = 10
(26) ÷ 2 = 13
(30) ÷ 2 = 15
SPIRAL REVIEW
55. 180° - (45° + 90°) = 45°
56. 180° - (120° + 40°) = 40°
57. 180° - (30° + 60°) = 90°
58. 25% =
25
1
____
= __
100
4
50
1
59. 50% = ____ = __
100
2
3
75
60. 75% = ____ = __
100
4
100
61. 100% = ____ = 1
100
62. add 8 to the previous term; 36, 44, 52
63. multiply the previous term by 3; 729, 2187, 6561
64. Add 1 to the previous term, then add 2, and then
add 3, and so on; 17, 23, 30.
2
Holt McDougal Algebra 1
3
1 right, then 12 left.
17. -11 __ ; start at 0, move __
4
4
3
2
18. 5 __ ; start at 0, move __ left, then 6 right.
5
5
1-2 ADDING AND SUBTRACTING REAL
NUMBERS, PAGES 14-19
CHECK IT OUT!
19. -18 + (-12) = -30
1a. 4; Start on -3 and move 7 to the right.
20. -2.3 + 3.5 = 1.2
b. -10; Start on -3 and move 7 to the left.
21. (-15) + 29 = 14
22. -4.8 + (-5.4) = -10.2
23. 12 - 22 = -10
3
1 = - __
1
24. - __ - - __
4
4
2
c. 1.5; Start on -5 and move 6.5 to the right.
2a. -12
b. -35.8
c. -16
( )
( )
1
1 - -3 __
b. __
2
2
8
= __ = 4
2
3a. -8
c. -2
25. 38 - (24.6) = 13.4
( )
3 __
2 - - __
1
1 = __
4 + __
1 = __
2 + __
26. __
= 7 = 1 __
3
6
2
3 2 6 6 6
27. Since we are trying to find the difference of the two
temperature, we subtract 17° by -6°.
17 - (-6) = 23°
4. 550 - (-12,468) = 13,018 ft
THINK AND DISCUSS
1. Subtraction of a negative number is addition of a
positive number. This means you move right on the
number line, making the sum greater than the first
number.
2.
28.
29.
30.
n
312
5.75
7
12
2
-7
5
__
_
n + (-5)
312 + (-5) = 307
5.75 + (-5) = 0.75
7
- 7 + (-5) = -5
12
12
2
2
-7 + (-5) = -12
5
5
__
_
__
_
Points
Sum
Difference
A, B
Neg.
Neg.
31.
B, A
Neg.
Pos.
C, B
Neg.
Pos.
32. -8 - 3 = -11
33. -9 + (-3) = -12
D, A
Pos.
Pos.
34. 16 - (-16) = 32
35. 100 - 63 = 37
36. 5.2 - 2.5 = 2.7
37. -4.7 - (-4.7) = 0
7
2 - __
38. __
5
8
16 ___
35
19
___
=
= - ___
40
40
40
3
2 - ___
39. __
5
10
3
1
4 - ___
= ___
= ___
10
10
10
EXERCISES
GUIDED PRACTICE
1. opposite
40a. You are looking for the total profit of January and
February, find the sum of the profits.
-415 + 1580 = $1165
2. 3; start at 0, move 4 left, then 7 right.
3. -8.5; start at 0, move 3.5 left, then 5 left.
4. -3.6; start at 0, move 5.6 right, then 9.2 left.
b. Total profit of January, February, March
1165 + (-245) = $920
1 right.
1 ; start at 0, move 3 right, then 6 __
5. 9 __
4
4
6. 91 + (-11) = 80
41. -4 - (-6) = 2 > -7 - 3 = -10
5
9
4=1
7. 1 __ + (-1 __ ) = __
4
4
42. ⎪-51⎥ = 51 > ⎪0⎥ = 0
4
43. 3 - (-3) = 6 > 0 - (-3) = 3
8. 15.6 + (-17.9) = -2.3
9
5
10 ___
1 + ___
1 + __
= - __
=
9. - ___
16
16 8
6 16
10. 23 - 36 = -13
11. 4.3 - 8.4 = -4.1
6 ___
1
4
14
__
__
__
12. 1 - 2 = 5
5 5
5
3
8
__
__
= - = -1
5
5
1
7
4 = ___
11 = 1 ___
2
7 + ___
___
__
13.
- = ___
5
10
10
10 10 10
44. -3 - 8 = -11 = -22 + 11 = -11
45. ⎪-10 + 5⎥ = 5 < ⎪-15⎥ = 15
46. 9 + (-8) = 1 = -12 + 13 = 1
( )
47. Highest location: Telescope Peak, 11,049 ft
Lowest location: Badwater, -282 ft
Highest - Lowest = 11,049 - (-282) = 11,331 ft
( )
48. always; possible answer: The value of -2 + n is
always two units less than the value of n.
14. Since we are looking for the sum of the decrease,
we add the two negative numbers.
49. never; possible answer: -b + (-b) = -2b. If b is not
equal to 0, then -2b cannot equal 0
-108.35 + (-507.99) = -616.34
PRACTICE AND PROBLEM SOLVING
50. sometimes; Possible answer: if x ≥ -1, then
x + 1 ≥ 0, and if x < -1, then x + 1 < 0
15. 4; start at 0, move 2 left, then 6 right.
51. A; The opposite of -8 should have been added.
16. 4; start at 0, move 6 right, then 2 left.
3
Holt McDougal Algebra 1
52a. plane’s altitude - building’s height
= (1800) - (150) = 1650 ft
1-3 MULTIPLYING AND DIVIDING REAL
NUMBERS, PAGES 20–25
CHECK IT OUT!
1a. 35 ÷ (-5) = -7
¶ÊvÌ
b. -11(-4) = 44
c. -6(7) = -42
£nääÊvÌ
3
2a. - __ ÷ -9
4
3 1
= - __ - __
4 9
3
1
___
= ___
=
36
12
£xäÊvÌ
( )
b. plane’s altitude - diver’s depth
= (1800) - (-80) = 1880 ft
b.
3
6
___
÷ (- __ )
=
5
2
c. - __ ÷ 1 __
3
6
3(-5)
= _____
6(5)
5(3)
= - ____
6(5)
3
1
= - __ = - __
6
2
5
10
3
5
___
× (- __ )
10
6
3
5 ___
__
=- ×
10
6
15
1
___
= - __
=60
4
£nääÊvÌ
¶ÊvÌ
ÊnäÊvÌ
( )
1 =0
3a. 0 ÷ -8 __
6
c. 1880 ft; because subtracting a negative number is
the same as adding a positive number.
b. 2.04 ÷ 0 = undefined
c. (-12,350)(0) = 0
53. Possible answer: The first example shows that
adding the opposite of 2 is the same as subtracting
2. The second example shows that subtracting the
opposite of 2 is the same as adding 2. After adding
two numbers, you can get back to the first number
by subtracting the second number.
4. distance = (speed)(time)
= (5.25 mi/h)(1.5 h) = 7.875 mi
THINK AND DISCUSS
54. B; ⎪-3 + 5⎥ = ⎪2⎥ = 2 - 3 + 5
1. a number multiplied by its reciprocal is 1. The
5
4 is __
.
reciprocal of __
5 4
55. F; -12 + 25 - 10 - 3 = 0°
2.
TEST PREP
56. C; 5.40 + 4.16 + 7.07 + 5.4 + 9.52 = $31.55
CHALLENGE AND EXTEND
Multiplying and Dividing Numbers
Multiplication
Division
pos pos = pos
pos ÷ pos = pos
57. -1.2 - 7.8 = -9
pos neg = neg
pos ÷ neg = neg
neg pos = neg
neg ÷ pos = neg
58. -0.2 + 2.1 = 1.9
neg neg = pos
neg ÷ neg = pos
59. 9.75 - 7.75 = 2
60. -2.3 + 8.5 = 6.2
EXERCISES
61. Possible answer: subtract 4; -2, -6, -10
GUIDED PRACTICE
1. switch the numerator and denominator. The
1 is __
2 , or 2.
reciprocal of __
2 1
2. -72 ÷ (-9) = 8
3. 11(-11) = -121
2
2 ; - __
2 , 0, __
62. Possible answer: add __
5 5
5
63. To find the average of the elevations, first find the
sum of the elevations then divide by the number of
locations.
19,347 + 17,159 + 5051 + 9085
___________________________
4
50,642
______
=
= 12,660.5 ft
4
4. -7.2 ÷ (3.6) = -2
5. 5 ÷
7
7=7
= 5 × __
5
SPIRAL REVIEW
3
___
= 0.1875
16
15
66. ___ = 1.25
64.
12
68. 2(180˚) = 360˚
__5
2 = 0.−
65. __
2
9
4 = 0.−−
67. ___
36
11
69. 4(180˚) = 720˚
( )
( )
4 ÷ - __
7
6. __
5
5
5
4 × - __
= __
5
7
4(5)
____
=5(7)
20
4
___
== - __
7
35
70. 3(180˚) = 540˚
4
Holt McDougal Algebra 1
( )
( )
1
37. bc = (-3) - __
2
3
= __
2
1
36. a ÷ c = (4) ÷ - __
2
= 4 × (-2) = -8
1 ÷ (4)
38. c ÷ a = - __
2
1 = - __
1 × __
1
= - __
4
2
8
39. negative
40. zero
41. negative
42. zero
43. positive
44. positive
45. undefined
46. zero
35. ab = (4)(-3)
= -12
( )
( )
2 ÷ - __
1
7. - __
3
3
2
__
= - × (-3)
3
-2(-3)
= _______ = 2
3
16
4
8. - ___ ÷ - __
5
25
16
5
___
=× - __
25
4
-16(-5)
= ________
25(4)
80
4
____
= __
=
5
100
( )
9. 3.8 ÷ 0 = undefined
10. 0(-27) = 0
2
7 ÷ 0 = undefined
11. 0 ÷ __ = 0
12. __
3
8
13. The total money spent is equal to the product of cost
per ticket and the number of tickets sold.
($30)(7,000,000) = $210,000,000
So, about $210,000,000.
47. y ÷
__3 = __3 ÷ __3
4
4
=1
4
( )
48. y ÷
3
9
__3 = -___
÷ __
4
15. 8(-4) = -32
16. (-25)(-12) = 300
3
1
17. - ___ ÷ (- __
)
20
49. y ÷
15
3
18. ___ ÷ ___
14
28
3
28
= ___ × ___
14
15
3(28)
______
=
14(15)
84
2
____
=
= __
5
210
6
3
= - ___ × (-6)
20
-3(-6)
= _______
20
18
9
= ___ = ___
20
10
( )
( )
( )
1 ÷ 1 __
1
19. -4 __
2
2
3
9
= - __ ÷ __
2
2
9 __
__
=- ×2
3
2
9(2)
= - ____
2(3)
18
= - ___ = -3
6
3
1
20. 2 __ ÷ -1 __
4
2
3
11
___
÷ - __
=
4
2
11
2
___
__
=
× 4
3
11(-2)
______
=
4(3)
22 = - ___
11
= - ___
12
6
21. 0 · 15 = 0
22. -0.25 ÷ 0 = undefined
23. 0 ÷ 1 = 0
24.
__0 ÷ 3
1
=0÷3=0
25. The temperature after 5 days is the total
temperature change. Since each day’s decrease is
constant, the total temperature is 5d, where d is the
constant decrease in degrees.
5d = 5(-3) = -15°
26. 21 ÷ (-3) = -7
28. -6 ÷ (-14) =
14
29. -6.2(10) = -62
31. -3.75(-5) = 18.75
( )
4
8
4
3 __
4
__
= ×
8
3
3(4)
= ____
8(3)
1
___
= 12 = __
24
2
50. y ÷
__3 = -2__1 ÷ __3
4
4
4
9
4
= - __ × __
3
4
9(4)
= - ____
4(3)
36
___
= -3
=12
5
1 ÷ - __
1 ÷ m = __
51. __
2
2
2
1 × - __
2
= __
5
2
1(-2)
= _____
2(5)
2 = - __
1
= - ___
5
10
1 ÷ __
7
1 ÷ m = __
52. __
2
2
8
8
1
__
__
= ×
7
2
1(8)
= ____
2(7)
8
4
___
= __
=
7
14
1 ÷ m = __
1 ÷ __
4
53. __
2
2
9
9
1
__
__
= ×
2
4
1(9)
= ____
2(4)
9
__
=
8
1 ÷ -5
1 ÷ m = __
54. __
2
2
1
1
__
__
= ×5
2
1
____
=2(5)
___
=-1
10
27. -100 ÷ 25 = -4
1 ÷ __
1=1
30. __
2
2
56. The underwater cave is 7 times the depth of the
original swimming depth before the dive.
-20 × 7 = -140
So, -140 ft.
( )
1 = -5 < 20 ÷ 4 = 5
57. 10 - __
2
3 ___
75
1 (-3) = 36 __
=
32. -12 __
2
2
2
1 =1
33. 17 ___
17
__3 = __3 ÷ __3
55. To find how many hours Benjamin must take each
semester to graduate in 8 semesters, divide total
credit hours required by the number of semesters.
120 ÷ 8 = 15.
So, 15 hours per semester.
6
3
___
= __
7
4
3
16
9(4)
= - _____
16(3)
3
36
___
= - __
=48
4
PRACTICE AND PROBLEM SOLVING
14. -30 ÷ (-6) = 5
16
9
4
= - ___ × __
58. 16 ÷ (-2) = -8 < -2(-4) = 8
()
34. 1
2 ÷ 3 = - __
4 > 5(-2.4) = -12
59. -2 __
3
9
5
Holt McDougal Algebra 1
60. 20 ÷ 4 = 5 >
__3 ÷ (-__1 ) = -__3
4
2
CHALLENGE AND EXTEND
2
61. 2.1(-3.4) = 7.14 = 2.1(-3.4) = 7.14
76. (-2)(-2)(-2) = -8
( )
77.
3
1 ÷ __
1=1
62. 0 - __ = 0 < __
5
2
2
63a. positive
( )( )
( )( )
3
4 - __
78. 5 - __
5
4
5
4 (-3) = 3
= __ - __
5
4
1
64. 12 ÷ -3 = 12(- __
)
1
65. 75 ÷ 15 = 75( ___
)
80
1
___
= 80(- __
)
-121 = -121 ___
1
67. _____
11
11
8
⎪ ⎥
()
5
2 · __
81. ⎪- __
5⎥ ⎪2⎥
5
2 · __
= __
=1
5 2
15
3
1 · __
2 · __
82. __
·
2 3 4
3
2
= 1 __ __
2 3
( )
( )(
68. always; A negative divided by a positive is always
negative.
__4
5
)(__4 )(__1 ) = __1
4 5
( )( )( )
3
3
3
27
83. - __ - __ - __ = - ___
4
4
4
64
5
84. (2 )
= 8 2 = 64
85. possible answer: multiply by -2; -16, 32, -64
9 , - ___
81
27 , ___
86. possible answer: multiply by -3; __
7 7
7
87. possible answer: The numbers are alternating
positive and negative multiples of 5; 30, -35, 40
3 2
69. never; A negative times a positive is always
negative.
70. sometimes; 4C > C only if C is positive.
71. You know that the product is positive and one factor
is negative. If the second factor were positive, the
product would be negative, because the product of a
negative factor and a positive factor is negative. This
is not true, so the second factor must be negative.
d
72a. To find the speed, use the formula, r = __ . d
t
represents the distance, and t represents time.
You swam 20 feet in 5 seconds, d = 20 ft, t = 5s.
Substitute these values into the formula to find
speed.
20
r = ___ ft/s = 4 ft/s.
5
b. Time (min)
1
2
5
49
1 · ⎪20⎥
79. - __
4
1 (20) = 5
= __
4
80. 5 · 4 · 3 · 2 · 1 = 120
d. No; it does not matter how many times you multiply
by a positive number, the sign does not change.
-8
7
7(7)
c. The product of two negative numbers is positive.
The product of a positive number and a negative
number is negative.
66.
7
5(5)
25
= ____ = ___
b. negative
3
__5 · __5
88. possible answer: multiply by 0.5; 0.03125, 0.015625,
0.0078125
89. For a job that takes 4 hours to complete, a cleaning
service will charge $49.00 plus the 2 additional
hours for $18 per hour.
49 + 2(18) = $85
SPIRAL REVIEW
90. SA = 2(3)(4) + 2(3)(12) + 2(4)(12)
= 24 + 72 + 96
= 192 cm 2
Depth (ft)
15
30
75
91. SA = 2(5)(21) + 2(5)(25) + 2(21)(25)
= 210 + 250 + 1050
SA = 1510 in
c. 5 · 15 = 75
15 + 15 + 15 + 15 + 15 = 75
2
92. 200 - t
93. -5 < 5
94. 14 > - 2
95. 4 = 4
96. -55 = -55
TEST PREP
1 ÷ __
1=
73. C; Divide to find the number of lemons: 1 __
2
4
2
3 __
__3 ÷ __1 = __
· 4 = 6. Multiply by $0.45 to find total
2
21 1
4
cost: 6($0.45) = $2.70
1-4 POWERS AND EXPONENTS,
PAGES 26-31
74. J; (15 × 12)(1.25) = $225
1a. 2 2
CHECK IT OUT!
75. Clarinets: 1 half note = _1 whole note; 8 half notes =
2
4 whole notes; find the number of quarter notes that
have the same length as 4 whole notes; 4 ÷ _1 = 16;
4
the flutes play 16 quarter notes.
b. x 3
3
2a. (-5) = (-5)(-5)(-5) = -125
2
b. -6 = -(6)(6) = -36
27
(__43 ) = (__34 )(__34 )(__43 ) = ___
64
3
c.
3a. 64 = 8 · 8 = 8
2
b. -27 = (-3)(-3)(-3) = (-3)
3
8
4. 2 = 256
6
Holt McDougal Algebra 1
35. -2 3 = -8 = (-1) 3 = -8
THINK AND DISCUSS
1. eight cubed; eight raised to the third power.
2
2
36. -3 = -9 < (-3) = 9
2.
2
6
37. 10 = 100 > 2 = 64
Even
Exponent
Odd
Exponent
Positive
Base
32 = 9
Positive
33 = 27
Positive
Negative
Base
(-3) = 9
(-3) = -27
Negative
2
2
1
38. 2 = 4 = 4 = 4
7
40. 1 = 1 · 1 · 1 · 1 · 1 · 1 · 1 = 1
3
41. (-4) = (-4)(-4)(-4) = -64
3
Positive
39. 2 3 = 2 · 2 · 2 = 8
3
42. -4 = -(4 · 4 · 4) = -64
EXERCISES
3
43. (-1) = (-1)(-1)(-1) = -1
GUIDED PRACTICE
4
44. (-1) = (-1)(-1)(-1)(-1) = 1
1
( ) = (__13 )(__13 )(__13 ) = ___
27
1. the number of times to use the base as a factor
2. 4
2
3. 2
4. 9
2
5. (7)(7) = 49
1
45. __
3
3
2
46. -2.2 = -(2.2 · 2.2)
6. (-2)(-2)(-2)(-2) = 16
2
( )( )( )( )
2
1 __
1 __
1 = - ___
1 __
1 9. 81 = 9 · 9 = 9 2
8. - __
2 2 2 2
16
c. A = s
= 36 - 9 = 27 in 2
10. 100,000 = (10)(10)(10)(10)(10) = 10 5
11. -64 = (-4)(-4)(-4) = (-4)
1
48. 3 · 3 · 3 · 3 = 3
3
2
21. -(4)(4) = -16
( )( )
9
3
3
22. - __ - __ = ___
5
5
25
23. 49 = (7)(7) = 7 2
24. 1000 = (10)(10)(10) = 10
56. 4 = 2 · 2 = 2
3
25. -8 = (-2)(-2)(-2) = (-2)
27. 64 = (4)(4)(4) = 4
3
2
59. 625 = 5 · 5 · 5 · 5 = 5
6
28. 343 = (7)(7)(7) = 7
61. 100 = 10 · 10 = 10
3
b. Since there are 3 tails, Becky’s score is 3 = 27
1.25 days
c. If the coin is fair, about half the tosses should result
in heads and half should result in tails. Becky’s
score is increasing by a greater factor each time
the coin lands tails up, so she will probably win.
2 25 ≈ 34,000,000 < 3 25 ≈ 847,289,000,000
30. Any number other than zero raised to an even
power is positive. Zero raised to any power other
than zero is zero.
34. 1 9 = 1 4
62. 125 = 5 · 5 · 5 = 5 3
4
Then you write an expression that represents the
problem. There was one protozoan on a slide 5 days
ago, and the number has doubled 4 times since.
1 × 2 × 2 × 2 × 2 = 2 4 = 16
So there are 16 protozoas now.
2
2
33. 4 = 16 = 2 = 16
3
63. 81 = 3 · 3 · 3 · 3 = 3
64a. Since there are 5 heads, Mark’s score is 2 5 = 32
5 days
______
= 4, So the number has doubled 4 times.
32. 5 2 = 25 < 2 5 = 32
2
4
4
60. -8 = -(2 · 2 · 2) = -2
3
29. First you need to find how many times the number
of protozoas has doubled.
31. 3 2 < 3 3
3
57. 16 = 4 · 4 = 4 2
58. 16 = (-2)(-2)(-2)(-2) = (-2)
3
26. 1,000,000 = (10)(10)(10)(10)(10)(10) = 10
( )( )( ) ( )
1 __
1 __
1 = __
1
53. __
9 9 9
9
3
2
19. (3)(3)(3) = 27
20. (-4)(-4) = 16
4
54. A = s
= 24 2 = 576 cm 2
55. First round 22.7 cm to 20 cm
V = s 3 ≈ 20 3 = 8000 cm 3
Then round 22.7 cm up, to 25 cm
V = s 3 ≈ 25 3 = 15,625 cm 3
So a good esitmate is between 8000 cm 3 and
15,625 cm 3.
17. 3 3
3
5
52. (-7)(-7)(-7) = (-7)
PRACTICE AND PROBLEM SOLVING
18. 5
49. 6 · 6 = 6 2
51. (-1)(-1)(-1)(-1) = (-1)
5
15. (3)(3)(3)(3)(3) = 3 = 243
16. 5 2
4
50. 8 · 8 · 8 · 8 · 8 = 8
13. 81 = (3)(3)(3)(3) = 3 4
14. 36 = (-6)(-6) = (-6)
b. A = s 2
= 3 2 = 9 in 2
47a. A = s
= 6 2 = 36 in 2
7. (-2)(-2)(-2)(-2)(-2) = -32
12. 10 = 10
3
2
65a. 10 = 100
10 3 = 1000
10 4 = 10,000
b. The exponent is the same as the number of zeros
in the answer.
7
Holt McDougal Algebra 1
F
66a. p = __
A
50
1 psi
p = ____ = __
100
2
( )
1 - __
4
86. __
2 5
1(-4)
= _____
2(5)
-4
2
___
= - __
=
5
10
85. -20(-14)
= 280
b. First determine the number of square inches in a
square foot.
1 ft = 12 in.
1 2 ft 2 = 12 2 in 2
1 ft 2 = 144 in 2
1-5 ROOTS AND REAL NUMBERS,
PAGES 32-37
F
p = __
A
=
64
4 psi
____
= __
144
CHECK IT OUT!
9
1a. √
4=
TEST PREP
4
c. √
81 =
67. C; 9 2 = 81 = 3 · 3 · 3 · 3
68. G; (-16)(-16)(-16)(-16) = (-16)
√
70. H; because 100 is an even number.
(
CHALLENGE AND EXTEND
2
2
2
72. (2 3)(2 3)(2 3)
= 8 · 8 · 8 = 512
2
2
b. side = 30 - 2(2.5) = 25ft
74.a. A = s = 30
2
= 900 ft
Area = 25 2 = 625 ft 2
c. A = 900 - 625 = 275 ft 2
d. 275 ÷ 10 = 27.5; 28 bags
4
10 + 9 + 9 + 12 + 12
__________________
78.
5
52
= ___ = 10.4
5
79. 5 minus x; x less than 5
1.
_2 = 0.6; _3 = 0.6; both numbers are rational, _2 is
5 3
3
3
repeating _ is a terminating decimal
5
2.
Rational number
__1 __1 -2.25
3
4
Yes
Irrational number
√21
1+3+5+7+9
_______________
No
5
=
25
___
=5
Integer
-15
5
Yes
No
Whole number
0
Yes
81. c divided by d; the quotient of c and d
82. the sum of a and b; b more than a
84. 0 ÷
=0
No
Natural number
25 24 (-1)2
4 √
80. 6 times n; the product of 6 and n
8
4 ÷ ___
83. __
5
25
25
4 × ___
= __
5
8
4(25)
_____
=
5(8)
5
100
= ____ = __
40
2
d. , , , , term. dec.
No
77.
b. , , term. dec.
THINK AND DISCUSS
SPIRAL REVIEW
30
___
= 7.5
√
c. irrational
2
3
c. 2 + 3 = 5; the sum of the exponents in 4 and 4
5
is the exponent in the product 4 .
=
)
4a. ; repeating decimal
2
75a. 4 = 4 · 4
43 = 4 · 4 · 4
b. 4 2 · 4 3 = (4 · 4) · (4 · 4 · 4) = 4 5
4
√
3. 2.9 = 24.389
3.03 = 27
Since 26 is closer to 3.03 than it is to 2.93, the length
of the side of the cube, to the nearest tenth, is 3.0 ft.
2
7+7+8+8
____________
1
1 · __
1 · __
1 = __
b. __
2 2 2 8
3 __1 = __1
8
2
3
73. (-4 )(-4 )(-4 )(-4 )
= (-16)(-16)(-16)(-16) = 65,536
76.
√4 34 = 3
2 · __
2 = __
4
2a. __
3 3
9
__4 = __2
9
3
2
4
__
2
__
= - ___
c. - ·
7 7
49
2
4 = - __
- ___
7
49
4
69. B; the number is negative
71. (2 2)(2 2)(2 2)
= 4 · 4 · 4 = 64
b. - √
25 = - √
5 2 = -5
√
22 = 2
EXERCISES
__6
GUIDED PRACTICE
7
1. Possible answer: √
3
64 = √
82 = 8
2. √
8
3. - √
225 = - √
15 2
= -15
Holt McDougal Algebra 1
4.
3
3
(-64) = √
(-4) 3
√
4
=
5. √625
√4 54 = 5
3
31. 4.0 = 64
4.1 3 = 68.921
Since 68 is closer to 4.1 3 than to 4.0 3, the
length of the side of the paperweight, to the nearest
tenth of a centimeter is 4.1.
= -4
3
3
6. √
81 = √
92 = 9
7. - √
27 = - √
3 3 = -3
3
3
-27 = - √
(-3) 3 = 3 9. - √
16 = - √
4 2 = -4
8. - √
1 · __
1 = ___
1
10. __
4 4
16
1 = __
1
___
4
16
1 · __
1
1 = - __
12. - __
3 3
9
__
1
__
= -1
3
9
2 · __
2=
2 · __
11. __
3 3 3
3 8 =
___
27
3 · __
3 = ___
9
13. __
8 8
64
9 = __
3
___
8
64
8
___
1 = ___
1
1 · __
14. __
6 6
36
1 = __
1
___
6
36
2 · __
4
2 = - ___
16. - __
9 9
81
2
4 = - __
- ___
9
81
1 · __
1=
1 · __
15. __
4 4 4
3 1 =
___
64
1
___
√
(
√
√
(
√
)
)
√
32. , repeating decimal
27
__2
3
33. , terminating decimal, , , 34. , terminating decimal, 35. irrational
36a. s = √343
3
3 = 7 cm
= √7
3
√
√
64
__1
4
b. A = s 2
= 7 2 = 49 cm 2
64 > √
63
37. 8 = √
38. √
88 > 9 = √
81
39. 6 = √
36 < √
40
40.
3 = 0.6 < 0.61
9 = __
___
√
25
5
1046 mi = 38.−−−
1485 mi = 45 mi/h
42. _______
41. _______
740 mi/h
33 h
27 h
, repeating decimal
, terminating decimal,
, , ( )( )( )
831 mi = 34.625 mi/h 44. ______
424 mi = 47.−
1 mi/h
43. ______
24 h
9h
, terminating decimal
, repeating decimal
1 - __
1 - __
1 = - ____
1
17. - __
5
5
5
125
3 1 = - __
1
- ____
5
125
√
45. always; mixed numbers can be written as improper
fractions
2
18. 6.7 = 44.89
6.8 2 = 46.24
Since 45 is closer to 6.7 2 than 6.8 2, the length of the
floor to the nearest tenth is 6.7 ft.
46. Never; the decimal form of an irrational number is a
nonterminating, nonrepeating decimal.
19. , terminating decimal, 47. Always; every terminating decimal can be written as
a fraction whose denominator is a power of 10.
20. , repeating decimal
2 is irrational, but -6.2 is rational.
48. Sometimes; - √
21. irrational
49. No; a positive number has only one cube root
because a negative number cubed results in a
negative number. A positive number has two fourth
roots because a negative number raised to the
fourth power results in a positive number.
22. , terminating decimal
PRACTICE AND PROBLEM SOLVING
23. √
121
11 2 = 11
= √
24. √
-1000
3
(-10) 3 = -10
= √
25. - √
100
10 2 = -10
= - √
4
26. √
256
4
44 = 4
= √
1 · __
1=
27. __
5 5
1 =
___
25
1 · __
1 · __
1=
1 · __
28. __
2 2 2 2
4 1 =
___
16
1
___
25
__1
5
3
√
50a.
1
___
16
a2 + b2 = c2
5 2 + 12 2 = c 2
25 + 144 = c 2
169 = c 2
13 = c
b. c 2 = a 2 + b 2
c 2 = 50 2 + 120 2
c 2 = 2500 + 144,000
c 2 = 169,000
c = √
169,000
c = 130 ft
51. s = √A
= √
324 = 18
So there are 18 squares on each side of the board.
__1
2
( ) ( ) ( )
√
( )
√
1 · - __
1 · - __
1 = - __
1
29. - __
2
2
2
8
3 1 = - __
1
- __
8
2
5 5
25
30. - __ · __ = - ___
6 6
36
25
5
___
__
=36
6
52. Possible answer: There is no number that when
squared results in a negative number, but when you
cube a negative number, the result is a negative
number.
TEST PREP
3
3
3
53. C; √
27 < √
36 < √
64 , or 3 < √
36 < 4
3
36 · √
16 = 6 · 4 = 24
54. F; √
40 is irrational.
55. D; 40 is not an exact square, so √
2
2
56. H; 13 = 169 < 175 < 196 = 14
9
Holt McDougal Algebra 1
CHALLENGE AND EXTEND
57. √0.81
0.9 2 = 0.9
= √
59.
READY TO GO ON? PAGE 39
58. √0.25
= √
0.5 2 = 0.5
-0.001
3
(-0.1) 3 = -0.1
= √
3
61. √
a + b = √
9+7
= √
16 = 4
1–4. Possible answers given
1. the sum of 4 and n; 4 increased by n
2. the difference of m and 9; 9 less than m
60. √2.25
= √
1.5 2 = 1.5
3. g divided by 2; the quotient of g and 2
4. 4 times z; the product of 4 and z
9-9
62. b √a
- a = 7 √
= 7(3) - 9
= 21 - 9 = 12
5. The amount of money earned will be the product of
15 and h, or 15h.
6. The number of minutes left after m minutes will
be the difference between total practice time and
elapsed time, 90 - m.
4
4
63. √
b + a + ab = √
7 + 9 + (9)(7)
4
= √
16 + 63
= 2 + 63 = 65
+1=
64. √ab
= √
64 = 8
7. y ÷ z = (6) ÷ (2)
8. xy = (3)(6)
=3
= 18
9. x + y = (3) + (6)
10. x - z = (3) - (2)
=9
=1
11. 81 - 15 = 66
12. 27 - 32 = -5
1
1 = 3 __
14. (-7) - 14 = -21
13. 2 + 1 __
4
4
15. -45 + 70 = 25
So Brandon’s balance will be $25.00
16. 9(-9) = -81
3
17. 6 ÷ __
18. 9.6 ÷ 0 = undefined
5
6 __
5
1
1 - __
1 = __
__
= ×
19. - __
1
3
4
2 2
6(5)
____
=
1(3)
30
___
=
= 10
3
20. Use the formula d = r · t to find the distance.
d=r·t
1
d = 55 · 2 __
2
55 5
d = ___ · __
1 2
55(5)
_____
d=
1(2)
275
____
d=
2
d = 137.5 mi
So Simon’s house is 138.5 mi from the beach.
(9)(7)+1
√
65a. No; possible answer: there are no integers between
1 and 2.
b. Possible answer: between 0 and 1, there is another
real number r. Between 0 and r, there is another
real number q. Between 0 and q, there is another
real number s, and so on. Therefore, there must be
infinitely many real numbers between 0 and 1.
SPIRAL REVEW
66. -14 + (-16) = -30
68. 25 - (17.6) = 7.4
( )
( )
( )
3
1 - - __
67. - __
4
4
2 = __
1
= __
4
2
( )
3
2 = __
1 · - __
1 ÷ - __
69. __
3
2
8
8
1(-3)
3
= _____ = - ___
16
8(2)
70. (-2.5)(-8) = 2.5(8)
= 20
7(3)
7
21 = -____
= - __
71. - ___
6
2
2(3)
or 3.5
72. -(3 · 3 · 3 · 3) = -81
( )( )( )
8
2 - __
2 - __
2 = - ____
73. - __
5
5
5
125
74. 14 · 14 = 196
2
21. (-3) = (-3)(-3)
=9
75. 4 · 4 · 4 = 64
22. -3 2 = -(3 · 3)
= -9
( ) = (-__23 )(-__32 )(-__23 )
2
23. - __
3
3
8
= - ___
27
1 5 = - __
1 - __
1 - __
1 - __
1 - __
1
24. - __
2
2
2
2
2
2
1
= - ___
32
25. 2 10 = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2
= 1024
26. √
225 = √
15 2
27. - √
49 = - √
72
= 15
= -7
3
3
16
__4 2
28. √
8 = √
2·2·2
29. ___ =
5
25
4
__
=2
=
5
( ) ( )( )( )( )( )
√
10
√( )
Holt McDougal Algebra 1
30. , repeating decimal
31. , repeating decimal
32. irrational number
33. , terminating decimal, , , 1-6 ORDER OF OPERATIONS,
PAGES 40-45
4. 50 - 6 +8
= 44 + 8 = 52
5. 12 ÷ (-4)(3)
= -3(3) = -9
7. 16 + (5 - (3 + 2 2))
= 16 + (5 - (3 + 4))
= 16 + (5 - 7)
= 16 + (-2) = 14
8. 5 + 2x - 9 = 5 + 2(4) - 9
=5+8-9
= 13 - 9 = 4
CHECK IT OUT!
b. 5.4 - 3 2 + 6.2
= 5.4 - 9 + 6.2
= 2.6
9. 30 ÷ 2 - d = 30 ÷ 2 - (14)
= 15 - 14 = 1
10. 51 - 91 + g = 51 - 91 + (20)
= -40 + 20 = -20
11. 2(3 + n) = 2(3 + (4))
12. 4(b - 4) 2 = 4((5) - 4) 2
2
= 4(1) = 4
= 2(7) = 14
13. 12 + (20(5 - k)) = 12 + (20(5 - 1))
= 12 + (20(4))
= 12 + (80) = 92
2a. 14 + x 2 ÷ 4 = 14 + (2) 2 ÷ 4
= 14 + 4 ÷ 4
= 14 +1
= 15
b. (x · 2 2) ÷ (2 + 6) = ((6) · 2 2) ÷ (2 + 6)
= (6 · 4) ÷ (2 + 6)
= 24 ÷ 8
=3
5
+
2(-8)
3a. _________
b. ⎪4 - 7⎥ 2 ÷ (-3)
(-2) 3 - 3
= ⎪-3⎥ 2 ÷ (-3)
5
16
= 3 2 ÷ -3
= ______
-8 -3
= 9 ÷ -3
-11
= -3
= ____
-11
=1
4. 6.2(9.4 + 8
c. 3 √
50 - 1
= 3 √
49
=3·7
= 21
14. 24 ÷ ⎪4 - 10⎥
= 24 ÷ ⎪-6⎥
= 24 ÷ 6 = 4
15. 4.5 - √
2(4.5)
= 4.5 - √
9
= 4.5 - 3 = 1.5
16. 5(2) + 16 ÷ ⎪-4⎥
= 10 + 16 ÷ 4
= 10 + 4 = 14
17.
18.
)
22.
20 - 3 + 2 5
20 - (3 + 2) 5
95
27
-5
6+2
24
= - ___
8
= -3
12 ÷ 3
19. -44 ÷ √
= -44 ÷ √
4
= -44 ÷ 2
= -22
21. 12(-2 +6)
14
_________
52 + (-3)
PRACTICE AND PROBLEM SOLVING
1. Not always; subtraction should be performed before
additon if it comes before addition from left to right
or if it is within grouping symbols.
(20 - 3) + 2 5
22
2 + 18
______
=
4
20
= ___
4
=5
0 - 24
______
23. Use the formula 2πr(h + r)
2π(3)(7 + 3)
= 6π(10)
= 60π ≈ 188.4 ft 2
THINK AND DISCUSS
(20 - 3 + 2) 5
2 + 3(6)
_______
20. 5⎪s + (-2)⎥
5. 223 + 46 + 2(7) + 3(39)
= 223 +46 + 14 + 117
= 400
2.
3. 30 - 5 · 3
= 30 - 15 = 15
6. (5 - 8)(3 - 9)
= (-3)(-6) = 18
34. , terminating decimal, 1·3
1a. 8 ÷ __
2
=8×2·3
= 16 · 3
= 48
c. -20 ÷ (-2(4 + 1))
= -20 ÷ (-2(5))
= -20 ÷ -10
=2
2. 5 - 12 ÷ (-2)
= 5 + 6 = 11
24. 3 + 4(-5)
= 3 - 20 = -17
25. 20 - 4 + 5 - 2
= 16 + 5 - 2
= 21 - 2 = 19
26. 41 + 12 ÷ 2
= 41 + 6 = 47
27. 3(-9) + (-2)(-6)
= -27 + 12 = -15
28. 10 2 ÷ (10 - 20)
29. (6 + 2 · 3) ÷ (9 -7) 2
= 100 ÷ (-10) = -10
= (6 + 6) ÷ 2 2
= 12 ÷ 4 = 3
EXERCISES
30. -9 - (-18) + 6
= 9 + 6 = 15
GUIDED PRACTICE
1. Use the order of operations to make sure that
everyone gets the same value for an expression.
11
31. 15 ÷ (2 - 5)
= 15 ÷ (-3) = -5
Holt McDougal Algebra 1
32. 5(1 - 2) - (3 - 2)
= 5(-1) - 1
= -5 - 1 = -6
33. -6(3 - p) = -6(3 - 7)
= -6(-4) = 24
2
35. 13 - (3 + (j - 12)) = 13 - (3 + (5 - 12))
= 13 - (3 + (-7))
= 13 - (-4) = 17
36. (-4 - a) 2 = (-4 - (-3)) 2
2
= (-1) = 1
2
2
37. 7 - (21 - h) = 7 - (21 - 25)
= 7 - (-4) 2
= 7 - 16 = -9
38. 10 + (8 ÷ (q - 3)) = 10 + (8 ÷ (2 - 3))
= 10 + (8 ÷ -1)
= 10 + (-8) = 2
50. 7(2 + d )
52. √
5 + (-4)
b. Each pair of opposite faces are the same size,
so find the surface area of the prism, multiply the
areas of the top, front, and sides by 2, and then
add the 3 products. 2(w) + 2(h) + 2(wh). The
area you get from this expression is equivalent to
the sum in part a.
8-8
_____
2 -1
0
= __ = 0
1
2
45. √3
-5÷8
c. They should be equal because the expression in
part b is another way of adding all 6 faces of the
prism.
66.
47.
(_______) (______)( )
b1 + b2
4 + 10
h=
6
2
2
14 (6)
= ___
2
= 7(6) = 42 cm 2
( )
6⎪5 - 7⎥
_______
14 -2
6⎪-2⎥
= _____
12
12
___
=
=1
12
49. (-6 + 24) ÷ ⎪-3⎥
= 18 ÷ 3 = 6
67. Possible answer: To make a sandwich, you need to
get out the ingredients, put the ingredients on either
slice of bread, and then put the two slices together.
You would not want to put the second slice of bread
on top before putting the ingredients in the middle.
TEST PREP
68. C;
2
51. 3 - __
5
70.
53. 8 - ⎪3 · 5⎥
54. 2( + w) = 2((8) + (4))
= 2(12) = 24
55a. 50 + 10 ÷ 2
= 50 + 5 = 55
63. 3 · 5 - 6 · 2
= 15 - 12 = 3
2 3 - (-12)
64. __
⎪
⎥
3
2 ⎪15⎥
= __
3
2 (15) = 10
= __
3
65a. 3 · 4 + 3 · 5 + 4 · 5 + 3 · 4 + 3 · 5 + 4 · 5
2
= 12 + 15 + 20 + 12 + 15 + 20 = 94 in
41. 7x(3 + 2x) = 7(-1)(3 + 2(-1))
= -7(3 + (-2))
= -7(1) = -7
43.
57. 2[9 + (-x)]
62. 8 + (-3 · 5)
= 8 + (-15) = -7
40. -2(11b - 3) = -2(11(5) - 3)
= -2(55 -3)
= -2(52) = -104
= √
25 - 16
= √
9=3
f. 50 + 10 · 2
= 50 + 20 = 70
61. Parentheses are not needed because the order
of operations tells you to do multiplication before
addition.
39. (4r - 2) + 7 = (4(3) - 2) + 7
= (12 - 2) + 7
= 10 + 7 = 17
√
52 - 42
e. 50 - 10 · 2
= 50 - 20 = 30
√7
2 (-2 - 8)
59. _____
58. __
3
3 · 10
60a. Use the hint provided in the text book, find the total
score of the different events, then divide by the
number of events.
9.725 + 9.700 + 9.587 + 9.137 + 9.837 + 9.837
________________________________________
6
57.823
= ______
6
b. 9.637
34. 5 + (r + 2) = 5 + (4 + 2)
= 5 + 62
= 5 + 36 = 41
48.
d. 50 ÷ 10 · 2
= 5 · 2 = 10
56. 8 - 4n
2
42. -4⎪2.5 - 6⎥
= -4⎪-3.5⎥
= -14
3 + ⎪8 - 10⎥
44. ___________
2
3 + ⎪-2⎥
________
=
2
5
= __
2
-18 - 36
_________
46.
-9
-54
= ____ = 6
-9
c. 50 · 10 ÷ 2
= 500 ÷ 2 = 250
69. H;
√___________
54 - (-2)(5)
=
20 - 4 2
54 - (-10)
__________
√
20 - 16
64
___
=
4
= √
16
=4
√
b. 50 · 10 - 2
= 500 - 2 = 498
12
Holt McDougal Algebra 1
CHALLENGE AND EXTEND
71.
3+9·2
________
2
2-3
3 + 18
= ______
2-9
21 = -3
= ___
-7
73.
√__________
8 + 10 2
13 + (-10)
√
√
8 + 100
_______
3
108
= ____
3
= √
36 = 6
=
b.
72. ((-6 · 4) ÷ -6 · 4) 2
= (-24 ÷ -6 · 4) 2
= (4 · 4)
2
Comm. Prop.
Combine like terms
THINK AND DISCUSS
2
= 16 = 256
1. The sentence describes the Associative Property of
Addition.
2.
74. Possible answer:
2 · 4 + 5 -8
Associative
2 + (3 + 4) = (2 + 3) + 4
Commutative
2 + 5 = 5 +2
Distributive
75. 2(9 - 6) - 5
2
76. (⊗ + 5) + 1
= 81 + 1 = 82
-12x - 5x + 3a + x
-12 - 5x + x + 3a
-16x + 3a
2(6 + 7) = 2(6) + 2(7)
77. (⊗ + 1) 2 - 5
2
= ((⊗ + 1) - 3) - 2
= 22 - 2 = 20
EXERCISES
GUIDED PRACTICE
SPIRAL REVIEW
78. obtuse
79. acute
80. right
81. 51 + 49 = 100
( )
1 = -6 __
1
82. -5 + -1 __
3
3
1. Associative
83. -3 - 8 = -11
84. 2.9 - 5.3 = -2.4
85. √
64
82 = 8
= √
87.
36
2
6 =6
= 4.
86. √324
= √
18 2 = 18
88. - √
121
= - √
11 2 = -11
6.
8.
1-7 SIMPLIFYING EXPRESSIONS,
PAGES 46-51
CHECK IT OUT!
1 + 4 + 1 __
2
1a. 15 __
3
3
1 + 1 __
2+4
= 15 __
3
3
= 17 + 4 = 21
1·7·8
c. __
2
1·8·7
= __
2
= 4 · 7 = 28
b. 12(98)
= 12(100 - 2)
= 12(100) - 12(2)
= 1200 - 24 = 1176
3a. 16p + 84p = 100p
10.
b. 410 + 58 + 90 + 2
= 410 + 90 + 58 + 2
= 500 + 60 = 560
12.
2a. 9(52)
= 9(50 + 2)
= 9(50) + 9(2)
= 450 + 18 = 418
c. 7(34)
= 7(30 + 4)
= 7(30) + 7(4)
= 210 + 28 = 238
b. -20t - 8.5t = -28.5t
14.
16.
18. 17x 2 + x
20.
c. 3m 2 + m 3
4a.
6(x - 4) + 9
6(x) - 6(4) + 9
6x - 24 + 9
6x - 15
1 + 4 + 1 __
1
3. 16 + 2 __
2
2
1
1
__
= 16 + 4 + 2 + 1 __
2
2
= 20 + 4 = 24
1 · 8 · 21
5. __
27 + 98 + 73
3
= 73 + 27 + 98
1 · 21 · 8
= __
= 100 + 98 = 198
3
= 7 · 8 = 56
2 · 38 · 50
7. 50 · 118 · 20
= 2 · 50 · 38
= 50 · 20 · 118
= 100 · 38 = 3800
= 1000 · 118 = 118,000
9. 16(19)
14(1002)
= 16(20 - 1)
= 14(1000 + 2)
= 16(20) - 16(1)
= 14(1000) + 14(2)
= 320 - 16 = 304
= 14,000 + 28 = 14028
11. 8(57)
9(38)
= 8(60 - 3)
= 9(40 - 2)
= 8(60) - 8(3)
= 9(40) - 9(2)
= 480 - 24 = 456
= 360 - 18 = 342
13. 7(109)
12(112)
= 7(100 + 9)
= 12(100 + 12)
= 7(100) + 7(9)
= 12(100) + 12(12)
= 700 + 63 = 763
= 1200 + 144 = 1344
6x + 10x = 16x
15. 35x - 15x = 20x
-3a + 9a = 6a
17. -8r - r
= -8r - 1r = -9r
2. -12 + 67 + 12 + 23
= (-12 + 12) +
(67 + 23)
= 0 + 90 = 90
Distribute the 6
Multiply
Combine like terms
21.
13
19. 3.2x + 4.7x = 7.9x
5(x + 3) - 7x
5(x) + 5(3) - 7x
5x - 7x + 15
-2x + 15
Distribute the 5
Multiply
Add like terms
9(a - 3) - 4
9(a) - 9(3) - 4
9a - 27 - 4
9a - 31
Distribute the 9
Multiply
Add like terms
Holt McDougal Algebra 1
22.
23.
24.
25.
43.
2
2
5x - 2(x - 3x )
2
2
5x - 2(x) - 2(-3x )
2
2
5x - 2x + 6x
2
11x - 2x
Distribute the -2
Multiply
Add like terms
2
6x - x - 3x + 2x
2
6x - x + 2x - 3x
2
7x - 3x
Comm. Prop.
Add like terms
12x + 8x + t - 7x
12x + 8x - 7x + t
13x + t
Comm. Prop.
Add like terms
4a - 2(a - 1)
4a - 2(a) -2(-1)
4a - 2a + 2
2a + 2
Distribute the -2
Multiply
Add like terms
27. 5 · 14 · 20
= 5 · 20 · 14
= 100 · 14 = 1400
28. 6 · 3 · 5
=6·5·3
= 30 · 3 = 90
29. 4.5 + 7.1 + 8.5 + 3.9
= 4.5 + 8.5 + 7.1 + 3.9
= 13 + 11 = 24
30. 9(62)
= 9(60 + 2)
= 9(60) + 9(2)
= 540 + 18 = 558
31. 8(29)
= 8(30 - 1)
= 8(30) - 8(1)
= 240 - 8 = 232
32. 11(25)
= (10 + 1)(25)
= 10(25) + 1(25)
= 250 + 25 = 275
33. 6(53)
= 6(50 + 3)
= 6(50) + 6(3)
= 300 + 18 = 318
34. 3x + 9x = 12x
35. 14x 2 - 5x 2 = 9x 2
36. -7x + 8x = x
2
37. 3x - 4
38.
39.
40.
41.
42.
4(y + 6) + 9
4(y) + 4(6) + 9
4y + 24 +9
4y + 33
Distribute the 4
Multiply
Add like terms
-7(x + 2) + 4x
-7(x) - 7(2) + 4x
-7x - 14 + 4x
-3x - 14
Distribute the -7
Multiply
Add like terms
3x + 2 - 2x - 1
3x - 2x + 2 - 1
x+1
Comm. Prop.
Add like terms
5x - 3x + 3x 2 + 9x
2
5x - 3x + 9x + 3x
2
11x + 3x
Comm. Prop.
Add like terms
8x + 2x - 3y - 9x
8x + 2x - 9x - 3y
x - 3y
Comm. Prop.
Add like terms
Comm. Prop.
Add like terms
44. To find the total cost of the school supplies, first
round the cost of each item to the nearest dollar.
Binder: $4.89 → $5.00
Notebook: $1.99 → $2.00
Pen: $2.11 → $2.00
1(5.00) + 3(2.00) + 1(2.00)
= 5.00 + 6.00 + 2.00 = $13.00
So, Tavon spent about $13.00.
45a. Amy: 18:51 + 45:17 + 34:13
= 97:81 = 98:21;
Julie: 17:13 + 40:27 + 23:32
= 80:72 = 81:12;
Mardi: 19:09 + 38:58 + 25:32
= 82:99 = 83:39
Sabine: 13:09 + 31:37 + 19:01
= 63:47
PRACTICE AND PROBLEM SOLVING
26. 53 + 28 + 17 + 12
= 53 + 17 + 28 + 12
= 70 + 40 = 110
7y - 3 + 6y - 7
7y + 6y - 3 - 7
13y - 10
b. Sabine, Julie, Mardi, Amy
46. Comm. Prop.
47. Comm. Prop.
48. Assoc. Prop.
49. Distrib. Prop.
50. Assoc. Prop.
51. Distrib. Prop.
52. 2(2w) + 2(w)
= 4w + 2w = 6w
53. (8 - p) + 4p + (3p + 1)
= 8 - p + 4p + 3p + 1
= -p + 4p + 3p + 8 + 1
= 6p + 9
54. (4(2s + 3)
= 4(2s) + 4(3)
= 8s + 12
55. 10 - (7 - 3) = 10 - 4 = 6
(10 - 7) -3 = 3 - 3 = 0
No; when the numbers are associated differently,
the answers are different.
56. Possible answer: newspaper delivery; the
newspaper is delivered to all the houses on one
block. A newspaper is delivered to each house on
the block.
n(a + b + c + d) = na + nb + nc + nd
n = newspaper
a, b, c, d = houses on the block
57a. The length of the rectangle and the circumference
of the circles are equal.
b. A = w, = 2πr
= (2πr)w
= 2π(4)(12) = 96π ≈ 301.44
2
c. A circle = r π
= 4 2π = 16π
So, the total surface area of the figure is
2(16π) + 96π = 128π ≈ 401.92.
14
Holt McDougal Algebra 1
75. 2 - (6 - 8 ÷ (3 + 1))
= 2 - (6 - 8 ÷ 4)
= 2 - (6 - 2)
= 2 - 4 = -2
TEST PREP
58. D; Tiffany has x CDs, Ariel has 19 + x, and Victor
has 3(19 + x).
x + (19 + x) + 3(19 + x)
= x + 19 + x + 57 + 3x
= 19 + 57 + x + x + 3x
= 76 + 5x
59. J; P = 2( + w)
(
1-8 INTRODUCTION TO FUNCTIONS,
PAGES 54-59
)
= 2 (2(k + 5)) + 3 + k
CHECK IT OUT!
= 2((2k + 10) + 3 + k)
= 2(3k + 13)
= 6k + 26
1a.
T(-2, 6) 8
4
b.
-8
60. C; 33 · (25 + 18)
= 33 · 25 + 33 · 18
4
c.
62. -3((x - 2) + 5(x - 2))
= -3(6(x - 2))
= -3(6x - 12)
= -18x + 36
d. Quadrant II; negative x value and positive y value.
3. Artist’s fee is $10 plus $20 for each person.
y = 10 + 20x;
10 + 20(1) = 30;
10 + 20(2) = 50;
10 + 20(3) = 70;
10 + 20(4) = 90.
4a.
Input
x
Output
y
Ordered Pair
(x, y)
-4
__1 (-4) - 4 = -6
(-4, -6)
2
__1 (-2) - 4 = -5
2
__1 (0) - 4 = -4
2
__1 (2) - 4 = -3
2
__1 (4) - 4 = -2
2
-2
c. Distributive Property
d. Rule for Subtraction 66a. Distributive Property
0
b. Multiplication
2
SPIRAL REVIEW
68. A parallelogram = bh
A parallelogram = (7)(13)
= 91 mm 2
6
4
8
y
(-2, -5)
(0, -4)
(2, -3)
(4, -2)
line
2
69. 2 = 2 · 2 · 2 · 2 · 2 · 2 70. 18 = 18 · 18
= 64
= 324
()
R(2, -3)
c. Quadrant III; negative x and y values.
65a. Commutative Property
1
71. - __
2
8
b. Quadrant I; positive x and y values.
1 10 - g + -6 + 3g
64. __
) (
))
((
2
1 10 - 6 - g + 3g
= __
)
(
2
1
= __ (4 + 2g)
2
=2+g
67. A square = s 2
A square = 6 2
= 36 ft 2
x
4
2a. none; not on the graph
63. (2b + 5) - (8b + 6) + 3(b - 2)
= 2b + 5 - 8b - 6 + 3b - 6
= 2b - 8b + 3b + 5 - 6 - 6
= -3b - 7
b. Associative Property
S(0, 2)
-8
CHALLENGE AND EXTEND
61. 4(3(x + 9) + 2)
= 4(3x + 27 + 2)
= 4(3x + 29)
= 12x + 116
0
-4
y
3
( )( )( )
1 __
1
1 __
= - __
2 2 2
1
= - __
8
73. 3 + 4 - 10 ÷ 2 + 1
=7-5+1=3
4
x
( ) ( )( )
1
72. - __
2
74.
2
-8
1 - __
1
= - __
2
2
1
__
=
4
4
0
-4
8
-8
82 - 62
_______
82 + 62
64 - 36
= _______
64 + 36
28
7
= ____ = ___
100
25
15
Holt McDougal Algebra 1
b.
Input
x
Output
y
Ordered Pair
(x, y)
-3
3(-3) 2 + 3 = 30
(-3, 30)
2
-1
3(-1) + 3 = 6
(-1, 6)
0
2
3(0) + 3 = 3
(0, 3)
2
3(1) + 3 = 6
1
2
3(3) + 3 = 30
3
y
2.–5.
J
K L x
(1, 6)
M
6. Quadrant II; negative x value and positive y value.
(3, 30)
7. none; Origin
U shape
8. Quadrant IV; positive x value and negative y value.
24
9. none; on the x-axis
16
10. none; on the y-axis
8
11. Quadrant I; positive x and y values.
x
Input
x
Output
y
Ordered Pair
(x, y)
0
⎪0 - 2⎥ = 2
(0, 2)
1
⎪1 - 2⎥ = 1
(1, 1)
2
⎪2 - 2⎥ = 0
(2, 0)
1x
12. y = __
4
1 (76) = 19
= __
4
__
= 1 (100) = 25
4
1 (120) = 30
= __
4
__
= 1 (168) = 42
4
(76, 19), (100, 25), (120, 30), (168, 42)
3
⎪3 - 2⎥ = 1
(3, 1)
13.
4
⎪4 - 2⎥ = 2
(4, 2)
-4
c.
y
4
-2
0
2
4
y
Input
x
Output
y
Ordered Pair
(x, y)
-2
(-2) + 2
(-2, 0)
-1
(-1) + 2
(-1, 1)
0
(0) + 2
(0, 2)
1
(1) + 2
(1, 3)
2
(2) + 2
(2, 4)
V shape
2
x
0
-2
4
2
6
-4
line
y
x
THINK AND DISCUSS
1. Start at the origin, and move three units left. Then
move up 6 units.
x is neg.
y is pos.
x is neg.
y is neg.
Quadrant lll
Input
x
Output
y
Ordered Pair
(x, y)
x is pos.
y is pos.
-2
-(-2)
(-2, 2)
-1
-(-1)
(-1, 1)
x is pos.
y is neg.
0
-(0)
(0, 0)
1
-(1)
(1, -1)
2
-(2)
(2, -2)
14.
Quadrant l
The
Coordinate
Plane
2. Check students’ work. The x-coordinate must be 0;
possible answer: (0, 4).
3. Quadrant ll
Quadrant lV
EXERCISES
GUIDED PRACTICE
line
y
x
1. The first coordinate tells which way to move, left
or right. The second coordinate tells which way to
move, up or down. If you switch the direction of
each coordinate, you will not get the same point.
16
Holt McDougal Algebra 1
15.
Input
x
28.
Ordered Pair
(x, y)
Input
x
Output
y
Ordered Pair
(x, y)
-2
Output
y
-2⎪(-2)⎥ = -4
(-2, 2)
-2
6 - 2(-2) = 10
(-2, 10)
-1
-2⎪(-1)⎥ = -2
(-1, 1)
-1
6 - 2(-1) = 8
(-1, 8)
0
-2⎪(0)⎥ = 0
(0, 0)
0
6 - 2(0) = 6
(0, 6)
1
-2⎪(1)⎥ = -2
(1, -1)
1
6 - 2(1) = 4
(1, 4)
2
-2⎪(2)⎥ = -4
(2, -2)
2
6 - 2(2) = 2
(2, 2)
V shape
y
line
y
x
x
16.
Input
x
Output
y
__1 (-2) 2
2
__1 (-1) 2
2
__1 (0) 2
2
__1 (1) 2
2
__1 (2) 2
2
-2
-1
0
1
2
29.
Input
x
Output
y
Ordered Pair
(x, y)
-2
-((-2) 2) = -4
(-2, -4)
(-2, 2)
-(
-1
(-1, _12 )
-((0) 2) = 0
0
-(
1
(0, 0)
-(
2
(1, _12 )
(2, 2)
) = -1
(-1) 2
) = -1
) = -4
(-1, -1)
(0, 0)
(1) 2
(1, -1)
(2) 2
(2, -4)
U shape
y
x
U shape
y
Ordered Pair
(x, y)
x
30.
17.–20.
Input
x
Output
y
Ordered Pair
(x, y)
-2
3⎪(-2)⎥ = 6
(-2, 6)
-1
3⎪(-1)⎥ = 3
(-1, 3)
0
3⎪(0)⎥ = 0
(0, 0)
1
3⎪(1)⎥ = 3
(1, 3)
2
3⎪(2)⎥ = 6
(2, 6)
y
D
x
E
G
F
21. none; on the y-axis
V shape
y
22. Quadrant IV; positive x value and negative y value.
x
23. none; on the x-axis
24. Quadrant IV; positive x value and negative y value.
25. Quadrant II; negative x value and positive y value.
26. Quadrant I; positive x and y values.
1
of his sales.
27. Jeremy’s wage is $500 plus __
10
y = 500 + 0.10x
500 + 0.10(500) = 550;
500 + 0.10(3000) = 800;
500 + 0.10(5000) = 1000;
500 + 0.10(7500) = 1250;
(500, 550), (3000, 800), (5000, 1000), (7500, 1250)
17
Holt McDougal Algebra 1
31.
Input
x
Output
y
Ordered Pair
(x, y)
-2
(-2) 2 + 3 = 7
(-2, 7)
-2
Output
y
y = 3 + ⎪-2⎥ = 5
-1
(-1) + 3 = 4
(-1, 4)
-1
y = 3 + ⎪-1⎥ = 4
(-1, 4)
0
2
(0) + 3 = 3
(0, 3)
0
y = 3 + ⎪0⎥ = 3
(0, 3)
2
(1, 4)
1
y = 3 + ⎪1⎥ = 4
(1, 4)
2
(2, 7)
2
y = 3 + ⎪2⎥ = 5
(2, 5)
2
(1) + 3 = 4
1
(2) + 3 = 7
2
Input
x
U shape
y
38.
x
4
33.
y
(-1, 1) 2
-4
0
-2
2
Output
y
Ordered Pair
(x, y)
-2
__1 (-4) + (-3) = -5
(-4, -5)
(4, 4)
-1
0
y
(-6, 7)
4
(-6, 5)
1
(4, 7)
2
(4, 5)
x
(6, 2)
2
6
(3, -1) (5, -1)
-8
-4
0
-4
4
8
(-2, -4)
(0, -3)
(2, -2)
(4, -1)
line
y
-8
x
Rectangle
36. Salary is equal to $32,000 plus $2700 per year
of experience. Let x be the number of years of
experience.
y = 32,000 + 2700x
40.
32,000 + 2700(0) = 32,000
32,000 + 2700(2) = 37,400
32,000 + 2700(5) = 45,500
32,000 + 2700(7) = 50,900
(0, 32,000), (2, 37,400), (5, 45,500), (7, 50,900)
Input
x
Output
y
Ordered Pair
(x, y)
-5
(-5) 2 + 1 = 26
(-5, 26)
2
(-3) + 1 = 10
-3
2
(-1) + 1 = 2
-1
37a. f = yards; c = total cost;
total cost is equal to $2.90 per yard
c = 2.90f
2
(1) + 1 = 2
1
c = 2.90f
c = 2.90(1) = $2.90
c = 2.90(2) = $5.80
c = 2.90(3) = $8.70
c = 2.90(4) = $11.60
c = 2.90(5) = $14.50
(-1, 2)
(1, 2)
(3, 10)
2
(5, 26)
(5) + 1 = 26
5
(-3, 10)
2
(3) + 1 = 10
3
b. f is input, and c is output.
f
1
2
3
4
5
2
__1 (-2) + (-3) = -4
2
__1 (0) + (-3) = -3
2
__1 (2) + (-3) = -2
2
__1 (4) + (-3) = -1
2
8
Triangle
Pentagon
c.
Input
x
-8
(4, -4)
x
0
4
4
(2, -2)
(-7, -3) -4
35.
(2, 2)
39.
-8 -4
2
y
4
y
x
Square
6
8
(-6, 3)
(4, 1)
x
(-1, -4)
34.
32.
(-2, 5)
V shape
y
x
Ordered Pair
(x, y)
U shape
y
x
d. 2.90f < c
2.90f < 21.00
f < 7.24
The whole yard less than 7.24 yards is 7 yards.
18
Holt McDougal Algebra 1
b. The coordinates of the second point are the
opposite of the coordinates of the first point. To
graph (4, 2), move right and then up. To graph
(-4, -2), move left and then down.
41a. Number of bottles is equal to 50 plus one and a
half bottles for every preregistered contestant. Let
y represent the number of bottles, and x represent
the number of preregistered contestants.
y = 50 + 1.5x
48. A; the first number was used as the y-coordinate and
the second number was used as the x-coordinate.
b. y = 50 + 1.5x
50 + 1.5(100) = 200
50 + 1.5(150) = 275
50 + 1.5(200) = 350
50 + 1.5(250) = 425
50 + 1.5(300) = 500
(100, 200), (150, 275), (200, 350), (250, 425),
(300, 500)
49. The line for y = x + 2 is 2 units higher than the line
for y = x at every value of x.
4
y=x+2
TEST PREP
50. C; both ordered pairs satisfy this equation
x
0
2
51. G; substituting 1, 2, 3, 4 into x for y = 2x - 4 will
result in the values in the y column of this table.
4
-2
8
7 and -3 < __
52. D; D(4, -3), 4 > __
2
3
53. H; (2 + 3, 5 - 2) = (5, 3)
-4
43. (1, 4), (2, 3), (3, 2); line
54. W(x + 4, y - 8) = W(5 + 4, 2 - 8)
= W(9, -6)
y
4
2
2
55. X(5 - x, y ) = X(5 - (-1), 3 )
= X(6, 9)
2
x
0
2
4
56. Y(x + y, y - x) = Y(6 + 3, 3 - 6)
= Y(9, -3)
-2
-4
2
2
57. Z(xy, x y) = Z((-1)(4), (-1) (4))
= Z(-4, 4)
44. (2, 1), (4, 2), (6, 3); line
4
y
CHALLENGE AND EXTEND
54.–57.
2
Z(-4, 4)
x
0
-2
2
6
4
-8
-4
X(6, 9)
4
0
-4
4
8
Y(9, -3)
W(9, -6)
58. The points make a vertical line at x = 3.
y
59. The points make a horizontal line at y = 6.
4
60. Plot the points on a coordinate plane, then connect
the points. = 8; w = 4.
P = 2( + w) = 2(8 + 4)
= 2(12) = 24 units.
x
0
y
4
-8
45. (3, 1), (6, 2), (9, 3); line
-4
8
x
-2
8
x
4
-4
2
-2
2
y
4
-4
y=x
-2
42. (1, 2), (2, 3), (3, 4); line
-2
2
-4
42–45. Possible coordinates given
-4
y
4
8
-4
-8
61. The coordinate of the fourth vertex are (-4, 5). The
area of the rectangle is 42 square units.
46. The points make a line that passes from Quadrant
II, goes through the origin and into Quadrant IV.
47a. Both ordered pairs have positive coordinates, but
to graph (4, 2), you move right 4 units and then up
2 units. To graph (2, 4), you move right 2 units and
then up 4 units.
62. quadrilateral
63. cylinder
64. pyramid
65. pentagon
66. rational, terminating decimal, integer, whole, natural
67. irrational
68. rational, repeating decimal
19
Holt McDougal Algebra 1
23.–25.
69. rational, terminating, integer
2
1 · 18 · 25
70. __
71. x + 3x
5
1 · 25 · 18
= __
5
= 5 · 18 = 90
72. 2a - b + a + 4b
= (2a + a) + (-b + 4b)
= 3a + 3b
y
4
C(1, 4)
2
x
-4
-2
0
-2
4
2
A(0, -3)
B(-2, -3)
26. Quadrant II; negative x value and positive y value.
27. None; on the y-axis.
READY TO GO ON? PAGE 61
28. Quadrant I; positive x and y values.
1. -6 + 12 ÷ (-3)
= -6 - 4 = -10
2. 30 - 9 + 4
= 21 + 4 = 25
3. (6 - 8) · (7 - 5)
= -2 · 2 = -4
4. 8 · (8 - (4 - 2))
= 8 · (8 - 2)
= 8 · 6 = 48
23
5
5. ___ - 3 · __
4
4
23
15
= ___ - ___
4
4
8
= __ = 2
4
16
________
7.
9 - (-7)
29. Quadrant III; negative x and y values.
30. Quadrant IV; positive x value and negative y value.
31. None; on the x-axis.
32.
6. ⎪3 - 9⎥ ÷ 2 + 5
=6÷2+5
=3+5=8
Input
x
Output
y
Ordered Pair
(x, y)
-2
2
(-2) + 1 = 5
(-2, 5)
(-1) + 1 = 2
-1
(0, 1)
2
(1, 2)
2
(2, 5)
(1) + 1 = 2
1
8. 5(6 + 4)
(2) + 1 = 5
2
U shape
y
1 (3 + 5) · 4
= __
2
1 (8) · 4
= __
2
= 4 · 4 = 16 square centimeters
6
4
x
-4
11. 5 · 18 · 20
= 5 · 20 · 18
= 100 · 18 = 1800
33.
12. 1/4 · 19 · 8
= 1/4 · 8 · 19
= 2 · 19 = 38
13. 7(67)
= 7(70 - 3)
= 7(70) - 7(3)
= 490 - 21 = 469
14. 9(29)
= 9(30 - 1)
= 9(30) - 9(1)
= 270 - 9 = 261
15. 17(18)
= 17(20 - 2)
= 17(20) - 17(2)
= 340 - 34 = 306
16. 8(106)
= 8(100 + 6)
= 8(100) + 8(6)
= 800 + 48 = 848
2
2
(-1, 2)
2
(0) + 1 = 1
0
1 (b + b )h
9. A trapezoid = __
2
2 1
10. 75 + 32 + 25
= 75 + 25 + 32
= 100 + 32
2
-2
0
2
4
Input
x
Output
y
Ordered Pair
(x, y)
-2
(-2) - 1 = -3
(-2, 5)
-1
(-1) - 1 = -2
(-1, 2)
0
(0) - 1 = -1
(0, 1)
1
(1) - 1 = 0
(1, 2)
2
(2) - 1 = 1
(2, 5)
4
line
y
2
x
2
17. 4k + 15k = 19k
18. x + 22x = 23x
19. -2g + 5g = 3g
20. 3(x + 2) - 3x
= 3x + 6 - 3x = 6
-4 -2
0
2
4
-4
2
2
21. x - 6x + 3x + 4x
2
2
= (-6x + 4x ) + (x + 3x)
= -2x 2 + 4x
22. -2(3x + 2y + 4x - 5y)
= -2(3x) - 2(2y) - 2(4x) - 2(-5y)
= -6x - 4y - 8x + 10y
= (-6x - 8x) + (-4y + 10y)
= -14x + 6y
20
Holt McDougal Algebra 1
34.
STUDY GUIDE: REVIEW, PAGES 62-65
Input
x
Output
y
Ordered Pair
(x, y)
-2
-⎪(-2)⎥ = -2
(-2, -2)
-1
-⎪(-1)⎥ = -1
(-1, -1)
0
-⎪(0)⎥ = 0
(0, 0)
1
-⎪(1)⎥ = -1
(1, -1)
5. 1.99g
6. t + 3
2
-⎪(2)⎥ = -2
(2, -2)
7. qp = (1)(5) = 5
8. p ÷ q = (5) ÷ (1) = 5
4
VOCABULARY
10. 150 ÷ m
150 ÷ (5) = 30
150 ÷ (6) = 25
150 ÷ (10) = 15
4
-4
35.
1-2 ADDING AND SUBTRACTING REAL
NUMBERS
Input
x
Output
y
Ordered Pair
(x, y)
-2
3(-2) + 3 = -3
(-2, -3)
-1
3(-1) + 3 = 0
(-1, 0)
0
3(0) + 3 = 3
(0, 3)
1
3(1) + 3 = 6
(1, 6)
2
3(2) + 3 = 9
(2, 9)
8
11. -2 + (-12) = -14
( )
3
1 + -4 __
13. 9 __
4
4
5
3
__
__
=8 -4
4
4
2
1
__
__
=4 =4
4
2
15. -8 -16 = -24
3
1 - __
14. __
2
2
2
__
= - = -1
2
16. 6.7 - (-7.6)
= 6.7 + 7.6 = 14.3
1-3 MULTIPLYING AND DIVIDING REAL
NUMBERS
x
4
12. -6 + 1.4 = -4.6
17. 2278 - 47 = 2231 ft
line
y
4
-8 -4 0
-4
4. origin
9. q + p = (1) + (5) = 6
x
0
-4
2. whole numbers
3. coefficient
1–1 VARIABLES AND EXPRESSIONS
V shape
y
1. constant
8
-8
36. Let y represent the volume of water in gallons and x
represent time in minutes.
y = 30,000 - 100x
Substitute 30 for x.
y = 30,000 - 100(30)
= 30,000 - 3000
= 27,000 (30, 27,000)
Substitute 60 for x.
y = 30,000 - 100(60)
= 30,000 - 6000
= 24,000 (60, 24,000)
18. -5(-18) = 90
19. 0 · 10 = 0
20. -4(3.8) = -15.2
21. -56 ÷ 7 = -8
22. 0 ÷ 0.75 = 0
23. 9 ÷ 0 = undefined
4
24. 4 ÷ __
9
9
4 × __
= __
1
4
4(9)
____
=
1(4)
36
___
=9
=
4
3
1 ÷ __
25. - __
4
2
4
1 × __
= - __
3
2
1(4)
= - ____
2(3)
2
4
__
= - = - __
6
3
26.
__6 ÷ __2
7
=
Substitute 90 for x.
y = 30,000 - 100(90)
= 30,000 - 9000
= 21,000 (90, 21,000)
5
__6 × __5
7
2
6(5)
= ____
7(2)
30
= ___ = 15/7
Substitute 120 for x.
y = 30,000 - 100(120)
= 30,000 - 12,000
= 18,000 (120, 18,000)
14
365 days
10,000
steps
27. ___________ × ________
1 year
1 day
10,000(365)
= __________
1(1)
= 3,650,000
21
Holt McDougal Algebra 1
60. 8(x - 8)3 = 8((9) - 8)3
1-4 POWERS AND EXPONENTS
28. 4 · 4 · 4 = 64
3
= 8(1)
= 8(1) = 8
29. (-3)(-3)(-3) = -27
30. (-3)(-3)(-3)(-3) = 81 31. -(5 · 5) = -25
( )( )( )
34. 16 = 2 · 2 · 2 · 2 = 2
4 - __
4 = 16/25
33. - __
5
5
2
= ((-4) + 4) ÷ 2
= (16 + 4) ÷ 2
= 20 ÷ 2 = 10
4
35. -1000 = (-10)(-10)(-10) = (-10)
36. 64 = (-8)(-8) = (-8)
37. 12 = 12
61. ((3 - x)2 + 4) ÷ 2 = ((3 - (7))2 + 4) ÷ 2
( )( )
8
2 __
2 __
2 = ___
32. __
3 3 3
27
3
62. 8 + 7(-2)
2
1
40. √
64 =
3
√
43 = 4
3
1-7 SIMPLIFYING EXPRESSIONS
41. - √
49 = - √
7 2 = -7
1
66. 18 + 26 - 8 + 4
67. 60 · 27 · __
6
= (18 - 8) + (26 + 4)
1 · 27
= 60 · __
= 10 + 30 = 40
6
= 10 · 27 = 270
68. 13(103)
69. 18(99)
= 13(100 + 3)
= 18(100 - 1)
= 13(100) + 13(3)
= 18(100) - 18(1)
= 1300 + 39 = 1339
= 1800 - 18 = 1782
42. - √
144 = - √
12 2 = -12
43.
25
___
√
36
=
=
44.
√
52
__
62
__5 2 = __5
6
6
√( )
1
___
√
27
3
=
√
3
13
__
33
3 __1 3 = __1
=
3
3
√( )
72. 6(x + 4) - 2x
= 6(x) + 6(4) - 2x
= 6x + 24 - 2x
= 6x - 2x + 24
= 4x + 24
46. rational number, terminating decimal, integer, whole
number
47. rational number, terminating decimal, integer
73. -2(x 2 - 1) + 4x 2
= -2(x 2) - 2(-1) + 4x 2
= -2x 2 + 2 + 4x 2
= -2x 2 + 4x 2 + 2
= 2x 2 + 2
48. rational number, terminating decimal,
49. irrational number
50. rational number, repeating decimal
A
51. s = √
= √
13 ≈ 3.6
So the length of one side of the table is about 3.6 ft.
2
74. -2y + 3y - 3y + y
= (-2y - 3y + y) + 3y 2
= -4y + 3y 2
75. 7y + 3y - a - 2y
= (7y + 3y - 2y) - a
= 8y - a
1-6 ORDER OF OPERATIONS
54. (8 + (2 - 6)
)÷4
2
= (8 + (-4) ) ÷ 4
2
= (8 + 16) ÷ 4
= 24 ÷ 4 = 6
71. 2y 2 + 5y 2 = 7y 2
70. 20x - 16x = 4x
45. rational number, terminating decimal, integer, whole
number, natural number
52. 5 · 4 + 3
= 20 + 3 = 23
8+3
65. Use the formula given, substitute 3 for t, and 8 for v.
16t 2 + vt = 16(3)2 + (3)(8)
= 16(9) + 24 = 144 + 24 = 168
So the distance traveled in 3 s is 168 ft.
1-5 ROOTS AND REAL NUMBERS
√
62 = 6
12
_____
20 - x
64. 4 √
3
38. V cube = s
= 9 3 = 9 · 9 · 9 = 729 in 3
=
39. √36
63.
53. 17 + 3(-3)
= 17 - 9 = 8
4 2 - 11
55. _______
10
16 - 11
_______
=
10
5
1
___
=
= __
10
2
57. √4 · 5 + 5 - 5
= √
20 + 5 - 5
=5-5=0
76. 4.99 + 2(1.48) + 0.89
= 4.99 + 2.96 + 0.89
≈5+3+1
= $9.00
1-8 INTRODUCTION TO FUNCTIONS
56. ⎪12 - 3 · 7⎥ · (-2)
= ⎪12 - 21⎥ · (-2)
= ⎪-9⎥ · (-2)
= 9 · (-2) = -18
58. 48 - x + 29 = 48 - (15) + 29
= 33 + 29 = 62
77.–80.
B
y
C
A
x
D
59. x + 4 · 6 - 10 = (-4) + 4 · 6 - 10
= (-4) + 24 - 10 = 10
81. Quadrant I; positive x and y values
22
Holt McDougal Algebra 1
14. (-3)(-6) = 18
1
1 ÷ __
15. - __
4
2
4
1
__
= - × __
1
2
1(4)
= - ____
2(1)
4 = -2
= - __
2
82. Quadrant IV; positive x value and negative y value
83. Quadrant I; positive x and y values
84. Quadrant II; negative x value and positive y value
85. Quadrant III; negative x and y values
86. Quadrant IV; positive x value and negative y value
87. Price after tax is equal to price of the item plus 1/20
of the price.
1 (P
)
P after tax = P before tax + ___
20 before tax
1 (2) = 2 + 0.1 = $2.1;
= (2) + ___
20
1 (15) = 15 + 0.75 = $15.75;
= (15) + ___
20
1 (30) = 30 + 1.50 = $31.50;
= (30) + ___
20
1 (40) = 40 + 2.00 = $42.00;
= (40) + ___
20
16. 12 ÷ (-3) = -4
17. (0) ÷ -4 = 0
18. 5 · 5 · 5 · 5 = 625
64
4 - __
4 - __
4 = - ____
19. - __
5
5
5
125
20. 2 · 2 · 2 · 2 · 2 = 32
21. -(6 · 6) = -36
( )( )( )
22. rational, terminating decimal, integer, whole number,
natural number
23. irrational
24. rational, terminating decimal, integer
The ordered pairs are: ($2, $2.10), ($15, $15.75),
($30, $31.50), ($40, $42)
88.
Input
x
Output
y
Ordered Pair
(x, y)
-4
__1 (-4) 2 = 4
(-4, 4)
4
__1 (-1) 2 = __1
4
4
__1 (0) 2 = 0
4
__1 (1) 2 = __1
4
4
__1 (4) 2 = 4
4
-1
0
1
4
(
1
-1, __
4
25. rational, terminating decimal
26.
)
(0, -3)
( )
(4, 4)
29. No; the first phrase represents the expression
2(n + 5), and the second phrase represents the
expression 2n + 5.
3
1 + 7 + 2 __
30. 5 __
31. -2(x + 5) + 4x
4
4
= -2(x) - 2(5) + 4x
3
1 + 2 __
= 5 __
+7
= -2x - 10 + 4x
4
4
= -2x + 4x - 10
= 8 + 7 = 15
= 2x - 10
32. 3x + 2x 2 - x
= 3x - x + 2x 2
= 2x + 2x 2
x
CHAPTER TEST, PAGE 66
33.–36.
1. c - a = (6) - (2) = 4
2. ab = (2)(3) = 6
3. c ÷ a = (6) ÷ (2) = 3
(6)
c
4. __ = ___ = 2
b
(2) 2
-8
= ___ = -2
4
28. 22 + (-2(19 - x)) = 22 + (-2(19 - 7))
= 22 + (-2(12))
= 22 + (-24) = -2
1
1, __
4
x2
27. 8(x - 1) 2 = 8(11 - 1) 2
= 8(10) 2
= 8(100) = 800
U shape
y
-2 - 6
-2 - 6 _______
_______
=
y
Y
X
(3)
5. b - a = (3) - (2) = 1
Z
x
W
6. five less than n; the difference of n and 5
7. 8n; 8(5) = 40 mi
8. -5 + 8 = 3
9. -3 - 4 = -7
10. 4 + (-7) = -3
11. 7 - (-2) = 9
12. ⎪(-80) - 12⎥
= ⎪-92⎥ = 92°F
13. ⎪(-47) - (-23)⎥
= ⎪-24⎥ = 24°F
23
Holt McDougal Algebra 1
37.
Input
x
Output
y
Ordered Pair
(x, y)
-2
2(-2) - 1 = -5
(-2, -5)
-1
2(-1) - 1 = -3
(-1, -3)
0
2(0) - 1 = -1
(0, -1)
1
2(1) - 1 = 1
(1, 1)
2
2(2) - 1 = 3
(2, 3)
line
y
x
24
Holt McDougal Algebra 1