Line Plots

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Answer Key & Explanations

Line Plots · Grade 5 · Worksheet 3

1. A line plot shows the lengths of 5 nails in inches: 4 3/8, 4 7/16, 4 5/8, 4 3/4, 4 15/16. What is the difference between the longest and shortest nail? Answer: 9/16 Solution: Convert all measurements to sixteenths of an inch: 4 3/8 = 4 + 6/16 = 4 6/16 4 7/16 = 4 + 7/16 = 4 7/16 4 5/8 = 4 + 10/16 = 4 10/16 4 3/4 = 4 + 12/16 = 4 12/16 4 15/16 = 4 + 15/16 = 4 15/16 Longest: 4 15/16 Shortest: 4 6/16 (4 3/8) 4 15/16 - 4 6/16 = (15/16 - 6/16) = 9/16 Check if 9/16 can be…
   Full step-by-step solution

   Step 1: Convert all measurements to sixteenths of an inch: 4 3/8 = 4 + 6/16 = 4 6/16 4 7/16 = 4 + 7/16 = 4 7/16 4 5/8 = 4 + 10/16 = 4 10/16 4 3/4 = 4 + 12/16 = 4 12/16 4 15/16 = 4 + 15/16 = 4 15/16 Step 2: Identify the longest and shortest nails: Longest: 4 15/16 Shortest: 4 6/16 (4 3/8) Step 3: Find the difference: 4 15/16 - 4 6/16 = (15/16 - 6/16) = 9/16 Step 4: Check if 9/16 can be simplified. Since 9 and 16 share no common factors other than 1, the fraction is already in simplest form. The answer is 9/16 inch.

2. Liam is tracking his daily reading time for a week. He records his reading times on a line plot: Monday 3/4 hour, Tuesday 1/2 hour, Wednesday 1 hour, Thursday 3/4 hour, Friday 1/4 hour, Saturday 1 1/4 hours, Sunday 1/2 hour. How many total hours did Liam spend reading during the week? Answer: 5 Solution: Monday: 3/4 hour Tuesday: 1/2 hour Wednesday: 1 hour Thursday: 3/4 hour Friday: 1/4 hour Saturday: 1 1/4 hours Sunday: 1/2 hour Combine the whole numbers and fractions separately.
   Full step-by-step solution

   Let's list all the reading times for each day: Monday: 3/4 hour Tuesday: 1/2 hour Wednesday: 1 hour Thursday: 3/4 hour Friday: 1/4 hour Saturday: 1 1/4 hours Sunday: 1/2 hour Step 1: Combine the whole numbers and fractions separately. First, note that 1 1/4 hours is the same as 1 + 1/4. So whole hours from the list: Wednesday (1), Saturday (1). That’s 1 + 1 = 2 whole hours so far. Step 2: Now list all the fractional parts in hours: Monday: 3/4 Tuesday: 1/2 Thursday: 3/4 Friday: 1/4 Saturday: 1/4 (from the 1 1/4) Sunday: 1/2 Step 3: Group fractions with the same denominator to add more easily. First, add all the 1/2 hours: Tuesday (1/2) + Sunday (1/2) = 1/2 + 1/2 = 1 hour. Step 4: Add all the 1/4 hours: Friday (1/4) + Saturday (1/4) = 1/4 + 1/4 = 2/4 = 1/2 hour. Step 5: Add all the 3/4 hours: Monday (3/4) + Thursday (3/4) = 3/4 + 3/4 = 6/4 = 3/2 = 1 1/2 hours. Step 6: Now combine all the fractional results from Steps 3–5: From Step 3: 1 hour From Step 4: 1/2 hour From Step 5: 1 1/2 hours Add these: 1 + 1/2 + 1 1/2 = 1 + 1/2 + 1 + 1/2 = (1 + 1) + (1/2 + 1/2) = 2 + 1 = 3 hours from fractions. Step 7: Add the whole hours from Step 1 (2 hours) to the total from fractions (3 hours): 2 + 3 = 5 hours. So Liam spent 5 hours reading during the week.

3. A line plot shows the lengths of 5 screws in inches: 6 1/8, 6 5/16, 6 3/8, 6 11/16, 6 7/8. What is the difference between the longest and shortest screw? Answer: 3/4 Solution: Convert all measurements to sixteenths of an inch: 6 1/8 = 6 + 2/16 = 6 2/16 6 5/16 = 6 + 5/16 = 6 5/16 6 3/8 = 6 + 6/16 = 6 6/16 6 11/16 = 6 + 11/16 = 6 11/16 6 7/8 = 6 + 14/16 = 6 14/16 Longest: 6 14/16 (6 7/8) Shortest: 6 2/16 (6 1/8) 6 14/16 - 6 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: 6 1/8 = 6 + 2/16 = 6 2/16 6 5/16 = 6 + 5/16 = 6 5/16 6 3/8 = 6 + 6/16 = 6 6/16 6 11/16 = 6 + 11/16 = 6 11/16 6 7/8 = 6 + 14/16 = 6 14/16 Step 2: Identify the longest and shortest screws: Longest: 6 14/16 (6 7/8) Shortest: 6 2/16 (6 1/8) Step 3: Find the difference: 6 14/16 - 6 2/16 = (14/16 - 2/16) = 12/16 Step 4: Simplify the fraction: 12/16 = 3/4 The answer is 3/4 inch.

4. Noah is measuring the lengths of different colored pipe cleaners in his art kit. He measures each pipe cleaner to the nearest eighth of an inch and records these lengths: 6 1/8 in, 6 3/8 in, 6 1/2 in, 6 5/8 in, 6 7/8 in, 6 1/8 in, 6 3/8 in, 6 5/8 in, 6 1/2 in, 6 7/8 in, 6 3/8 in, and 6 5/8 in. If Noah makes a line plot of all these measurements, how many pipe cleaners are shorter than 6 5/8 inches? Answer: 7 Solution: List all the measurements: 6 1/8, 6 3/8, 6 1/2, 6 5/8, 6 7/8, 6 1/8, 6 3/8, 6 5/8, 6 1/2, 6 7/8, 6 3/8, 6 5/8. Identify which measurements are shorter than 6 5/8 inches.
   Full step-by-step solution

   Step 1: List all the measurements: 6 1/8, 6 3/8, 6 1/2, 6 5/8, 6 7/8, 6 1/8, 6 3/8, 6 5/8, 6 1/2, 6 7/8, 6 3/8, 6 5/8. Step 2: Identify which measurements are shorter than 6 5/8 inches. Compare each to 6 5/8 (which is 6 5/8): - 6 1/8 is less than 6 5/8, so YES - 6 3/8 is less than 6 5/8, so YES - 6 1/2 (which is 6 4/8) is less than 6 5/8, so YES - 6 5/8 is equal to 6 5/8, so NOT shorter - 6 7/8 is greater than 6 5/8, so NOT shorter Step 3: Count how many pipe cleaners are shorter than 6 5/8: - 6 1/8 appears 2 times - 6 3/8 appears 3 times - 6 1/2 appears 2 times - Total = 2 + 3 + 2 = 7 The answer is 7 pipe cleaners.

5. A line plot shows the lengths of 6 pencils measured in inches: 5 1/8, 5 3/16, 5 1/4, 5 7/16, 5 5/8, 5 3/4. What is the difference between the longest and shortest pencil? Answer: 5/8 Solution: Convert all measurements to sixteenths for easy comparison: - 5 1/8 = 5 + 2/16 = 5 2/16 - 5 3/16 = 5 + 3/16 = 5 3/16 - 5 1/4 = 5 + 4/16 = 5 4/16 - 5 7/16 = 5 + 7/16 = 5 7/16 - 5 5/8 = 5 + 10/16 = 5 10/16 - 5 3/4 = 5 + 12/16 = 5 12/16 Longest: 5 12/16 (5 3/4) Shortest: 5 2/16 (5 1/8) 5 12/16 - 5…
   Full step-by-step solution

   Step 1: Convert all measurements to sixteenths for easy comparison: - 5 1/8 = 5 + 2/16 = 5 2/16 - 5 3/16 = 5 + 3/16 = 5 3/16 - 5 1/4 = 5 + 4/16 = 5 4/16 - 5 7/16 = 5 + 7/16 = 5 7/16 - 5 5/8 = 5 + 10/16 = 5 10/16 - 5 3/4 = 5 + 12/16 = 5 12/16 Step 2: Identify the longest and shortest pencils: Longest: 5 12/16 (5 3/4) Shortest: 5 2/16 (5 1/8) Step 3: Find the difference: 5 12/16 - 5 2/16 = (12/16 - 2/16) = 10/16 Step 4: Simplify the fraction: 10/16 = 5/8 The answer is 5/8.

6. A rectangular prism has a length of 12 cm, a width of 5.5 cm, and a height of 8.25 cm. What is the volume of this rectangular prism? Answer: 544.5 Solution: To find the volume of a rectangular prism, we use the formula: Volume = length × width × height Write down the given dimensions.
   Full step-by-step solution

   To find the volume of a rectangular prism, we use the formula: Volume = length × width × height Step 1: Write down the given dimensions. Length = 12 cm Width = 5.5 cm Height = 8.25 cm Step 2: Substitute the given numbers into the formula. Volume = 12 × 5.5 × 8.25 Step 3: Perform the multiplication step by step. First, multiply the length and the width. 12 × 5.5 = 66 So now we have: Volume = 66 × 8.25 Step 4: Now multiply the result by the height. We can calculate 66 × 8.25 by breaking it down: First, 66 × 8 = 528 Next, 66 × 0.25 = 16.5 (since 0.25 is one quarter, and one quarter of 66 is 66/4 = 16.5) Step 5: Add the two results together. 528 + 16.5 = 544.5 Step 6: State the final answer with the correct units. The volume of the rectangular prism is 544.5 cubic centimeters. Final Answer: 544.5

7. A line plot shows the lengths of 5 screws in inches: 5 3/8, 5 1/16, 5 9/16, 5 3/4, 5 5/8. What is the difference between the longest and shortest screw? Answer: 11/16 Solution: Convert all measurements to sixteenths of an inch: 5 3/8 = 5 + 6/16 = 5 6/16 5 1/16 = 5 + 1/16 = 5 1/16 5 9/16 = 5 + 9/16 = 5 9/16 5 3/4 = 5 + 12/16 = 5 12/16 5 5/8 = 5 + 10/16 = 5 10/16 Longest: 5 12/16 (5 3/4) Shortest: 5 1/16 5 12/16 - 5 1/16 = (12/16 - 1/16) = 11/16 Check if 11/16 can be…
   Full step-by-step solution

   Step 1: Convert all measurements to sixteenths of an inch: 5 3/8 = 5 + 6/16 = 5 6/16 5 1/16 = 5 + 1/16 = 5 1/16 5 9/16 = 5 + 9/16 = 5 9/16 5 3/4 = 5 + 12/16 = 5 12/16 5 5/8 = 5 + 10/16 = 5 10/16 Step 2: Identify the longest and shortest screws: Longest: 5 12/16 (5 3/4) Shortest: 5 1/16 Step 3: Find the difference: 5 12/16 - 5 1/16 = (12/16 - 1/16) = 11/16 Step 4: Check if 11/16 can be simplified. Since 11 and 16 share no common factors other than 1, the fraction is already in simplest form. The answer is 11/16 inch.