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Virginia Standards of Learning Mathematics Grade 5

Decimals, fraction operations, volume, and numerical expressions.

These questions are original. This is not an official Virginia Standards of Learning test, and FreeExam is not affiliated with the Virginia Department of Education.

  1. 1.A milepost on the Virginia Creeper Trail near Damascus shows 4.275 miles still to go. What is the value of the digit 7?

  2. 2.A bait shop on Chincoteague sells a crabber 2.4 pounds of bait, and the crabber adds 1.75 pounds of eel. How many pounds is that altogether?

  3. 3.A Winchester lumber yard cuts a board measured at 6.348 meters. What is that length rounded to the nearest hundredth of a meter?

  4. 4.A cyclist on the Arlington trail rides 12.6 miles on Saturday and 8.75 miles on Sunday. How much farther is Saturday's ride?

  5. 5.Three teams at a Fairfax food drive each collect (8 − 2) cans. The total is given by 3 × (8 − 2). What is that value?

  6. 6.A cook in Abingdon pours 1/2 cup of broth into a saucepan and then stirs in 1/3 cup of cream. How many cups of liquid are in the pan?

  7. 7.A ticket window in Bristol starts with 18 paper passes and holds back a stack of (5 + 1) passes. What is the value of 18 − (5 + 1)?

  8. 8.A painter in Front Royal has 3/4 gallon of paint and uses 1/6 gallon on a shutter. How much paint is left?

  9. 9.A Norfolk warehouse crate is 9 feet long, 4 feet wide, and 5 feet high. What is the volume of the crate?

  10. 10.On a grid of paths in Williamsburg, a bakery sits at the point (3, 7). How is that point located from the origin?

  11. 11.Packers in Chesapeake fill a carton by stacking 1-inch cubes with no gaps. The carton is 6 inches long, 6 inches wide, and 6 inches high. How many cubes fill it?

  12. 12.A harbor chart in Norfolk plots a buoy at (0, 5). Which description matches that point?

  13. 13.A small theater in Richmond sets out 4 rows, and each row has (6 + 3) seats. What is the value of 4 × (6 + 3)?

  14. 14.A sandbox at a Virginia Beach park is 8 feet long, 3 feet wide, and 2 feet deep. How much sand fills it level with the rim?

  15. 15.A planning card in a Hampton workshop shows the expression (7 + 5) ÷ 4 + 2. What is the value?

  16. 16.A porch planter in Richmond is 10 inches long, 4 inches wide, and 3 inches deep. How much potting soil fills it to the top?

  17. 17.At a class picnic in Orange, one tray holds 2/5 of a pizza and another holds 1/4 of a pizza. What fraction of a pizza is that in all?

  18. 18.A print shop in Richmond uses 0.3 liter of ink for each poster and prints 6 posters. How much ink is used?

  19. 19.A runner in Lexington has 5/6 mile left on a loop and then covers 1/2 mile of that distance. What fraction of a mile is still left, in simplest form?

  20. 20.Gardeners in Williamsburg divide a 9.6-meter brick path into 4 equal sections. How long is each section?

  21. 21.On a Shenandoah campsite grid, a tent is at (6, 2) and a spring is at (6, 8). How far apart are the tent and the spring?

  22. 22.Rain gauges in Charlottesville record 2.406 inches on Monday and 2.46 inches on Tuesday. Which statement is true?

  23. 23.A grid of downtown Richmond blocks starts at an information booth. Which ordered pair is 4 units right and 9 units up from that origin?

  24. 24.A science table in Hampton lists a sample mass of 0.083 kilogram. Which expression is the expanded form of 0.083?

  25. 25.A recipe card in Staunton calls for 5/8 pound of butter. Which decimal names the same amount?

  26. 26.A quilter in Floyd sews a 3/8-yard strip to a 1/6-yard strip. What is the total length in simplest form?

  27. 27.A ferry notice in Cape Charles lists a crossing of 1.609 kilometers. Which digit is in the thousandths place?

  28. 28.A shop in Monterey starts with 7/8 pound of cheese and cuts off 1/3 pound for a customer. How much cheese is left, in simplest form?

  29. 29.A scout troop near Shenandoah packs (9 − 4) bags, with 5 sandwiches in each bag. How many sandwiches is (9 − 4) × 5?

  30. 30.On a Virginia Beach boardwalk grid, a bench is at (2, 3). It is moved 5 units to the right. Which ordered pair names the new location?

  31. 31.A homework board in Roanoke shows 6 + 2 × (10 − 7). What is the value of the expression?

  32. 32.A grid in a Vienna classroom shows the first quadrant, including the axes. Which ordered pair is inside that quadrant and not on either axis?

  33. 33.Shipbuilders in Newport News scale a model part that is 0.25 meter by multiplying by 0.4. What is the product?

  34. 34.The classroom aquarium in Newport News is 20 inches long, 10 inches wide, and 12 inches tall. What volume of water fills it completely?

  35. 35.A shop in Fairfax marks a $20.00 book down by $3.48. What price remains after the discount?

  36. 36.A shallow drawer in the Monticello museum shop is 12 inches from front to back, 8 inches across, and 2 inches high. What is the volume inside the drawer?

  37. 37.A storage bin in a Roanoke closet has a square floor that is 5 feet on each side, and the bin is 4 feet tall. What is its volume?

  38. 38.A kite pattern on a Chincoteague grid has corners at (1, 2), (1, 6), and (5, 6). Which point completes the rectangle?

  39. 39.Before a picnic in Hampton, a cooler is measured as 15 inches long, 8 inches wide, and 10 inches high. What is the volume of the cooler?

  40. 40.On a coordinate grid in Staunton, which point is the same distance from the x-axis as it is from the y-axis?

  41. 41.An orchard stand near Harrisonburg packs 1.25 kilograms of apples into each of 8 bags. What is the total mass?

  42. 42.A trail crew near Luray mixes 1/2 bag of gravel with 3/10 bag of sand. How many bags is that in simplest form?

  43. 43.A bus route from Petersburg to Hopewell is 13.8 miles. After 6.45 miles, how many miles remain?

  44. 44.A student in Staunton subtracts 2/9 from 1/2 while comparing two ribbon lengths. What is the difference in simplest form?

  45. 45.A seating chart in Petersburg uses (15 − 3) ÷ (2 + 2). What is the value of that expression?

  46. 46.Three sounding lines in the Chesapeake Bay read 3.2 meters, 3.029 meters, and 3.19 meters. Which list orders them from least to greatest?

  47. 47.A bakery in Lexington packs 5 boxes of 4 muffins and then sets 3 extra muffins on the counter. What is the value of (5 × 4) + 3?

  48. 48.A workshop in Lexington measures a brass rod as 8.462 centimeters. What is that length rounded to the nearest tenth of a centimeter?

  49. 49.A survey stake in Blacksburg is marked 12.007 meters. Which expression has the same value?

  50. 50.A community garden in Lynchburg builds a raised bed 7 feet long, 2 feet wide, and 1 foot deep. How many cubic feet of soil fill the bed?

  51. 51.Two seedlings in a Roanoke greenhouse measure 0.45 meter and 0.405 meter. Which statement is true?

  52. 52.Masons in Fredericksburg stack pavers into a solid block 9 inches long, 6 inches wide, and 3 inches high. What is the volume of the block?

  53. 53.A lab in Charlottesville multiplies a 4.06-meter measurement by 10 to change the unit scale. What is the product?

  54. 54.A shop in Covington joins a ribbon of 3/4 yard to a ribbon of 5/12 yard. What is the total length as a mixed number in simplest form?

  55. 55.An orchard in Bedford pours 7.5 liters of cider into 5 jugs, with the same amount in each jug. How many liters go into each jug?

  56. 56.A jar of sorghum in Warrenton is 11/12 full. A cook pours out 2/3 of a jar. What fraction of a jar remains, in simplest form?

  57. 57.On an orchard grid in Crozet, young trees stand at (1, 2), (2, 4), and (3, 6). If the pattern continues, where is the next tree?

  58. 58.A math team in Blacksburg evaluates 4 × (3 + 2 × 5). What is the value?

  59. 59.A ferry grid in Irvington marks a dock at (10, 2). The mark is moved 3 units up. What is the new ordered pair?

  60. 60.A class in Suffolk uses 30 ÷ (2 + 3) × 2 to count equal groups. What is the value?

  61. 61.A moving box in Alexandria is a cube measuring 2 feet on each edge. What is the volume of the box?

  62. 62.Along the James River in Scottsville, a walker covers 1/5 mile and then 2/3 mile. How far is the walk in simplest form?

  63. 63.Under a window in Williamsburg, a flower box is 16 inches long, 5 inches wide, and 4 inches deep. What is its volume?

  64. 64.A boat tank in Tappahannock is 4/5 full. The captain uses 3/10 of a tank. What fraction of a tank remains, in simplest form?

  65. 65.A street corner on a Lexington map is plotted at (7, 11). What is the x-coordinate of that point?

  66. 66.A farm stand in Culpeper uses 8 − 2 × (3 − 1) to count crates still on a table. What is the value?

  67. 67.On a classroom grid in Blacksburg, two pins sit at (2, 5) and (9, 5). What is the horizontal distance between them?

  68. 68.Volunteers in Manassas compute (9 − 4) × 6 while packing supply kits. What is the value?

  69. 69.Two water samples in a Virginia Beach classroom have masses 0.608 kilogram and 0.39 kilogram. What is the combined mass?

  70. 70.A river gauge in Fredericksburg is read aloud as nine and seventy-three thousandths. Which decimal matches that reading?

  71. 71.A marina in Portsmouth has a rope 5.2 meters long. A sailor cuts off 1.86 meters. How much rope is left?

  72. 72.A coin display in Yorktown lists a thickness of 1.95 millimeters. Which decimal is equivalent to 1.95?

  73. 73.A weather log in Lynchburg records 7.184 centimeters of rain. In which place is the digit 1?

  74. 74.A carpenter in Galax glues a board 5/6 foot long to a board 1/4 foot long. What is the total length as a mixed number in simplest form?

  75. 75.A scale in Suffolk shows 15.276 pounds of peanuts. What is that mass rounded to the nearest hundredth of a pound?

  76. 76.A baker in Smithfield has 2 1/2 cups of flour and uses 3/4 cup for a crust. How much flour is left?

  77. 77.On a trail map near Luray, the origin is a trailhead and a cabin is at (6, 0). Where is the cabin?

  78. 78.A clerk in Manassas subtracts 4 from 9 and then multiplies the result by 6. Which expression matches that order?

  79. 79.On a block grid in Alexandria, a library is at (3, 4). A mural is 2 units directly above the library. Which point is the mural?

  80. 80.Students in Waynesboro evaluate (6 + 6) ÷ 3 + 5. What is the value?

  81. 81.A shipping crate in Suffolk has a volume of 240 cubic inches. Its base is 10 inches long and 6 inches wide. What is the height?

  82. 82.A baker in Alexandria triples a dough recipe that uses 2.75 pounds of flour. How many pounds of flour are needed?

  83. 83.Librarians in Charlottesville use a bin 11 inches long, 8 inches wide, and 6 inches high for returned picture books. What is the volume of the bin?

  84. 84.A donation jar in Danville holds $14.60. A student adds $0.85 and then $1.20. How much money is in the jar?

  85. 85.A hiker on Skyline Drive descends 2.8 kilometers and then another 1.45 kilometers. How far is the whole descent?

  86. 86.A map note in Leesburg says a trail segment is 0.6 kilometer. Which decimal is equivalent to 0.6?

  87. 87.A dye recipe in Waynesboro starts with 0.6 liter of blue and uses half of that amount. How many liters is 0.6 × 0.5?

  88. 88.On a number line in a Culpeper classroom, which decimal is greater than 4.25 and less than 4.3?

  89. 89.A score card in Staunton uses 7 × (10 − 8) + 1. What is the value?

  90. 90.A robot on a grid in a Herndon library starts at (1, 1), moves 4 units right, and then moves 3 units up. Where does it stop?

  91. 91.A class in Falls Church evaluates 2 × (4 + 6) − 5. What is the value?

  92. 92.On a first-quadrant grid in Winchester, a right triangle has vertices at (2, 1), (2, 6), and (8, 1). How long is the vertical side?

  93. 93.Hikers near Monterey combine 2/7 liter of spring water with 1/2 liter from a bottle. How many liters is that in simplest form?

  94. 94.A Winchester exhibit uses two rectangular bases. One is 4 feet by 3 feet by 2 feet, and the other is 5 feet by 3 feet by 2 feet. What is the total volume of the two bases?

  95. 95.A lesson in Marion lasts 5/6 hour, and warm-up takes 1/8 hour of that time. How long is the rest of the lesson, in simplest form?

  96. 96.A hallway locker in Harrisonburg is 12 inches deep, 10 inches wide, and 36 inches tall. What is the volume of the locker?

  97. 97.A farmers-market map in Leesburg uses the rule that the y-coordinate is twice the x-coordinate. Which point follows the rule?

  98. 98.A foot measurement near Natural Bridge changes by 0.504 foot. Which expression is the expanded form of 0.504?

  99. 99.An overlook marker on a Skyline Drive grid is at (3, 9). It is moved 3 units down. What is the new point?

  100. 100.A draft speed sign in Manassas compares 8.03 and 8.3. Which symbol makes the statement 8.03 ___ 8.3 true?

  101. 101.A tank in Bristol holds 48.6 gallons and is emptied into 6 barrels with the same amount in each. How many gallons go into each barrel?

  102. 102.At a bake sale in Emporia, one plate has 1/3 of a pecan pie and another has 1/4 of a pecan pie. What fraction of a pie is that altogether?

  103. 103.A pharmacy balance in Salem starts at 1 kilogram and a 0.075-kilogram weight is removed. What mass remains?

  104. 104.A tailor in Pulaski has 3/4 yard of cloth and cuts off 5/12 yard. How much cloth is left, in simplest form?

  105. 105.Students in Radford cut a foam block that is 7 centimeters long, 3 centimeters wide, and 4 centimeters high. What is the volume of the foam?

  106. 106.A scoreboard formula in Salem is (12 + 8) ÷ (2 × 2). What is the value?

  107. 107.A cedar chest in Leesburg is 8 feet long, 3 feet wide, and 3 feet high. What is the volume of the chest?

  108. 108.Students in Purcellville evaluate (9 + 3) × 4 − 6. What is the value?