Line Plots

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Answer Key & Explanations

Line Plots · Grade 5 · Worksheet 2

1. A rectangular prism is made from centimeter cubes. It has a length of 15 cubes, a width of 6 cubes, and a height of 10 cubes. What is the total volume of the prism in cubic centimeters? Answer: 900 Solution: The volume of a rectangular prism is found by multiplying length × width × height. Length = 15 cubes, width = 6 cubes, height = 10 cubes.
   Full step-by-step solution

   Step 1: The volume of a rectangular prism is found by multiplying length × width × height. Step 2: Length = 15 cubes, width = 6 cubes, height = 10 cubes. Step 3: Multiply the dimensions: 15 × 6 = 90 Step 4: Multiply the result by the height: 90 × 10 = 900 Step 5: Since each cube represents 1 cubic centimeter, the volume is 900 cubic centimeters. The answer is 900.

2. A line plot shows the lengths of 5 pencils in inches: 5 1/8, 5 5/16, 5 3/8, 5 11/16, 5 7/8. What is the difference between the longest and shortest pencil? Answer: 3/4 Solution: Convert all measurements to sixteenths of an inch: 5 1/8 = 5 + 2/16 = 5 2/16 5 5/16 = 5 + 5/16 = 5 5/16 5 3/8 = 5 + 6/16 = 5 6/16 5 11/16 = 5 + 11/16 = 5 11/16 5 7/8 = 5 + 14/16 = 5 14/16 Longest: 5 14/16 (5 7/8) Shortest: 5 2/16 (5 1/8) 5 14/16 - 5 2/16 = (14/16 - 2/16) = 12/16 12/16 = 3/4 The…
   Full step-by-step solution

   Step 1: Convert all measurements to sixteenths of an inch: 5 1/8 = 5 + 2/16 = 5 2/16 5 5/16 = 5 + 5/16 = 5 5/16 5 3/8 = 5 + 6/16 = 5 6/16 5 11/16 = 5 + 11/16 = 5 11/16 5 7/8 = 5 + 14/16 = 5 14/16 Step 2: Identify the longest and shortest pencils: Longest: 5 14/16 (5 7/8) Shortest: 5 2/16 (5 1/8) Step 3: Find the difference: 5 14/16 - 5 2/16 = (14/16 - 2/16) = 12/16 Step 4: Simplify the fraction: 12/16 = 3/4 The answer is 3/4 inch.

3. The line plot shows the lengths of 8 ribbons measured to the nearest 1/8 inch: X X X X X X X X at 2 1/8, 2 1/4, 2 3/8, 2 1/2, 2 5/8, 2 3/4, 2 7/8, and 3 inches. What is the difference in inches between the longest and shortest ribbon? Answer: 7/8 Solution: Identify the shortest ribbon length from the plot: 2 1/8 inches. Identify the longest ribbon length from the plot: 3 inches. Convert 3 inches to a fraction with denominator 8: 3 = 24/8.
   Full step-by-step solution

   Step 1: Identify the shortest ribbon length from the plot: 2 1/8 inches. Step 2: Identify the longest ribbon length from the plot: 3 inches. Step 3: Convert 3 inches to a fraction with denominator 8: 3 = 24/8. Step 4: Convert 2 1/8 inches to an improper fraction: 2 1/8 = 17/8. Step 5: Subtract the shortest length from the longest length: 24/8 - 17/8 = 7/8. The difference is 7/8 inch.

4. Emma measured the lengths of 10 craft ribbons to the nearest eighth of an inch. She recorded the following lengths: 5 0/8 in, 5 5/8 in, 5 5/8 in, 5 5/8 in, 6 0/8 in, 6 0/8 in, 6 5/8 in, 6 5/8 in, 7 0/8 in, and 7 0/8 in. Imagine you create a line plot with an 'X' above each length. How many more ribbons measure exactly 5 5/8 inches than ribbons that measure exactly 7 inches? Answer: 1 Solution: Count the ribbons at each length. 5 0/8 in: 1 ribbon 5 5/8 in: 3 ribbons 6 0/8 in: 2 ribbons 6 5/8 in: 2 ribbons 7 0/8 in: 2 ribbons Ribbons at 5 5/8 in = 3 Ribbons at 7 in = 2 Find the difference: 3 - 2 = 1 The answer is 1.
   Full step-by-step solution

   Step 1: Count the ribbons at each length. 5 0/8 in: 1 ribbon 5 5/8 in: 3 ribbons 6 0/8 in: 2 ribbons 6 5/8 in: 2 ribbons 7 0/8 in: 2 ribbons Step 2: Ribbons at 5 5/8 in = 3 Ribbons at 7 in = 2 Step 3: Find the difference: 3 - 2 = 1 The answer is 1.

5. Liam is measuring rainfall for his science project. He records the amounts in inches: 1/4, 1/2, 3/4, 1/2, 1/4, 1/2, 3/4, 1/4, 1/2, 1/4. He wants to create a line plot to display this data. How many days did Liam record exactly 1/2 inch of rainfall? Answer: 4 Solution: We are given the rainfall amounts recorded by Liam: 1/4, 1/2, 3/4, 1/2, 1/4, 1/2, 3/4, 1/4, 1/2, 1/4. We need to count how many days he recorded exactly 1/2 inch.
   Full step-by-step solution

   Let's go step by step. We are given the rainfall amounts recorded by Liam: 1/4, 1/2, 3/4, 1/2, 1/4, 1/2, 3/4, 1/4, 1/2, 1/4. We need to count how many days he recorded exactly 1/2 inch. Step 1: List all the measurements in order as given: Day 1: 1/4 Day 2: 1/2 Day 3: 3/4 Day 4: 1/2 Day 5: 1/4 Day 6: 1/2 Day 7: 3/4 Day 8: 1/4 Day 9: 1/2 Day 10: 1/4 Step 2: Go through the list and count only the entries equal to 1/2. - Day 2: 1/2 → count = 1 - Day 4: 1/2 → count = 2 - Day 6: 1/2 → count = 3 - Day 9: 1/2 → count = 4 Step 3: Check if any other days have 1/2. Day 1: 1/4 → no Day 3: 3/4 → no Day 5: 1/4 → no Day 7: 3/4 → no Day 8: 1/4 → no Day 10: 1/4 → no Step 4: Total count for 1/2 inch = 4. So, Liam recorded exactly 1/2 inch of rainfall on 4 days. ANSWER: 4

6. Mere measured the lengths of 10 earthworms in her garden to the nearest eighth of an inch. She recorded the following lengths: 5 1/8 in, 5 3/8 in, 5 3/8 in, 5 1/2 in, 5 1/2 in, 5 5/8 in, 5 5/8 in, 5 5/8 in, 5 3/4 in, and 5 7/8 in. If Mere creates a line plot of this data, how many more earthworms are 5 5/8 inches long than the number of earthworms that are 5 1/8 inches long? Answer: 2 Solution: List the data: 5 1/8, 5 3/8, 5 3/8, 5 1/2, 5 1/2, 5 5/8, 5 5/8, 5 5/8, 5 3/4, 5 7/8. Count the number of earthworms at each length.
   Full step-by-step solution

   Step 1: List the data: 5 1/8, 5 3/8, 5 3/8, 5 1/2, 5 1/2, 5 5/8, 5 5/8, 5 5/8, 5 3/4, 5 7/8. Step 2: Count the number of earthworms at each length. - 5 1/8 inches: 1 earthworm - 5 3/8 inches: 2 earthworms - 5 1/2 inches: 2 earthworms - 5 5/8 inches: 3 earthworms - 5 3/4 inches: 1 earthworm - 5 7/8 inches: 1 earthworm Step 3: Find the number of earthworms that are 5 5/8 inches long: 3 earthworms. Step 4: Find the number of earthworms that are 5 1/8 inches long: 1 earthworm. Step 5: Subtract to find the difference: 3 - 1 = 2. The answer is 2.

7. A line plot shows the lengths of 5 nails in inches: 4 1/8, 4 5/16, 4 3/8, 4 11/16, 4 7/8. What is the difference between the longest and shortest nail? Answer: 3/4 Solution: Convert all measurements to sixteenths of an inch: 4 1/8 = 4 + 2/16 = 4 2/16 4 5/16 = 4 + 5/16 = 4 5/16 4 3/8 = 4 + 6/16 = 4 6/16 4 11/16 = 4 + 11/16 = 4 11/16 4 7/8 = 4 + 14/16 = 4 14/16 Longest: 4 14/16 (4 7/8) Shortest: 4 2/16 (4 1/8) 4 14/16 - 4 2/16 = (14/16 - 2/16) = 12/16 12/16 = 3/4 The…
   Full step-by-step solution

   Step 1: Convert all measurements to sixteenths of an inch: 4 1/8 = 4 + 2/16 = 4 2/16 4 5/16 = 4 + 5/16 = 4 5/16 4 3/8 = 4 + 6/16 = 4 6/16 4 11/16 = 4 + 11/16 = 4 11/16 4 7/8 = 4 + 14/16 = 4 14/16 Step 2: Identify the longest and shortest nails: Longest: 4 14/16 (4 7/8) Shortest: 4 2/16 (4 1/8) Step 3: Find the difference: 4 14/16 - 4 2/16 = (14/16 - 2/16) = 12/16 Step 4: Simplify the fraction: 12/16 = 3/4 The answer is 3/4 inch.

8. Liam measured the lengths of 5 different caterpillars he found in his garden. Their lengths were: 3/4 inch, 1/2 inch, 5/8 inch, 7/8 inch, and 3/8 inch. He wants to create a line plot to display this data. What is the total length of all the caterpillars combined? Answer: 3 1/8 inches Solution: 3/4 inch, 1/2 inch, 5/8 inch, 7/8 inch, 3/8 inch. The denominators are 4, 2, and 8. The least common denominator is 8.
   Full step-by-step solution

   Let's add the lengths of the caterpillars step by step. The lengths are: 3/4 inch, 1/2 inch, 5/8 inch, 7/8 inch, 3/8 inch. --- **Step 1: Write all fractions with a common denominator** The denominators are 4, 2, and 8. The least common denominator is 8. 3/4 = (3 × 2)/(4 × 2) = 6/8 1/2 = (1 × 4)/(2 × 4) = 4/8 5/8 = 5/8 7/8 = 7/8 3/8 = 3/8 So the lengths in eighths are: 6/8, 4/8, 5/8, 7/8, 3/8. --- **Step 2: Add the fractions** Add the numerators: 6 + 4 + 5 + 7 + 3 = 25 So total length = 25/8 inches. --- **Step 3: Convert to a mixed number** 25 ÷ 8 = 3 remainder 1, so: 25/8 = 3 1/8 inches. --- **Final Answer:** 3 1/8 inches