Determine whether you need an estimate or an exact answer. Then solve. 1. SHOPPING Addison paid $1.29 for gum and $0.89 for a package of notebook paper. She gave the cashier a $5 bill. If the tax was $0.14, how much change should Addison receive? This problem requires an exact answer. To find how much change Addison should receive, find the sum of the things she bought and the tax and subtract that from the amount she gave the cashier. 5 (1.29 + 0.89 + 0.14) = 2.68 So, Addison should receive $2.68 in change. 2. DISTANCE Luis rode his bike 1.2 miles to his friend s house, then 0.7 mile to the video store, then 1.9 miles to the library. If he rode the same route back home, about how far did he travel in all? Because the question asks about how far, this problem requires an estimate. Round each of the distances Luis rode on his bike to the nearest mile. Then find the sum. 1.2 1 0.7 1 1.9 2 1 + 1 + 2 = 4 Because Luis rode about 4 miles and then back the same route, multiply 4 by 2 to find the total distance. 4 2 = 8 So, Luis rode about 8 miles in all. Find each sum or difference. 3. 20 + ( 7) 20 has greater absolute value, so the sum is positive. 4. 15 + 6 15 has greater absolute value, so the sum is negative. esolutions Manual - Powered by Cognero Page 1
5. 9 22 Both numbers are negative, so the sum is negative. 6. 18.4 ( 3.2) To subtract 32, add its inverse. 7. 23.1 + ( 9.81) 12.1 has greater absolute value, so the sum is positive. 8. 5.6 + ( 30.7) Both numbers are negative, so the sum is negative. Find each product or quotient. 9. 11( 8) The product of two integers with different signs is negative. 11( 8) = 88 10. 15( 2) The product of two integers with the same sign is positive. 15( 2) = 30 esolutions Manual - Powered by Cognero Page 2
11. 63 ( 9) The quotient of two integers with different signs is negative. 63 ( 9) = 7 12. 22 11 The quotient of two integers with different signs is negative. 22 11 = 2 Replace each with <, >, or = to make a true sentence. 13. To compare the fractions, write both fractions with a common denominator. So, <. 14. 0.15 To compare these numbers, write as a decimal. 0.15 > 0.125 So, 0.15 >. esolutions Manual - Powered by Cognero Page 3
15. Order 0.5,, 0.2, and from least to greatest. To order these numbers from least to greatest, write the fractions as decimals. The decimals in order from least to greatest are 0.2,,, 0.5. So, the numbers in order from least to greatest are 0.2,,, 0.5. Find each sum or difference. Write in simplest form. 16. + 17. esolutions Manual - Powered by Cognero Page 4
18. + 19. Find each product or quotient. 20. 2.4( 0.7) The product of two numbers with different signs is negative. 2.4( 0.7) = 1.68 21. 40.5 ( 8.1) 22. The quotient of two numbers with the same sign is positive. 40.5 ( 8.1) = 5 Name the reciprocal of each number. The product of a number and its reciprocal is 1. So, is the reciprocal of. 23. The product of a number and its reciprocal is 1. So, is the reciprocal of. esolutions Manual - Powered by Cognero Page 5
Find each product or quotient. Write in simplest form. 24. 25. 26. To divide, multiply by the reciprocal. Write each mixed number as an improper fraction. 27. esolutions Manual - Powered by Cognero Page 6
28. 29. Express each percent as a fraction in simplest form. 30. 20% 31. 7.5% esolutions Manual - Powered by Cognero Page 7
Use the percent proportion to find each number. 32. 18 is what percent of 72? The part is 18 and the base is 72. Let p represent the percent. So, 18 is 25% of 72. 33. 35 is what percent of 200? The part is 35 and the base is 200. Let p represent the percent. So, 35 is 17.5% of 200. 34. 24 is 60% of what number? The part is 24 and the percent is 60. Let b represent the base. So, 24 is 60% of 40. esolutions Manual - Powered by Cognero Page 8
35. TEST SCORES James answered 14 items correctly on a 16-item quiz. What percent did he answer correctly? To find the percent that James answered correctly, find what percent 14 is of 16. The part is 14 and the base is 16. Let p represent the percent. So, James answered 87.5% of the items correctly. 36. BASKETBALL Emily made 75% of the baskets that she attempted. If she made 9 baskets, how many attempts did she make? To find the number of attempts Emily made, find what number 9 is 75% of. The part is 9 and the percent is 75. Let b represent the base. So, Emily made 12 attempts. esolutions Manual - Powered by Cognero Page 9
Find the perimeter and area of each figure. 37. So, the perimeter is 36 inches. So, the area is 81 square inches. 38. So, the perimeter is 48 centimeters. So, the area is 96 square centimeters. esolutions Manual - Powered by Cognero Page 10
39. A parallelogram has side lengths of 7 inches and 11 inches. Find the perimeter. To find the perimeter, find the sum of the sides of the parallelogram. So, the perimeter is 36 inches. 40. GARDENS Find the perimeter of the garden. So, the perimeter of the garden is 23 meters. Find the circumference and area of each circle. Round to the nearest tenth. 41. So, the circumference is approximately 12.6 meters. So, the area is approximately 12 square meters. esolutions Manual - Powered by Cognero Page 11
42. So, the circumference is approximately 50.3 centimeters. So, the area is approximately 201.1 square centimeters. 43. BIRDS The floor of a birdcage is a circle with a circumference of about 47.1 inches. What is the diameter of the birdcage floor? Round to the nearest inch. To find the diameter of the birdcage floor, solve the formula for the circumference of a circle for r. So, the diameter is approximately 15 inches. esolutions Manual - Powered by Cognero Page 12
Find the volume and surface area of each rectangular prism given the measurements. 44. l = 3 cm, w = 1 cm, h = 3 cm So, the volume is 9 cubic centimeters. So, the surface area is 30 square centimeters. 45. l = 6 ft, w = 2 ft, h = 5 ft So, the volume is 60 cubic feet. So, the surface area is 104 square feet. esolutions Manual - Powered by Cognero Page 13
46. Find the volume and surface area of the rectangular prism. So, the volume is 30 cubic inches. So, the surface area is 63 square centimeters. One pencil is randomly selected from a case containing 3 red, 4 green, 2 black, and 6 blue pencils. Find each probability. 47. P(green) The number of possible outcomes is 3 + 4 + 2 + 6, or 15. probability = P(green) = 48. P(red or blue) The number of possible outcomes is 3 + 4 + 2 + 6, or 15. probability = P(red or blue) = = esolutions Manual - Powered by Cognero Page 14
49. Use a tree diagram to find the sample space for the event a die is rolled, and a coin is tossed. State the number of possible outcomes. The tree diagram shows that there are 12 possible outcomes. One coin is randomly selected from a jar containing 20 pennies, 15 nickels, 3 dimes, and 12 quarters. Find the odds of each outcome. Write in simplest form. 50. a penny There are 50 possible outcomes; 20 are successes and 30 are failures. So, the odds of selecting a penny are 20:30 or 2:3. 51. a penny or nickel There are 50 possible outcomes; 35 are successes and 15 are failures. So, the odds of selecting a penny or a nickel are 7:3 or 7:3. 52. A coin is tossed 50 times. The results are shown in the table. Find the experimental probability of heads. Write as a fraction in simplest form. probability = The number of possible outcomes is 22 + 28, or 50. So, the experimental probability of a coin landing heads up is or. esolutions Manual - Powered by Cognero Page 15
Find the mean, median, and mode for each set of data. 53. {10, 11, 18, 24, 30} So, the mean is 18.6. The numbers are already in numerical order. The median, or middle number, is 18. Because all of the numbers appear only once in the set of data, there is no mode. 54. {4, 8, 9, 9, 10, 14, 16} So, the mean is 10. The numbers are already in numerical order. The median, or middle number, is 9. The number 9 appears most often, so the mode is 9. 55. Find the range, median, lower quartile, and upper quartile for {16, 19, 21, 24, 25, 31, 35}. So, the range is 19. The numbers are already in numerical order. {16, 19, 21, 24, 25, 31, 35} Since there is an odd number of values, the median or Q 2 is the middle value. So, Q 2 is 24. Q 1 is the median of the lower half of the data set. The lower half is {16, 19, 21}. Since there is an odd number of values, the median is the middle valuer or 19. So, 19 is the lower quartile. Q 3 is the median of the upper half of the data set. The upper half is {25, 31, 35}. Since there is an odd number of values, the median is the middle valuer or 31. So, the upper quartile is 31. esolutions Manual - Powered by Cognero Page 16
56. SCHOOL Devonte s scores on his first four Spanish tests are 92, 85, 90, and 92. What test score must Devonte earn on the fifth test so that the mean will be exactly 90? Let x be the score Devonte must earn on the fifth test so that the mean will be exactly 90. So, Devonte must earn a score of 91on his fifth test. 57. MUSIC The table shows the results of a survey in which students were asked to choose which of four instruments they would like to learn. Make a bar graph of the data. Draw a bar to represent each instrument. The vertical scale is the number of students who chose each instrument. The horizontal scale identifies the instrument chosen. esolutions Manual - Powered by Cognero Page 17
58. Make a double box-and-whisker plot of the data. A: 42, 50, 38, 59, 50, 44, 46, 62, 47, 35, 55, 56 B: 47, 49, 48, 49, 40, 54, 56, 42, 57, 45, 45, 46 Put data A into L 1 and data B into L 2 on your graphing calculator. Turn the stat plots on, choose a suitable window and graph the box-and-whisker plots. 59. EXPENSES The table shows how Dylan spent his money at the fair. Make a circle graph of the data. How Spent rides Ratio Degrees for Section of Graph food games esolutions Manual - Powered by Cognero Page 18