Selected A n s w e r s
Ch ap t er T
Get Read y! p. 1
- 6 2. 5 3. 1 4. 20 5. 15 6. 44 7. 72 8. 150 9. 400
- 8 11. $294 12. | 13. j 14. \ 15. {§ 16. 0.7
17.0.6 18.0.65 19.0.93 20.0.46 21,^1114 - 10^ 23. ^ 24. 3j^- 25. Answers may vary.
Sample: 20 + 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
Go t I t? 1. n + 18 2a. 6n b. ^ c. No; 6 less a number
y means 6 - y and 6 less than a number y means
y - 6. 3a. 4x - 8 b. 2(x + 8) c. 125+x 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
Lesson Check 1a. numerical b. algebraic c. numerical
2a. 9t b. x - j c. m + 7.1 d. ^ 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 + 0.75n
Exercises 9. p + 4 11. | 13. ^ 15. 5n + 6.7 - 5 more than a number q 19. the product of 12 and x
- one more than the product of 9 and a number n
- the difference of 15 and the quotient of 1.5 and d
- 5 more than the product of 9 and a number n;
9n + 5 27.8-9r 29.fy-4 31. It should be "the
quotient of 5 and n." 33a. 4.50n b. $40.50 35. A - Answers may vary. Sample: An umpire picks up b
baseballs for a game in addition to the three he had. - Answers may vary. Sample: Yes; sometimes you cannot
be sure from a verbal description what order is intended for
the operations. 41. 2x+ 6 or 6 + 2x 43. G 45. | - ^ 47. ^ 48. I 49. 3 50. 3 51. 1 52. 4
Lesson 1-2 pp. 10-15
Got It? 1a. 81 b. Yi c- °-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 4. c + ^ c ; $47.30, $86.90, $104.50,
$113.30
Lesson Check 1. 25 2. 8 3. | 4. 23 5. 1728 6. 0
- exponent 3; base 4 8. The student subtracted before
multiplying; 23 - 8 2 + 32 = 23 - 8 2 + 9
= 23-16 + 9= 7 + 9= 16
Exercises 9. 243 11. 16 13. 15. 0.004096 17. 2 - 4.5 21. 53 23. 16 25. 1728 27. 4 29. 1024
- 496 33. 3458 35. mv, 15,000, 20,000, 25,000
- 256 39. 5 41. 12
Lesso n 1-3 pp. 16-22
Got It? 1a. 8 b. 5 c^ d. pp 2. about 6 3a. rational
numbers, natural numbers, whole numbers, integers
b. rational numbers c. rational numbers d. irrational
numbers 4a. V129 < 11.52 b,
compares the two numbers.
Yes; 4 j > VT7 also
5- l l - 3 - 2-1 o i *V a’ -2.1. V5, V9, 3.5
Lesson Check 1. irrational numbers 2. rational
numbers, integers 3. -5, VT6, 4.1, 4. about 4 in.
- 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, y. 8. Irrational;
VO.29 is a nonrepeating, nonterminating number.
Exercises 9 .6 1 1 .4 13. j 15. j 17.1.4 19. about 4 - 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 - 5§> V29 39. |< V2 41. — ^ j - < —0. 6 3
- -§f< -0.8 45. -2, V5, 2.4 47. -6,
4.3, V20 49. -f, -2.1, -j§ 51. about 12 ft - 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. 59. ^ - f§§ 63. about 12 ft 65. §§§; its value 3.14181
closer to the value of tt than VTO, which is 3.16227 ... - no; no the real number line extends indefinitely in
both the positive and negative direction. 69. It is true for
products involving two numbers greater than 0 and less
than 1. 71a. 4 b. 10 c. 7 d. 13 73. 1 75. 16 76. 78 - 512 78. 14+x 79. 4(y+ 1) 80. ^
- 18 83. 72 84. 442 85. 9
is
81 .ft
Lesso n 1- 4 pp. 23-28
Got It? 1a. Identity Prop, of Mult. b. Commutative
Prop, of Add. 2. 720 tennis balls 3a. 9.45x b. 9 + 4h
c. ^ 4 a. True; Commutative Prop, of Mult, and Identity
C
Po w er A l g eb r a.co m Selected Answers 863