Today in class students worked again with positive and negative numbers, learning how to use them in the context of rewriting expressions and past/present events.
Answers to Lesson 13 Near and Far From Zero: 1. a b -a -4b −a+b a÷−b a squared b cubed -1/2 6 1/2 -24 6 1/2 1/12 1/4 216 1/2 -6 -1/2 24 -6 1/2 1/12 1/4 -216 -6 -1/2 6 2 5 1/2 -12 36 -1/8 2. a. b cubed = 216 b. -4b = −24 c. a ÷ (-b) = 1/12 3. a. -4b = 24 b. b cubed = -216 c. a ÷ (-b) = 1/12 4. a. a squared = 36 b. a ÷ (-b) = -12 c. b cubed = -1/8 Answers to Lesson 13 HW: 1.a. 11 tablespoons; from the information, one can determine that 1 tablespoon of coffee will be used for every 3 ounces of water, therefore for 33 ounces of water one would need 11 tablespoons of coffee. b. 70 minutes; from the information, one can determine that it would take the runner 7 minutes to run 1 km, therefore it would take the runner 70 minutes to run 10 km. 2. 8 %; Between 7.85 % and 8.15 % is close enough. 3. a. -17 b. -17 c. 110 d. -4.4 4. Agree with Lin. The soap in the old box represents 100% and the new box now holds 125% which is 2 kg. 5. x − 1, x, 1 − x, -1 ÷ x.The expressions’ values are -54, -14, 54, and 4. 6. -14 + (-12), 14 − 1, -3 ⋅ 14, -3 ÷ 4, 1 ÷ 4 − 1 Answers to Lesson 14 HW: 1. a. $2,400, because 1,200 ÷ 0.5 = 2,400. b. $1,600, because 2,400 ÷ 1.5 = 1,600. 2. a. January: 252.20; February: 88; March 1.70; April: -836.90 b. -123.75, because [252.20 + 88 + 1.70 + (-836.9)] ÷ 4 = -123.75 3. 12, because 85 ÷ 7.50 = 1113 which means it will take 12 months to have a negative balance in the account 4. a. 300 litres (225 + 15 ⋅ 5 = 300) b. 120 litres (225 + 15 ⋅ (-7) = 120) 5. a. $24.15 b. C, D, F
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