Download Algebra I Summer Homework Tips and Answer Key

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