1i) c.

1g) b.

1f) Answers will vary.

2i) a.

2g) Answers will vary.

2f) Answers will vary.

3i)

1. b.
2. a.
3. c.

3g)

1. a.
2. b.

3f)

1. 100
2. 150
3. 111

4i) c.

4g) Answers will vary.

4f) 2 pies = 12 slices; ¹²/₁₂ - ²/₁₂ - ²/₁₂ = ⁸/₁₂, or ²/₃, of the slices remain after 2 people have taken 2 slices each.

⁸/₁₂ - ¹/₁₂ - ¹/₁₂ - ¹/₁₂ = ⁵/₁₂ of the slices remain after 3 more people have taken 1 slice each.

5i)

1. b.
2. a.
3. c.

5g)

1. b.
2. a.
3. c.

5f) Answers will vary.

6i) a.

6g) c.

6f) ^$30.66/₆ can be simplified to $30.00/6 = $5.00 and $0.66/6 = $0.11. Therefore, ^$30.66/₆ = $5.11. A twelve-month subscription would cost $5.11 x 12 = $61.32.

7i)

1. b.
2. b.
3. c.

7g)

1. 0.555 x 100 = 55.5, false
2. 0.555 x 1000 = 555, true
3. 75 x 10 = 7.5, false

7f)

1. 220
2. 6.7
3. 943

8i)

1. a.
2. b.
3. c.

8g) $5.95 x 0.06 = $0.357; $5.95 + $0.357 = $6.307 = $6.31

If there are 5 students in the group, the books would cost $5.95 x 5 = $29.75. The tax is then $29.75 x 0.06 = $1.785, and the total cost is $29.75 + $1.785 = $31.535 = $31.54. If you had bought them individually, you would have paid $6.31 x 5 = $31.55, or $0.01 more.

8f) $15.99 for gas that costs $1.599 per gallon; $15.90 for gas that costs $1.590 per gallon

9i)

1. b.
2. a.
3. a.

9g) The prime numbers between 1 and 20 are 2, 3, 5, 7, 11, 13, 17, and 19. There are 8 of them. The prime numbers between 20 and 40 are 23, 29, 31, and 37. There are 4 of them. There are fewer prime numbers between 20 and 40 because there are more prime factors available.

9f) The prime numbers between 1 and 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.

10i)

1. a.
2. b.
3. b.

10g)

1. 336 = 3 x 7 x 2 x 2 x 2 x 2; 384 = 3 x 2 x 2 x 2 x 2 x 2 x 2; this reduces to ⁷/₈.
2. 315 = 3 x 7 x 3 x 5; 378 = 3 x 7 x 3 x 6; this reduces to ⁵/₆.
3. 153 = 3 x 3 x 17; 204 = 17 x 3 x 4; this reduces to ³/₄.

10f)

1. ³²⁰/₂₅₆₀ = (10 x 32) / (10 x 256) = ³²/₂₅₆ = ¹/₈
2. ⁶³⁰/₇₅₆ = (2 x 315) / (2 x 378) = ³¹⁵/₃₇₈ = ⁵/₆
3. ⁴⁰⁸/₄₅₉ = (8 x 51) / (9 x 51) = ⁸/₉

12i) c.

12g) Answers will vary. If each person in the group can invite 1 friend in 3 minutes, each person can invite 3 friends in 9 minutes, so 3 friends times the number of people in the group is the answer.

12f) An hour is 60 minutes, so the ratio we set up is ¹²/₈ = ^x/₆₀. x = 60 x ¹²/₈ = 90 cookies in 1 hour.

11i) a.

11g) c.

11f) Answers will vary.

13i) b.

13g) Answers will vary.

13f) Answers will vary.

14i)

1. a.
2. b.
3. c.

14g) Answers will vary.

14f) Answers will vary.

15i) a.

15g) Answers will vary; some possible answers are:

1. ⁵/₆ = ¹⁰/₁₂ = ¹⁵/₁₈ = ²⁰/₂₄
2. ⁷/₈ = ¹⁴/₁₆ = ²¹/₂₄ = ²⁸/₃₂
3. ⁶⁵/₇₀ = ¹³/₁₄

15f)

1. n =  3
2. n = 18
3. n =  3

16i) b.

16g) You need n x $15.00, where n is the number of students in the group. Calculate ^$100.00/n. Answers will vary depending on the number of students in the group.

16f) ^$23.00/_$5 = 4 r $3.00; ^$23.00/_$4 = 5 r $3.00

17i) a.

17g) The distance to the first rest stop is 4¹/₃ miles. The distances of the second and third parts of the hike are 3⁵/₆ miles and 3 miles respectively.

17f) Answers will vary.

18i)

1. a.
2. b.
3. c.

18g)

1. a.
2. b.
3. c.

18f)

1. -21
2. +15
3. -70

19i) c.

19g) The probability of flipping 2 heads is ¹/₄. The probability of flipping 1 head and 1 tail, or 1 tail and 1 head, is ¹/₄ + ¹/₄ = ¹/₂. The probability of flipping 2 tails is ¹/₄. Has about ¹/₂ of the group flipped 1 head and 1 tail? ¹/₄ flipped 2 tails in a row? ¹/₄ flipped 2 heads in a row?

19f) There are 4 aces in a 52-card deck. The probability of drawing 1 ace is ⁴/₅₂ = ¹/₁₃. Once you've drawn one ace from the deck, there are 3 aces and 51 cards left. The probability of drawing a second ace is ³/₅₁. The probability of drawing two aces in a row is ¹/₁₃ x ³/₅₁ = ³/₆₆₃ = ¹/₂₂₁.

20i)

1. a.
2. b.
3. c.

20g)

1. c.
2. b.
3. a.

20f) Answers will vary.