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Algebra I Summer Homework Tips and Answer Key Note: To receive credit for your summer assignment, you must show all work. There will be no credit for answers only. # 1 – 8 Use the Order of Operations to evaluate. PEMDAS 1. 1 2. 15 3. 1 4. 6 5. 3 6. 45 7. 24 8. 2 #9 – 14 Plug in values for the variables. Then use the Order of Operations to evaluate. PEMDAS 9. 23 10. 28 11. 11 12. 3 13. 6 14. 8 #15 – 34 Solving Equations. There is more than one way to solve an equation. But follow the steps below to guarantee a correct answer every time. 1. Clear any fractions (Multiply every term in the equation by the denominator of the fraction—this will cause the denominator to be cancelled out) 2. Distribute 3. Combine like terms on either side of the = sign 4. Use inverse operations to move the variables to one side of the = sign 5. Use inverse operations to isolate the variable. Tips: Remember to always keep the = sign in your problem. It should never disappear. Whatever you do to one side of the = sign must also be done on the other side of the equal sign. 15. x = 10 20. n = -14 25. v = -19 30. b = 1 16. p = -3 21. k = -8 26. x = -11 31. m = -15 17. n = -11 22. a = -18 27. r = 14 32. k = 9 18. x = -20 23. p = -15 28. x = 10 33. x = 17 19. x = 12 24. n = 5 29. k = -3 34. a = 0 #35 – 54 Addition and Subtraction of Fractions. Our Strategy: Change mixed #’s to improper fractions before attempting addition/subtraction. To do that, multiply the denominator by the whole number and add it to the numerator. Example: 5 3/4 = 23/4 (The denominator stayed 4, but to get the numerator, multiply 4 ∙ 5 to get 20, then add 3 to get 23) Always find a common denominator before adding or subtracting fractions. To find a common denominator, you have to find the Least Common Multiple of the denominators in the problem. Answers will be accepted in two forms, either as a mixed number or as an improper fraction. Either way will be considered correct. Note: there should be no decimals. 35. 45/8 or 5 5/8 40. 12/5 or 2 2/5 45. 1/6 50. 39/28 or 1 1 1/28 36. 29/10 or 2 9/10 41. 1/10 46. 23/20 or 1 3/20 51. -5/2 or -2 1/2 37. 5/6 42. 23/6 or 3 5/6 47. 1 1/2 or 5 1/2 52. -43/12 or -3 7/12 38. 9/2 or 4 1/2 43. 33/35 48. 33/28 or 1 5/28 53. 29/6 or 4 5/6 39. 5 44. 3 49. 3 54. -20/21 #55 – 64 Multiplying Fractions Our Strategy: Change mixed #’s to improper fractions before attempting anything else. To do that, multiply the denominator by the whole number and add it to the numerator. Example: 5 3/4 = 23/4 (The denominator stayed 4, but to get the numerator, multiply 4 ∙ 5 to get 20, then add 3 to get 23) There is no need for a common denominator when multiplying fractions. Just multiply top times top over bottom times bottom. Simplify. Answers will be accepted in two forms, either as a mixed number or as an improper fraction. Either way will be considered correct. Note: there should be no decimals. 55. 1 1/16 -1 60. /3 56. 61. -2 -5 /5 57. 253/120 or 2 13/120 /2 62. /2 -1 58. 221 63. -4 /45 or 4 41/45 /5 59. 64. -1 1 /48 -52 /9 or -5 7/9 #65 – 74 Dividing Fractions Our Strategy: Change mixed #’s to improper fractions before anything else. To do that, multiply the denominator by the whole number and add it to the numerator. Example: 5 3/4 = 23 /4 (The denominator stayed 4, but to get the numerator, multiply 4 ∙ 5 to get 20, then add 3 to get 23) To divide fractions, take the reciprocal of the divisor (that means, flip the second term— see “Skip-Change-Flip” below) and change the operation from division to multiplication. Treat the problem like multiplication from then on, multiply top times top over bottom times bottom. “Skip-Change-Flip” Skip the first term, change the operation from division to multiplication, and then flip the second term in the division problem. Answers will be accepted in two forms, either as a mixed number or as an improper fraction. Either way will be considered correct. Note: there should be no decimals. 65. 70. -1 1 /5 or -2 1/5 66. /41 71. -6 50 35 /63 /52 67. 72. -3 -5 /2 or -1 1/2 /24 68. -19/43 73. 15/17 69. 30 /17 or 1 13/17 74. 3/1 1