Fractions Unit Review Packet 1. There are 1,716 students participating in Wellness Day. They are put into teams of 16 for the competition. How many teams are created? Will there be any extra students? If so, how many students will be remaining? 2. Suppose that at a track meet, the lead runner is 1 mile ahead of the secondplace runner and the second-place runner is 3 mile ahead of the third-place 8 8 runner. How far apart are the lead runner and the third-place runner? 3. Use the rule add 3 to write the first numbers in a sequence starting with 0. Use the rule add 6 to write the first numbers in a sequence starting with 0. What do you notice about the pattern? How do the rules affect the pattern? Write a list of ordered pairs using the two sequences of numbers where the first quantity in each ordered pair comes from the first sequence. Graph the points on a coordinate grid. 4. There are types of grains of sand: very fine, fine, medium, coarse, and very coarse. Marie measured the diameters of a grain of sand from each type and recorded the following: 0.716 mm, 0.7 mm, 0.61 mm, 0.608 mm, and 0.79 mm. Can you help Marie determine which diameter corresponds to which type by ordering the numbers from least to greatest?. Amanda bought a 40 lb bag of candy. She decided to split it equally with her two sisters. How many pounds will each receive? Write your answer as a mixed number. 6. Devin uses fourteen 12.9 oz cans of chicken broth when he makes his famous chicken noodle soup at his restaurant. How many total ounces of chicken broth does he use? 7. Popcorn Mania sells different flavored popcorn in rectangular metal bins. The caramel popcorn comes in a bin that measures 2 inches in height and the area of its base measures 13 1 square inches. How many cubic inches of popcorn 2 can the container hold? 8. The total number of calories in a super value size bag of honey barbecue flavored potato chips is 3,200 calories. If each bag contains 1 servings, about how many calories are in each serving? 9. Plot the following ordered pairs on a coordinate grid: A(2, 6), B(4, 6), C(6, 3), D(2, 3). What geometric figure is formed? What attributes did you use to identify it? 10. The average length of the head and body of a field mouse is 2.9 inches. The average length of the tail is 2.8 inches. What is the actual total length of a field mouse? 11. Alexia is making trail mix bags for each of her students to take on their field trip. She puts in 1 1 oz of dried cranberries, 2 4 oz of almonds, 2 2 oz of walnuts and 2 1 3 oz of dried pineapples. How much does each trail mix bag weigh? If she has 4 8 students, how much will the bags weight altogether? NJ Center for Teaching and Learning ~ 1 ~ www.njctl.org
12. The average length of a humpback whale is 13.6 meters. The average length of a killer whale is 6.8 meters. How much longer is the humpback whale than the killer whale? 13. Two afterschool clubs are having pizza parties. For the Debate Club, the teacher will order 3 pizzas for every students. For the Science Club, the teacher will order pizzas for every 9 students. Since you are in both groups, you need to decide which party to attend. How much pizza would you get at each party? If you want to have the most pizza, which party should you attend? Show your work. 14. Write the mathematical expression that is equivalent to the number sentence: subtract 1 from 4, and then divide by 3. Solve the expression. 1. The perimeter of a triangle is 10 in. One side measures 3 1 in. and the second 6 side measures 1 in. What is the measure of the third side? 6 16. What number is one-tenth of the number shown in expanded form below? 1(10,000) + 2(1,000) + 4(100) + 3(10) + 2(1) + (1/10) + 3(1/100) 17. There are 2 servings in a 16.8 ounce bottle of cooking oil. How many ounces are in a serving? 18. Darren and Robert love to catch lightning bugs. The chart below shows the total number of lightning bugs Darren and Robert have at the end of each day (including previous catches). Days Darren s Total Number of Lightning Bugs Robert s Total Number of Lightning Bugs 0 0 0 1 2 4 2 4 8 3 6 12 4 8 16?? Describe the pattern of how many lightning bugs each catches per day. Compare the pattern. How many lightning bugs will each have at the end of day? Make a graph of the number of lightning bugs. 19. A bag of pecans has a mass of 1 oz. The mass of a bag of almonds is 4 that of the bag of pecans. What is the mass of the bag of almonds? What is the total mass of the pecans and almonds? 20. How many times greater is the value of the digit in 83,607 than the value of the digit in 362,01? NJ Center for Teaching and Learning ~ 2 ~ www.njctl.org
21. Meteorologists recorded the average rainfall in several major cities. Copy the chart and round the average rainfall in each city to the nearest tenth and hundredth. Average Rainfall City New York City Los Angeles New Orleans Houston Average Rainfall (in inches) 60.187 inches 71.03 inches 8.49 inches 47.908 inches nearest tenth nearest hundredth 22. The total mass of a watermelon, honeydew melon, and a cantaloupe is 6 9 kg. The watermelon has a mass of 3 2 kg. The honeydew melon has a mass that is 3 kg lighter than the watermelon. What is the mass of the cantaloupe? 1 6 23. At the Ice Cream Shoppe, the top selling sundae is the Ultimate Strawberry sundae. Each sundae gets 16 strawberries. This week they used 6,912 strawberries. How many Ultimate Strawberry sundaes did they sell? 24. Write the mathematical expression that is equivalent to the number sentence: the sum of nine and five subtracted by the product of four and three. Solve the expression. 2. There are 2 1 bus loads of students standing in the parking lot. The students are 2 getting ready to go on a field trip. Two-fifths of the students on each bus are girls. How many busses would it take to carry only the girls? 26. One gallon of orange juice is equivalent to (3.7841 x 10 3 ) ml. Evaluate the expression to find out how many milliliters is equivalent to one gallon. How many liters is it equivalent to? 27. Jim needs to buy different size nails in order to build a tree house. He needs nails that measure 1.27 inches and 1.243 inches long. Write an inequality statement to compare the two nail lengths. 28. Jefferson Middle School is planning a Spring concert for the 6 th graders. Half of the auditorium will be used to set up the stage. The other half will seat 3 equalsized sixth grade classes. What fraction of the auditorium will one of the sixth grade classes need? 29. Jackie helps her family out on their farm during her summer vacation. It takes her 2.7 hours to drive to the farm and back. She usually goes to the farm twice a week. How much time does Jackie spend driving if she takes 8 trips to the farm each month? NJ Center for Teaching and Learning ~ 3 ~ www.njctl.org
30. David wants to build small concrete steps that lead from his backyard to his patio door. He drew the following sketch: How many cubic feet of concrete will he need to purchase to build the steps? 31. Write the mathematical expression that is equivalent to the number sentence: double and then add 34. Solve the expression. 32. Terrance bought 4 lbs of laffy taffy the last time he visited the boardwalk. He wants to separate the container into small storage bags so that he can bring some to work every day. Each storage bag can hold 1/ lb of laffy taffy. How many storage bags will he need to separate all the laffy taffy? 33. Justin weights 97.36 pounds. Write this number in expanded form. 34. A jewelry box measures 30 cm in length, 8 cm in height, and 12 cm in depth. What is the volume, in cubic centimeters, of the jewelry box? 3. In science class, students measured the volume of soda in ten identical glasses and created the line plot below. Soda Experiment Volume of Soda (in Liters) If the soda is redistributed equally among the same glasses, how much soda would each glass have? 36. Jonathan ordered 3 baseball card binders so that he can organize his collection of baseball trading cards. Each binder cost $19.99 and shipping for the entire order cost only $4.7. How much did Jonathan spend in all on his order? 37. The most popular cheese crackers at Craig s Convenience store come in a case of 18 packages. Craig sold 1,90 packages last month. How many cases did he sell? Did he need to open an extra case? If yes, how many packages did he need to take out from the extra case? 38. Kim needs to purchase 6.3 meters of tape for her class project. If each roll of tape contains 90 cm and costs $4.2, what is the total cost of the tape that Kim must buy? NJ Center for Teaching and Learning ~ 4 ~ www.njctl.org
Answer Key 1. 107 teams; 4 students 1 2. mile 2 3. Add 3 Sequence: 0, 3, 6, 9, 12 Add 6 Sequence: 0, 6, 12, 18, 24 30 2 20 1 10 Add 3 Add 6 0 0 1 2 3 4 6 4. 0.608 mm, 0.61 mm, 0.7 mm, 0.716mm, 0.79 mm. 13 1 lbs each 3 6. 180.6 oz 7. 72 9 cubic inches 10 8. 213 1 calories 3 9. Trapezoid; AB and DC are parallel 10..7 inches 11. 8 9 oz; 67 3 oz 20 12. 6.7 m 13. 3/ of the pizza from the Debate Club, /9 of the pizza from the Science Club; More pizza from the Debate Club because 3/ > /9 14. (4 1) 3; 10 1. 1 2 in. 3 16. 1,243.23 17. 0.672 oz NJ Center for Teaching and Learning ~ ~ www.njctl.org
18. Darren catches 2 lightning bugs each day. Robert catches 4 lightning bugs each day. Robert catches twice as many Darren every day so Robert s total is always greater and is always twice as much as Darren s total. At the end of day, Darren will have 10 lightning bugs and Robert will have 20. 2 Catching Lightning Bugs Lightning Bugs 20 1 10 Darren's Total Number of Lightning Bugs Robert's Total Number of Lightning Bugs 0 0 1 2 3 4 19. Bag of almonds 12 oz., Total mass 27 oz. 20. 1,000 times 21. Average Rainfall City Average Rainfall (in inches) nearest tenth nearest hundredth New York City 60.187 inches 60.2 inches 60.19 inches Los Angeles 71.03 inches 71.1 inches 71.0 inches New Orleans 8.49 inches 8. inches 8.0 inches Houston 47.908 inches 47.9 inches 47.91 inches Day 22. 1 1 18 kg 23. 432 sundaes 24. (9 + ) (4 x 3); 2 2. 1 whole bus 26. 3,78.41 ml; 3.7841 L 27. 1.27 > 1.243 or 1.243 < 1.27 28. 1/6 29. 22 hr 30. 24 cubic feet 31. (2 x ) + 34; 44 32. 20 bags 33. 9(10) + 7(1) + 3(1/10) + (1/100) + 6(1/1,000) 34. 2,880 cubic centimeters 3. /16 L 36. $64.72 37. 108 cases; Yes; 6 packages 38. $29.7 NJ Center for Teaching and Learning ~ 6 ~ www.njctl.org