Express each ratio as a fraction in simplest form. 1. 10 girls out of 24 students 2. 6 red cars to 4 blue cars 3. 10 yards to 8 inches Convert 10 yards to inches. Three are 36 inches in 1 yard. esolutions Manual - Powered by Cognero Page 1
4. 18 ounces to 3 cups Convert 3 cups to ounces. Three are 8 ounces in 1 cup. 5. Jean got 12 hits out of 16 times at bat. Express this rate as a fraction in simplest form. Explain its meaning. For every 4 times at bat, Jean got 3 hits or on of his at bats, he got a hit. ; For every 4 times at bat, Jean got 3 hits or on of his at bats, he got a hit. Express each rate as a unit rate. Round to the nearest tenth, if necessary. 6. $25.97 for 8 boxes The unit rate is $3.25 per box. $3.25 per box 7. 400 meters in 5 minutes The unit rate is 80 meters per minute. 80 meters per minute esolutions Manual - Powered by Cognero Page 2
8. $175 for 4 concert tickets The unit rate is $43.75 per ticket. $43.75 per ticket 9. 125 miles in 200 minutes The unit rate is 0.6 mile per minute. 0.6 mile per minute 10. Financial Literacy An eight pack of juice boxes costs $4.79, and a twelve pack of juice boxes costs $6.59. Which is a better buy? Explain. The eight pack costs $0.60 per juice box. The twelve pack of juice boxes costs $0.55 per juice box. The twelve pack is a better buy because the cost per juice box is less. 12 juice boxes for $6.59; Sample answer: The eight pack of juice boxes costs $0.60 per juice box and the twelve pack of juice boxes costs $0.55 per juice box. esolutions Manual - Powered by Cognero Page 3
Simplify. 11. 15 12. esolutions Manual - Powered by Cognero Page 4
13. Noreen can walk miles in hour. Find her average speed in miles per hour. Write a rate that compares the number of miles to hours. So, Noreen walks at an average speed of miles per hour. mph 14. Write as a fraction in simplest form. So,. esolutions Manual - Powered by Cognero Page 5
15. Write as a fraction in simplest form. 16. Write as a fraction in simplest form. esolutions Manual - Powered by Cognero Page 6
Complete each conversion. Round to the nearest hundredth, if necessary. 17. 7 in. _ cm Use 1 in. 2.54 cm. 17.78 18. 20 m _ yd Use 1 m 1.094 yd. 21.88 19. 25 fl oz _ ml Use 1 fl oz 29.574 ml. 739.35 20. 4 L _ gal Use 1 L 0.264 gal. 1.06 esolutions Manual - Powered by Cognero Page 7
21. 18 pt _ L Use 1 pt 0.473 L. 8.51 22. 12 oz _ g Use 1 oz 28.35 g. 340.2 23. 26 cm _ in. Use 1 cm 0.394 in. 10.24 24. 3 qt _ L Use 1 qt 0.946 L. 2.84 esolutions Manual - Powered by Cognero Page 8
25. 4 m _ ft Use 1 m 3.279 ft. 13.12 26. 68 g _ oz Use 1 g = 0.035 oz. 2.38 27. A plane is flying at a speed of 425 miles per hour. How far will the plane travel in 0.75 hour? The plane will travel 318.75 miles. 318.75 mi 28. A swimming pool is being drained at a rate of 50 gallons per hour. How many milliliters per second is this? Round to the nearest tenth. The pool is being drained at a rate of about 52.6 milliliters per second. 52.6 milliliters per second esolutions Manual - Powered by Cognero Page 9
29. A runner runs 2 miles in 9.56 minutes. How many meters per second is this? The runner runs about 5.61 meters per second. 5.61 meters per second 30. A family drives their car 135 miles in 3 hours. How many kilometers per hour is this? The family drives about 72.41 kilometers per hour. 72.41 kilometers per hour Determine whether the cost is proportional to the number of books purchased. If the relationship is proportional, find the constant of proportionality. Explain your reasoning. 31. Write the rate of cost to books in simplest form. Since the rates are equal, the cost is proportional to the number of books purchased. The constant of proportionality is 8. Yes; 8; each rate is equal to 8. esolutions Manual - Powered by Cognero Page 10
32. Write the rate of cost to books in simplest form. Since the rates are not equal, the cost is not proportional to the number of books purchased, and there is no constant of proportionality. No; the rates are not equal. 33. A customer at the ring toss booth gets 8 rings for $2. Find the constant of proportionality. Write an equation relating the cost to the number of rings. At this same rate, how much would a customer pay for 11 rings? for 20 rings? Find the constant of proportionality. The cost is $0.25 times the number of rings, r. The equation is c = 0.25r. To find the cost of 11 rings, substitute 11 for r. 11 rings cost $2.75. To find the cost of 20 rings, substitute 20 for r. 20 rings cost $5. 0.25; c = 0.25r, 11 rings cost $2.75; 20 rings cost $5 esolutions Manual - Powered by Cognero Page 11
34. Mrs. Tebon buys 25 party favors for $5. At this same rate, how much would she pay for 40 party favors? for 60 party favors? Find the constant of proportionality. The cost is $0.20 per party favor. To find the cost of 40 party favors, multiply 0.20 by 40. 0.20(40) = 8 40 party favors cost $8.00. To find the cost of 60 party favors, multiply 0.20 by 60. 0.20(60) = 12 60 party favors cost $12.00. $8.00; $12.00 esolutions Manual - Powered by Cognero Page 12
35. Determine whether the relationship is proportional by graphing on the coordinate plane. Explain your reasoning. Graph the ordered pairs on the coordinate plane. Then connect the ordered pairs. The graph passes through the origin and is a straight line, so distance is proportional to time. Proportional; the line passes through the origin and is a straight line. esolutions Manual - Powered by Cognero Page 13
36. The cost of dance lessons is $12 for 1 lesson, $22 for 2 lessons, and $32 for 3 lessons. Determine whether the cost is proportional to the number of lessons by graphing the ordered pairs on the coordinate plane. Explain your reasoning. Graph the ordered pairs (1, 12), (2, 22) and (3, 32). Then connect the ordered pairs. The line does not pass through the origin, so the total cost is not proportional to the number of dance lessons. Nonproportional; the line does not pass through the origin. 37. The number of squirrels is proportional to the number of trees. A graph of the relationship includes the points (0, 0), (3, 9), and (5, 15). a. Find and interpret the constant of proportionality. b. Explain what the points (0, 0), (3, 9), and (5, 15) represent. a. Use the point (3, 9) from the graph. The constant of proportionality, or unit rate, is 3. There are 3 squirrels for every tree. b. The point (0, 0) represents the number of squirrels, 0, when there are no trees. The point (3, 9) represents the number of squirrels, 9, when there are 3 trees. The point (5, 15) represents the number of squirrels, 15, when there are 5 trees. a. 3; there are 3 squirrels for every tree. b. The point (0, 0) represents the number of squirrels, 0, when there are no trees. The point (3, 9) represents the number of squirrels, 9, when there are 3 trees. The point (5, 15) represents the number of squirrels, 15, when there are 5 trees. esolutions Manual - Powered by Cognero Page 14
Solve each proportion. 38. 12 39. 7.2 40. 14 esolutions Manual - Powered by Cognero Page 15
41. 7 42. Financial Literacy A homeowner whose house is assessed for $120,000 pays $1800 in taxes. At the same rate, what is the tax on a house assessed at $135,000? Let t represent the tax on a house assessed at $135,000. The tax on a house assessed at $135,000 is $2025. $2025 On the scale drawing of a museum, the scale is 0.5 inch = 10 feet. Find the actual length of each gallery. 43. Let x = the actual length of the Modern Art gallery. The actual length of the Modern Art gallery is 120 feet. 120 ft esolutions Manual - Powered by Cognero Page 16
44. Let x = the actual length of the Renaissance gallery. 45. The actual length of the Renaissance gallery is 85 feet. 85 ft Let x = the actual length of the Egypt gallery. The actual length of the Egypt gallery is 150 feet. 150 ft 46. The length of a highway is 900 miles. If 0.5 inch on a map represents 50 miles, what is the length of the highway on the map? Let x = the length of the highway on the map. The length of the highway on the map is 9 inches. 9 in. esolutions Manual - Powered by Cognero Page 17
The figures are similar. Determine each missing measure. 47. Since ABC ~ WXY, the corresponding sides are proportional. The length of is 7.2 in. 7.2 in. 48. Since Figure EFGH ~ RUST, the corresponding sides are proportional. The length of is 8 cm. 8 cm esolutions Manual - Powered by Cognero Page 18
49. A mosaic is created using rectangular blocks. Block A has a length of 5 centimeters and a width of 2.5 centimeters. Block B is similar to block A and has a length of 7 centimeters. What is the width of block B? Since Block A ~ Block B, the length and width are proportional. The width of Block B is 3.5 cm. 3.5 cm 50. Keshawn enlarges a rectangular photograph to make a poster that is similar to the photograph. The photograph is 4 inches wide and 6 inches long. The poster is 51 inches long. What is the width of the poster? Since photograph ~ picture, the length and width are proportional. The width of the poster is 34 inches. 34 in. esolutions Manual - Powered by Cognero Page 19
51. At 7 feet 8 inches, the world s tallest woman casts a 46-inch shadow. At the same time, the world s shortest woman casts a 15.5-inch shadow. How tall is the world s shortest woman? Use 12 inches = 1 foot. 7 feet 8 inches = 12 7 + 8 = 84 + 7 = 92 inches The world s shortest woman is 31 inches tall. 31 in. 52. The largest known pyramid is the Pyramid of Khufu. At a certain time of day, a vertical yard stick casts a shadow 1.5 feet long, and the pyramid casts a shadow 241 feet long. How tall is the pyramid? The pyramid is 482 feet tall. 482 ft esolutions Manual - Powered by Cognero Page 20
53. Mylie s house is 9 meters tall and casts a shadow 1.5 meters long. At the same time of day, a nearby doghouse casts a shadow that is 0.2 meter long. How tall is the dog house? The doghouse is 1.2 meters tall. 1.2 m 54. In the figure below,. What is the distance across the pond? Since ABE ~ ACD, the corresponding sides are proportional. The distance across the pond is 70 meters. 70 m esolutions Manual - Powered by Cognero Page 21