Selected Answers
Chapter 1
Get Ready! p. 1
1. 6 2. 5 3. 1 4. 20 5. 15 6. 44 7. 72 8. 150 9. 400 10. 8 11. $294 12.
4
5
4 fifths 13.
5
7
5 sevenths 14.
1
7
1 seventh 15.
12
13
12 over 13 16. 0.7 17. 0.6 18. 0.65 19. 0.93 20.
0.4
6
¯
0.4 , 6 bar 21.
11
14
11 over 14 22.
10
7
15
10 , and 7 fifteenths 23.
1
10
1 tenth 24.
3
11
12
3 , and 11 over 12 25. Answers may vary. Sample:
20
+
15
20 plus 15 26. Answers may vary. Sample: A simplified expression is one that is briefer or easier to work with than the original expression. 27. Answers may vary. Sample: To evaluate an expression means to find its numeric value for given values of the variables.
Lesson 1-1 pp. 4-9
Got It? 1.
n
+
18
n plus 18 2a.
6
n
6 n b.
18
n
18 over n c. No; 6 less a number y means
6
−
y
6 minus y and 6 less than a number y means
y
−
6
.
y minus 6 . 3a.
4
x
−
8
4 x minus 8 b.
2
(
x
+
8
)
2 open x plus 8 close c.
5
12
+
x
fraction 5 , over 12 plus x end fraction 4a. the sum of a number x and 8.1 b. the sum of ten times a number x and 9 c. the quotient of a number n and 3 d. five times a number x less 1 5. subtract 2 from the number of sides in the polygon;
n
−
2
n minus 2
Lesson Check 1a. numerical b. algebraic c. numerical 2a.
9
t
9 t b.
x
−
1
2
x minus , 1 half c.
m
+
7.1
m plus 7.1 d.
207
n
207 over n 3. six times a number c
4. one less than a number x
5. the quotient of a number t and 2 6. 4 less than the product of 3 and a number t
7. Numerical expressions are mathematical phrases involving only numbers and operations. Algebraic expressions are mathematical phrases that include one or more variables. An algebraic expression includes at least one variable. A numerical expression does not include any variables. 8.
49
+
0
.
75
n
49 plus 0 . 75 n
Exercises 9.
p
+
4
p plus 4 11.
n
−
12
n minus 12 13.
n
8
n over 8 15.
x
−
23
x minus 23 17.
1
3
n
1 third , n 19.
2
w
+
2
2 w plus 2 21.
(
17
−
k
)
+
9
open 17 minus k close plus 9 23.
37
t
−
9.85
37 t minus , 9.85 25.
15
+
60
w
15 plus , 60 over w 27. 5 more than a number q
29. the quotient of y and 5 31. 14.1 less a number w
33. one more than the product of 9 and a number n
35. the quotient of z and 8 less 9 37. the difference of 15 and the quotient of 1.5 and d
39. 5 more than the product of 9 and a number n;
9
n
+
5
9 n plus 5 41.
8
−
9
r
8 minus 9 r 43.
3
7
y
−
4
3 sevenths , y minus 4 45. It should be “the Quotient of 5 and n.” 47.
4.50
t
4.50 , t 49. A 59.
3
4
3 fourths 60.
5
14
5 fourteenths 61.
7
10
7 tenths 62.
1
6
1 sixth 63. 3 64. 3 65. 1 66. 4
Lesson 1-2 pp. 10-15
Got It? 1a. 81 b.
8
27
8 twenty sevenths c. 0.125 2a. 27 b. 7 c. 17 d. A fraction bar acts as a grouping symbol since you simplify numerator and denominator before you divide. 3a. 3 b. 11 c. 20;
(
x
y
)
2
≠
x
y
2
open , x y , close squared . not equal to x , y squared 4.
c
+
1
10
c
;
c plus , 1 tenth , c semicolon $47.30, $86.90, $104.50, $113.30
Lesson Check 1. 25 2. 8 3.
9
16
9 sixteenths 4. 23 5. 1728 6. 0 7. exponent 3; base 4 8. The student subtracted before multiplying;
23
−
8
·
2
+
3
2
=
23
−
8
·
2
+
9
=
23
−
16
+
9
=
7
+
9
=
16
23 minus 8 middle dot 2 plus , 3 squared , equals 23 minus 8 middle dot 2 plus 9 equals 23 minus 16 plus 9 equals 7 plus 9 equals 16
Exercises 9. 243 11. 16 13.
8
27
8 twenty sevenths 15. 0.004096 17. 2 19. 4.5 21. 53 23. 16 25. 1728 27. 1024 29. 1024 31. 496 33. 3458 35.
mv; 15,000, 20,000, 25,000 37. 256 39. 5 41. 12 43.
3
8
s
;
6
3 eighths , s semicolon 6 oz; 9 oz; 30 oz; 37.5 oz 45. 27 47. 6 49. 68 51. 3 53. Yes; you can simplify the expression in the first set of parentheses first, or you can simplify the expression in the second set of parentheses first. 55. 20;
14
−
5
·
3
+
3
2
14 minus 5 middle dot 3 plus , 3 squared 65.
p
+
4
p plus 4 66.
5
−
3
y
5 minus 3 y 67.
m
10
m over 10 68.
3
(
7
−
d
)
3 open 7 minus d close 69. prime 70. composite 71. prime 72. composite 73. 0.6 74. 0.875 75.
0.
6
¯
0. , 6 bar 76.
0.
571428
¯
0. . 571428 bar 77.
7
10
7 tenths 78.
7
100
7 100ths 79.
4
1
4
or
17
4
4 , and 1 fourth , or , 17 over 4 80.
17
40
17 over 40
Lesson 1-3 pp. 16-22
Got It? 1a. 8 b. 5 c.
1
6
1 sixth d.
9
11
9 elevenths 2. about 6 3a. rational numbers, natural numbers, whole numbers, integers b. rational numbers c. rational numbers d. irrational numbers 4a.
129
<
11.52
square root of 129 , less than , 11.52 b. Yes;
4
1
3
>
17
4 , and 1 third , greater than square root of 17 also compares the two numbers.
5.
−
7
2
,
−
2.1
,
5
,
9
,
3.5
negative , 7 halves , comma minus 2.1 comma square root of 5 comma square root of 9 comma 3.5
Lesson Check 1. irrational numbers 2. rational numbers, integers 3.
−
5
,
16
,
4.1
,
47
10
negative 5 comma square root of 16 comma 4.1 comma , 47 over 10 4. about 4 in. 5. rational numbers and irrational numbers 6. Answers may vary. Sample: 0.5 7. Rational; its value is 10, which can be written as a ratio of two integers,
10
1
.
10 over 1 , . 8. Irrational;
0.29
square root of 0.29 is a nonrepeating, nonterminating number.
Exercises 9. 6 11. 4 13.
6
7
6 sevenths 15.
1
3
1 third 17. 1.4 19. about 4 21. about 16 23. about 18 25. about 13 in. 27. rational numbers 29. rational numbers, integers 31. irrational numbers 33. rational numbers 35. irrational numbers 37.
5
2
3
>
29
5 , and 2 thirds , greater than square root of 29 39.
4
3
<
2
4 thirds , less than square root of 2 41.
−
7
11
<
−
0.63
negative , 7 elevenths , less than negative , 0.63 43.
−
22
25
<
−
0.
8
¯
negative , 22 over 25 , less than negative 0. , 8 bar 45.
−
2
,
−
7
4
,
1
2
,
5
,
2.4
negative 2 comma negative , 7 fourths , comma , 1 half , comma square root of 5 comma 2.4 47.
−
59
9
,
−
6,4.3
,
20
negative , 59 over 9 , comma negative , 6,4.3 , comma square root of 20 49.
−
9
4
,
−
13
6
,
−
2.1
,
−
26
13
negative , 9 fourths , comma negative , 13 over 6 , comma negative 2.1 comma negative , 26 over 13 51. about 12 ft 53. True; Answers may vary; any integer can be expressed as a rational number. 55. False; Answers may vary; 2 is a positive number and an integer. 57.
417
1
417 over 1 59.
201
100
201 over 100 61.
306
100
306 over 100 63. about 12 ft 65.
864
275
;
its value
3.14181
…
864 over 275 , semicolon . itsvalue . 3.14181 , dot dot dot is closer to the value of
π
pi than
10
,
which is
3.16227
…
square root of 10 comma . whichis . 3.16227 , dot dot dot 67. no; no the real number line extends indefinitely in both the positive and negative direction. 75. 16 76. 78 77. 512 78.
14
+
x
14 plus x 79.
4
(
y
+
1
)
4 open y plus 1 close 80.
3880
z
3880 over z 81.
19
3
t
19 over 3 , t 82. 18 83. 72 84. 442 85. 9
Lesson 1-4 pp. 23-28
Got It? 1a. Identity Prop. of Mult. b. Commutative
