Must show work or no credit. Page # Prob. # Problem Solution 311-313 20 A tangram is a geometric puzzle made from seven pieces that form a square. Trace the pieces, cut them out, and answer the following questions. a. If the area of the entire square equals 1 unit, label each piece with its rational number area. b. If the area of piece (a) equals 1 unit, label each piece with its rational number area. 22 Explain why the definition of a fraction restricts the denominator to being a nonzero integer. 26 a. Separate the fractions 2/6, 2/5, 6/13, 1/25, 7/8, and 9/29 into two categories: those that can be written as a terminating decimal and those that cannot. Write an explanation of how you made your decisions. b. Form a conjecture about which fractions can be expressed as terminating decimals. c. Test your conjecture on the following fractions: 6/12, 7/15, 28/140, and 0/7. d. Use the ideas of equivalent fractions and common multiples to verify your conjecture. 321-324 2c Make an illustration depicting the number line to find each sum or difference. 1 2/3 + 1 5/6 12a Without finding the exact answer, select which of the following numbers is the best estimate of each sum or difference and justify your choices: -2/3, 0, 2/3. a. 1/9 + 2/5 – 1/3 – 3/4 16 For the following equations, write a word problem, draw a picture, and find the solution to the equation: a. 5/12 – 1/3 = ? b. 1/2 – 2/3 = ? 38 With a partner, discuss the possible advantages and disadvantages of using least common denominators when adding and subtracting fractions. Write two paragraphs summarizing the two parts of your discussion. 340-343 4c Find the following product: c. (1 1/3 + 3 1/2)(3/4) 12 Identify which of the following situations can be represented by 4 3/4, and explain your reasoning: a. Sue had 3/4 of a room to paint in 4 hours. How much of the room must she paint each hour to finish on time? b. Kendra has 4 yards of electrical wiring to use in setting up her science fair experiment. She needs to cut it into lengths of 3/4 yard. How many pieces will she be able to make from the 4 yards? c. A rotating video camera in the parking garage goes through 4 complete rotations in 3/4 hour. How many rotations will it make in 1 hour? d. In a local farmers’ market, 3/4 of the profits are cycled back into the local farming community. If you spend $4 there, how much of your money goes to local farmers? 14 Use the common denominator method to find the quotient 3/5 2/3. 16 Use the missing factor method to find the quotient 3/5 2/3. 34 The Rental Depreciation Problem. The owner of a rental house can depreciate its value over a period of 27 1/2 years, meaning that the value of the house declines at an even rate over that period of time until the value is $0. a. By what fraction does the value of the house depreciate the first year? b. If the house is judged to be worth $85,000, what is the value of the first year’s depreciation? 351-354 2b Using a number line (or metric ruler), show how to find each sum or difference. b. 1.3 + 1.8 4 Using base-ten blocks, show the following quotients: a. 0.9 3 (Hint: Use a sharing model by separating 0.9 into three equal groups.) b. 3 0.6 (Hint: Use a measurement model by finding how many groups of 0.6 there are in 3.) 22 The Olympic Race. At the 1988 Summer Olympics in Seoul, South Korea, Florence Griffith-Joyner ran the 100-meter dash in 10.49 seconds (a world record). What was her speed in miles per hour? (1 meter is approximately 39.37 inches.) 363-365 2b Use a linear model (for example, a number line, a ruler) to compare the pairs of rational numbers that follow. Identify which one is greater in each pair and use the model to justify your answer. b. 1/4, 1/6 4d Use common denominators to compare the pairs of rational numbers. In each of the following, identify which one is greater and explain how you know. d. 5/7, 5/8 20 Is the product of two irrational numbers always an irrational number? Justify your answer. 368-369 2 State the Fundamental Law of Fractions and give an example of it. 4 Write the following rational numbers in scientific notation: a. 0.000005 b. 30 million c. 0.036754 d. 24,000,059 6 Find each sum or difference. a. 15.6 + 8.305 + 0.4 b. 14/3 – 16/5 c. 20.096 - 42.3 d. -3 1/8 + 4 5/6 8 Find each quotient. a. 3/4 -12 b. 5/4 2 2/3 c. 18 4.6 d. 3.06 0.22 10 Order the following sets of rational numbers from least to greatest: a. 2 1/2; 2.333…; 2.51; 6000/29 b. 3.33; 577/154; 3.121212…; 3 5/8 c. 22; 32/11; 477/154; 2.7171… 12 Describe the connections between rational numbers and division. 14 Use the ideas of additive and multiplicative inverses of rational numbers to solve the following equations: a. -5x + 13 = -12 b. 1/3x - 7 = 25 c. 3x - 4 = x + 12 d. x + 11/9 = 2/3 16 The Sewing Supplies Problem. The seamstress purchased 2.4 meters of $1.90-per-meter fabric, 5.4 meters at $3.90 per meter, 7.5 meters at $4.95 per meter, 25.20 meters of cording at $0.25 per meter, and two spools of thread at $0.70 per spool. a. How much did she spend on this purchase? b. If she charges $10.50 per hour for sewing, how many hours must she work to pay for these supplies? 18 Let A be the set containing all rational numbers that are less than 5. Is there a rational number q in set A such that all other numbers in set A are less than q? Why or why not?