Chapter 1
NUMBERS AND ALGEBRAIC
EXPRESSIONS
24.
32. 36−
8
Real Numbers
9
32.
(
)
(
)
18 18
−+−
=−
10
()
10
10 C
=
°
$1.786 billion
=
1. a.
Real Numbers
Exercises
2.
22
=−
431
+−−
11
14.
()
21 21
−−
16.
036
−
18.
25 25
−−
20.
()
819
−−
(
)
32. 47
−−
38.
12 4 9
+− −−
()
312
=+−
12
52.
()
28 17
−−−
54.
() ()
()
532 9
532 9
−−− + +−
=− + + + −
60. Alabama
114 ( 27) 141−− =
114 ( 64) 178−− =
=
238 196
=− +
178 196
=− +
b. When the difference is rewritten as a sum,
()
415.−− = The difference,
5, is larger than the two numbers, 4 and 1.
−
13
Real Numbers
6. The associative property of multiplication
14. Multiplicative identity property
(
)
32.
()()
9122
−−
0
=
(
)
(
)
48.
()
⎟
(
)
()
52 6
=− −
14
54.
()
54 6 9
−−
=
58. a.
()
62 2
12 2
10
−+
=− +
=−
b.
()
61 2
−+
e.
()
62 2
12 2
−−+
=+
5.17
≈−
64. Commutative property of multiplication
1
4
9
=
2
18
−
⋅
()
3
1
−−
85 2 0
83
=−+
=
b.
() ( ) ()
19 5 1 2 0 0
+−+
1. Since multiplication can be thought of as
repeated addition, we can use the number
3.
()()
() ( )
32
62 1 32 5
61 3 3
⎢
⎥
⎣
⎦
⎡
⎤
=− − −
⎢
⎥
⎣
⎦
Answers may vary.
15
Real Numbers
6. Any nonzero real number a has a
10. a. 1
(
)
71
⎛⎞
⎜⎟
⎜
⎝⎠
34.
()
210
⎜
⎝⎠
(
)
12 0.3 40÷− =−
(
)
(
)
16
56.
()()
32 8 5 6
÷− +− ⋅
58.
() ()
610
35
−÷ +−
⎟⎟
⎜⎜
⎟⎟
⎜⎜
⎝⎠ ⎝⎠
64. a.
d. 11
, or
−
20
The client lost an average of 1
1lb
3 per
1.
()
62 3
331
−÷ =−
−÷− =
17
Translations, and
(
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18
(
)
(
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(
)
(
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(
)
(
)
(
)
()
()
Formulas
(
)
(
)
6
=−
24
=
14.
(
)
=
18.
24
42
ca
+−+
+
19
()
()
()
2
99
512
9
=−−
(
)
()()
()()
90.52
90.52
9
4
=
()
()
30 1 0 1 1
31 1 3 1 4
+=+=
+=+=
32. 3
n
()
51
−=−
36. 2
g
(
)
()
2
2
00
11
=
=
20
(
)
(
)
() ()
2
2
02020022
1212 122 1
−− +=−+=
− − +=−−+=−
()
9
=−−
42.
(
)
1
AP rt=+
44. 22Plw=+
13
23 22
24
P⎛⎞ ⎛⎞
⎟⎟
⎜⎜
=+
⎟⎟
⎜⎜
⎟⎟
⎜⎜
⎝⎠ ⎝⎠
4
376.8 m
=
50.
150lb
40lb
120 mg 150lb
=⋅
()
2
37.5 cm
=
()
()
4
386
4
−=−
()
60. 23
43
ba
=
−−−
21
()
a bababa baba b aba b ab++++=++≥+
n
12. 1
24. Terms: 30 and 2 ; unlikeA−
(
)
(
)
p
22
62.
()( )
13 1 84 5
aa a
+− + + +
66.
(
)
[
]
23
3. a. Combining like terms means
combining like measures – feet with
feet and inches with inches.
b. Combining like terms means
