Understand ratio concepts and use ratio reasoning to solve problems. 1. What is the ratio of triangles to circles? 2. What is the ratio of moons to pentagons? 3. For every 6 hotdogs sold at the malt shop, there are 2 hamburgers sold. What is the ratio of hotdogs sold to hamburgers sold? 4. At the thrift store for every 9 long sleeve shirts, there were 7 short sleeve shirts. What is the ratio of long sleeve shirts to short sleeve shirts? 5. An experienced carpenter could build a house in 7 days. How much would he have to finish if he worked 6 days? 6. A gardener used 5 kilograms of fertilizer over the course of 6 weeks. How much fertilizer did he use each week? Determine the number that correctly fills in the blank in the function machine. 7. 8. 9. At a school fundraiser for every 9 boxes of chocolate sold, you earn 6 points. If you were to sell 18 boxes, how many points would you have earned? 10. On her MP3 player for every 3 pop songs Jasmine had, she also had 8 country songs. If she has 24 pop songs on her MP3 player, how many country songs does she have? Page 1 of 7
Find the ratio and unit rate for each problem. Summer Mathematics Review 11. 40 centimeters of snow in 8 hours 12. 376 points for defeating 94 enemies 13. A fast food restaurant has 4 boxes of chicken nuggets for $25.44. A competing restaurant has 6 boxes of chicken fingers for $39.00. Which food has a higher unit price? 14. At the toy store you could get 4 board games for $22.96. Online the price for 6 board games is $33.60. Which place has the highest price for a board game? 15. What is 10% of 173? 16. What is 42% of 91? 17. What is 128% of 87? 18. A recipe called for the ratio of sugar to flour to be 10:3. If you used 40 ounces of sugar, how many ounces of flour would you need to use? 19. During a class election the ratio of students who voted for candidate A compared to candidate B was 3:2. If candidate A received 12 votes, what is the combined amount of votes candidate A and candidate B received? Reduce each ratio to its lowest form. 20. 48:18 21. 14:20 22. 6:30 23. Every quarter is 25 pennies. This can be expressed using the equation y x 25 = z, where y is equal to the number of quarters and z is equal to the total number of pennies. Using this equation, find the total pennies in 10 quarters. 24. For each pound there are 16 ounces. This can be expressed using the equation y x 16 = z, where y is equal to the number of pounds and z is equal to the total number of ounces. Using this equation, find the total ounces in 7 pounds. 25. For each pound there are 16 ounces. Write an equation to express the total number of quarters (z) in (y) dollars. Page 2 of 7
Apply and extend previous understandings of multiplication and division to divide fractions by fractions. Solve each problem and write the answer as a mixed number in simplest form (if possible). 26. 2 1 2 1 3 4 = 27. 4 11 2 = 28. 20 6 2 3 = 29. 3 4 3 1 2 = 30. 3 5 27 6 = 31. 4 1 6 4 3 = 32. 2 3 1 6 33. 1 2 1 6 34. 9 12 1 4 35. 2 5 3 4 7 35. 4 1 3 4 7 37. 5 8 2 7 12 Use the number line to solve each problem. 38. 5 5 8 = 39. 2 1 4 = Solve each problem. 40. 7.768 8 41. 9.367 3 42. 760 38 43. 54.4 0.34 44. 23.004 + 35.935 45. 100 89.7 Page 3 of 7
Apply and extend previous understandings of numbers to the system of rational numbers. Solve each problem. 46. What number is opposite of (-14)? 47. What number is opposite 29? 48. What number is opposite of 45? 49. What number is opposite (93)? 50. Which number is more? -94 or 101 51. Which number is less? -49 or -41 Determine the coordinate and/or quadrants of each problem. ` 52. Starting at (0, 0), if you were to go 4 units left and 6 units down, what coordinates would you end up at? What quadrant would you be in? 53. Starting at (0, 0), if you were to go 6 units up and 8 units right, what coordinates would you end up at? What quadrant would you be in? 54. (11, 1), (- 11, - 1), (11, - 1), (-11, 1) 55. (- 17, 8), (17, 8), (17, - 8), (-17, - 8) Mark each location described. 56. (8, 4), (- 8, - 4), (8, 4), (-8, 4) 57. Mark the location -3 5 7 Page 4 of 7
58. Mark the location 1 2 4 59. Determine the coordinates of each figure. A. Circle B. Moon C. Heart D. Diamond 60. Determine which letter is at each coordinate. A. (1, -10) B. (4, 6) C. (-10, 5) D. (-6, -9) Use >, < or = to compare. 61. -94-46 62. -51 58 63. -36-26 64. -60-66 Page 5 of 7
Solve each problem below. 65. Which letter best shows -37? 66. Which letter best shows -107? Use the graph below to answer questions 67 68. 67. What is the value of A? 68. What is the absolute value of A? Find the distance between points on the grids below. 69. 70. Apply and extend previous understandings of arithmetic to algebraic expressions. Reason about and solve one-variable equations and inequalities. Simplify the given expressions: 71. 3 3 72. What is 2 squared? 73. What is 7 to the power of two? 74. Find K times as much as 16 75. Add 3 to C 76. Divide 15 by T Solve the given equations or inequalities. 77. 9 + 6g = 45 78. 3a + 8 < 29 79. 2x + 3 = 15 Page 6 of 7
Simplify the given expressions. Summer Mathematics Review 80. 6x 8y + 9x + 4y 81. -8x + y x + 7y 82. 184 35 5 Page 7 of 7