Algebra 1 Common Core Student Edition, Grade 8-9

Selected A n s w e r s

Ch ap t er T

Get Read y! p. 1

1. 6 2. 5 3. 1 4. 20 5. 15 6. 44 7. 72 8. 150 9. 400


2. 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


3. 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


4. 5 more than a number q 19. the product of 12 and x


5. one more than the product of 9 and a number n


6. the difference of 15 and the quotient of 1.5 and d


7. 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


8. Answers may vary. Sample: An umpire picks up b
   baseballs for a game in addition to the three he had.


9. 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. |


10. ^ 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

7. 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


8. 4.5 21. 53 23. 16 25. 1728 27. 4 29. 1024


9. 496 33. 3458 35. mv, 15,000, 20,000, 25,000


10. 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.

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, 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


6. 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


7. 5§> V29 39. |< V2 41. — ^ j - < —0. 6 3


8. -§f< -0.8 45. -2, V5, 2.4 47. -6,
   4.3, V20 49. -f, -2.1, -j§ 51. about 12 ft


9. 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. ^


10. f§§ 63. about 12 ft 65. §§§; its value 3.14181
    closer to the value of tt than VTO, which is 3.16227 ...


11. 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


12. 512 78. 14+x 79. 4(y+ 1) 80. ^


13. 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