Line Plots

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Answer Key & Explanations

Line Plots · Grade 5 · Worksheet 2

1. A line plot shows the lengths of 8 ribbons measured to the nearest eighth of an inch. The data points are: 3 1/8, 3 1/4, 3 1/4, 3 3/8, 3 1/2, 3 1/2, 3 5/8, and 3 3/4. What is the total length of all the ribbons combined? Answer: 27 3/4 Solution: Convert all measurements to eighths of an inch. 3 1/8 = 25/8 3 1/4 = 3 2/8 = 26/8 3 1/4 = 3 2/8 = 26/8 3 3/8 = 27/8 3 1/2 = 3 4/8 = 28/8 3 1/2 = 3 4/8 = 28/8 3 5/8 = 29/8 3 3/4 = 3 6/8 = 30/8 Add all the eighths together.
   Full step-by-step solution

   Step 1: Convert all measurements to eighths of an inch. 3 1/8 = 25/8 3 1/4 = 3 2/8 = 26/8 3 1/4 = 3 2/8 = 26/8 3 3/8 = 27/8 3 1/2 = 3 4/8 = 28/8 3 1/2 = 3 4/8 = 28/8 3 5/8 = 29/8 3 3/4 = 3 6/8 = 30/8 Step 2: Add all the eighths together. 25/8 + 26/8 + 26/8 + 27/8 + 28/8 + 28/8 + 29/8 + 30/8 = 219/8 Step 3: Convert the improper fraction to a mixed number. 219 ÷ 8 = 27 with remainder 3, so 219/8 = 27 3/8 Step 4: Simplify if possible. 27 3/8 is already in simplest form. The total length of all ribbons is 27 3/8 inches.

2. Kaia is measuring the lengths of different leaves she collected for a nature project. She measured each leaf to the nearest eighth of an inch and recorded the lengths: 1 3/8 in, 1 5/8 in, 1 1/2 in, 1 3/8 in, 1 7/8 in, 1 5/8 in, 1 1/2 in, 1 3/8 in, 1 7/8 in, and 1 1/2 in. If she makes a line plot of all these measurements, what is the total combined length of all the leaves? Answer: 15 5/8 Solution: - 1 3/8 in: 3 leaves - 1 1/2 in: 3 leaves - 1 5/8 in: 2 leaves - 1 7/8 in: 2 leaves Convert each mixed number to an improper fraction with denominator 8: - 1 3/8 = 11/8 - 1 1/2 = 1 4/8 = 12/8 - 1 5/8 = 13/8 - 1 7/8 = 15/8 - 3 × 11/8 = 33/8 - 3 × 12/8 = 36/8 - 2 × 13/8 = 26/8 - 2 × 15/8 = 30/8…
   Full step-by-step solution

   Step 1: Count how many of each measurement there are: - 1 3/8 in: 3 leaves - 1 1/2 in: 3 leaves - 1 5/8 in: 2 leaves - 1 7/8 in: 2 leaves Step 2: Convert each mixed number to an improper fraction with denominator 8: - 1 3/8 = 11/8 - 1 1/2 = 1 4/8 = 12/8 - 1 5/8 = 13/8 - 1 7/8 = 15/8 Step 3: Multiply each measurement by the count: - 3 × 11/8 = 33/8 - 3 × 12/8 = 36/8 - 2 × 13/8 = 26/8 - 2 × 15/8 = 30/8 Step 4: Add all the totals: 33/8 + 36/8 + 26/8 + 30/8 = 125/8 Step 5: Convert to a mixed number: 125 ÷ 8 = 15 remainder 5, so 125/8 = 15 5/8 The total combined length of all the leaves is 15 5/8 inches.

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

   Step 1: Convert all measurements to sixteenths of an inch for easier comparison: 6 1/8 = 6 + 2/16 = 6 2/16 6 5/16 = 6 + 5/16 = 6 5/16 6 3/4 = 6 + 12/16 = 6 12/16 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 ribbons: 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. A line plot shows the lengths of 5 pencils in inches: 4 3/8, 4 5/16, 4 11/16, 4 1/2, 4 7/8. What is the difference between the longest and shortest pencil? Answer: 9/16 Solution: Convert all measurements to sixteenths of an inch: 4 3/8 = 4 + 6/16 = 4 6/16 4 5/16 = 4 + 5/16 = 4 5/16 4 11/16 = 4 + 11/16 = 4 11/16 4 1/2 = 4 + 8/16 = 4 8/16 4 7/8 = 4 + 14/16 = 4 14/16 Longest: 4 14/16 (4 7/8) Shortest: 4 5/16 4 14/16 - 4 5/16 = (14/16 - 5/16) = 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 5/16 = 4 + 5/16 = 4 5/16 4 11/16 = 4 + 11/16 = 4 11/16 4 1/2 = 4 + 8/16 = 4 8/16 4 7/8 = 4 + 14/16 = 4 14/16 Step 2: Identify the longest and shortest pencils: Longest: 4 14/16 (4 7/8) Shortest: 4 5/16 Step 3: Find the difference: 4 14/16 - 4 5/16 = (14/16 - 5/16) = 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.

5. A line plot shows the lengths of 5 nails in inches: 2 3/8, 2 5/16, 2 1/2, 2 11/16, 2 7/8. What is the difference between the longest and shortest nail? Answer: 9/16 Solution: Convert all measurements to sixteenths of an inch: 2 3/8 = 2 + 6/16 = 2 6/16 2 5/16 = 2 + 5/16 = 2 5/16 2 1/2 = 2 + 8/16 = 2 8/16 2 11/16 = 2 + 11/16 = 2 11/16 2 7/8 = 2 + 14/16 = 2 14/16 Longest: 2 14/16 (2 7/8) Shortest: 2 5/16 2 14/16 - 2 5/16 = (14/16 - 5/16) = 9/16 Check if 9/16 can be…
   Full step-by-step solution

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

6. A line plot shows the lengths of 8 different ribbons measured to the nearest quarter inch. The data points are: 3 1/4, 3 1/2, 3 1/2, 3 3/4, 4, 4 1/4, 4 1/4, 4 1/2. What is the total length of all the ribbons combined? Answer: 31 Solution: List all the ribbon lengths: 3 1/4, 3 1/2, 3 1/2, 3 3/4, 4, 4 1/4, 4 1/4, 4 1/2. Group the ribbons with the same length. - One ribbon is 3 1/4.
   Full step-by-step solution

   Step 1: List all the ribbon lengths: 3 1/4, 3 1/2, 3 1/2, 3 3/4, 4, 4 1/4, 4 1/4, 4 1/2. Step 2: Group the ribbons with the same length. - One ribbon is 3 1/4. - Two ribbons are 3 1/2. 3 1/2 + 3 1/2 = 7. - One ribbon is 3 3/4. - One ribbon is 4. - Two ribbons are 4 1/4. 4 1/4 + 4 1/4 = 8 1/2. - One ribbon is 4 1/2. Step 3: Add the lengths step by step. Start with 3 1/4 + 7 = 10 1/4. 10 1/4 + 3 3/4 = 14. 14 + 4 = 18. 18 + 8 1/2 = 26 1/2. 26 1/2 + 4 1/2 = 31. The total length of all the ribbons is 31 inches.

7. A line plot shows the lengths of 7 ribbons measured in inches: 2 1/8, 2 3/16, 2 1/4, 2 7/16, 2 5/8, 2 3/4, 2 15/16. What is the difference between the longest and shortest ribbon? Answer: 13/16 Solution: Identify the longest and shortest ribbon lengths from the list: 2 1/8 (shortest) and 2 15/16 (longest).
   Full step-by-step solution

   Step 1: Identify the longest and shortest ribbon lengths from the list: 2 1/8 (shortest) and 2 15/16 (longest). Step 2: Convert both measurements to sixteenths for easy subtraction: - 2 1/8 = 2 + 2/16 = 34/16 - 2 15/16 = 2 + 15/16 = 47/16 Step 3: Subtract the shortest length from the longest length: 47/16 - 34/16 = 13/16. The answer is 13/16 inch.

8. Liam is measuring the lengths of different caterpillars he found in his garden. He records their lengths in inches on a line plot: 3 1/4, 3 1/2, 3 3/4, 3 1/2, 3 1/4, 4, 3 3/4. What is the total length of all the caterpillars combined? Answer: 25 Solution: Convert mixed numbers to improper fractions or decimals for easier addition. 3 1/4 = 3 + 1/4 = 3.25 3 1/2 = 3 + 1/2 = 3.5 3 3/4 = 3 + 3/4 = 3.75 4 = 4.0 Group identical lengths and count them.
   Full step-by-step solution

   Let's list the caterpillar lengths from the problem: 3 1/4, 3 1/2, 3 3/4, 3 1/2, 3 1/4, 4, 3 3/4. Step 1: Convert mixed numbers to improper fractions or decimals for easier addition. 3 1/4 = 3 + 1/4 = 3.25 3 1/2 = 3 + 1/2 = 3.5 3 3/4 = 3 + 3/4 = 3.75 4 = 4.0 Step 2: Group identical lengths and count them. 3 1/4 appears 2 times → 2 × 3.25 = 6.5 3 1/2 appears 2 times → 2 × 3.5 = 7.0 3 3/4 appears 2 times → 2 × 3.75 = 7.5 4 appears 1 time → 1 × 4.0 = 4.0 Step 3: Add them step by step. First, 6.5 + 7.0 = 13.5 Next, 13.5 + 7.5 = 21.0 Then, 21.0 + 4.0 = 25.0 Step 4: Check by adding all original numbers directly in fraction form to avoid decimal conversion errors. 3 1/4 + 3 1/4 = 6 2/4 = 6 1/2 3 1/2 + 3 1/2 = 7 3 3/4 + 3 3/4 = 6 6/4 = 6 + 1 2/4 = 7 1/2 Now add: 6 1/2 + 7 = 13 1/2 13 1/2 + 7 1/2 = 21 21 + 4 = 25 Both methods give the same result. Final answer: 25

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