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Line Plots with Fractions

Grade 4 · Fractions · Worksheet 1

  1. Matiu is measuring the lengths of 12 different kōwhai leaves he collected for a science project. He measures each leaf to the nearest quarter of an inch and records the data on a line plot. The lengths are: 2 1/4 in, 2 1/2 in, 2 3/4 in, 2 1/4 in, 2 1/2 in, 2 1/4 in, 2 3/4 in, 2 1/2 in, 2 1/2 in, 2 1/4 in, 2 3/4 in, and 2 1/2 in. Matiu notices that one specific leaf length appears more than any other. How many leaves have that most common length? Answer: ______________
  2. Sophia is helping her class collect data on how far different toy cars roll down a ramp. She measures the distances to the nearest eighth of a meter and records the data on a line plot. The distances are: 7/8 m, 1/2 m, 5/8 m, 7/8 m, 1/4 m, 5/8 m, 7/8 m, 1/2 m, 5/8 m, and 3/4 m. How many cars rolled a distance greater than 5/8 of a meter? Answer: ______________
  3. A line plot shows the lengths of 9 pencils: 1/4, 1/2, 3/4, 1/2, 1/4, 1/2, 3/4, 1/4, 1/2. What fraction appears most often? Answer: ______________
  4. Noah is collecting data for his science project on the lengths of different sticks he found in the forest. He measures each stick to the nearest eighth of a foot and records the data on a line plot. The lengths are: 7 1/4 ft, 7 5/8 ft, 7 3/8 ft, 7 1/4 ft, 7 1/2 ft, 7 5/8 ft, 7 1/4 ft, 7 3/8 ft, 7 1/2 ft, 7 5/8 ft, 7 1/4 ft, and 7 1/2 ft. Which stick length appears most often on Noah's line plot? Answer: ______________
  5. A line plot shows the lengths of 9 ribbons: 1/8, 1/4, 3/8, 1/2, 1/4, 5/8, 3/8, 1/8, 3/8. What fraction appears most often? Answer: ______________
  6. A line plot shows the lengths of 10 pencils: 1/8, 1/4, 3/8, 1/2, 5/8, 1/8, 1/4, 3/8, 1/8, 5/8. What is the most common pencil length? Answer: ______________
  7. Liam measured the lengths of different colored pencils for his art class and recorded them on a line plot. The line plot shows these measurements in inches: 4 1/4, 4 1/2, 4 1/2, 4 3/4, 4 1/2, 4 1/4, 4 3/4, and 4 1/2. What is the total length of all the colored pencils combined? Answer: ______________
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Answer Key & Explanations

Line Plots with Fractions · Grade 4 · Worksheet 1

  1. Matiu is measuring the lengths of 12 different kōwhai leaves he collected for a science project. He measures each leaf to the nearest quarter of an inch and records the data on a line plot. The lengths are: 2 1/4 in, 2 1/2 in, 2 3/4 in, 2 1/4 in, 2 1/2 in, 2 1/4 in, 2 3/4 in, 2 1/2 in, 2 1/2 in, 2 1/4 in, 2 3/4 in, and 2 1/2 in. Matiu notices that one specific leaf length appears more than any other. How many leaves have that most common length? Answer: 5 leaves Solution: List all the leaf lengths: 2 1/4, 2 1/2, 2 3/4, 2 1/4, 2 1/2, 2 1/4, 2 3/4, 2 1/2, 2 1/2, 2 1/4, 2 3/4, 2 1/2.
    Full step-by-step solution

    Step 1: List all the leaf lengths: 2 1/4, 2 1/2, 2 3/4, 2 1/4, 2 1/2, 2 1/4, 2 3/4, 2 1/2, 2 1/2, 2 1/4, 2 3/4, 2 1/2. Step 2: Count how many times each length appears: - 2 1/4 appears: position 1, 4, 6, 10 = 4 times - 2 1/2 appears: position 2, 5, 8, 9, 12 = 5 times - 2 3/4 appears: position 3, 7, 11 = 3 times Step 3: Compare the counts: 4, 5, and 3. The largest count is 5, which belongs to the length 2 1/2 inches. Step 4: Therefore, the most common leaf length is 2 1/2 inches, and it appears 5 times. The answer is 5 leaves.

  2. Sophia is helping her class collect data on how far different toy cars roll down a ramp. She measures the distances to the nearest eighth of a meter and records the data on a line plot. The distances are: 7/8 m, 1/2 m, 5/8 m, 7/8 m, 1/4 m, 5/8 m, 7/8 m, 1/2 m, 5/8 m, and 3/4 m. How many cars rolled a distance greater than 5/8 of a meter? Answer: 4 Solution: List all the distances: 7/8, 1/2, 5/8, 7/8, 1/4, 5/8, 7/8, 1/2, 5/8, 3/4. Convert all fractions to eighths to compare easily: 1/2 = 4/8, 1/4 = 2/8, 3/4 = 6/8.
    Full step-by-step solution

    Step 1: List all the distances: 7/8, 1/2, 5/8, 7/8, 1/4, 5/8, 7/8, 1/2, 5/8, 3/4. Step 2: Convert all fractions to eighths to compare easily: 1/2 = 4/8, 1/4 = 2/8, 3/4 = 6/8. Step 3: Now the distances in eighths are: 7/8, 4/8, 5/8, 7/8, 2/8, 5/8, 7/8, 4/8, 5/8, 6/8. Step 4: Find the distances greater than 5/8: 7/8 (three times) and 6/8 (once). Step 5: Count them: 3 + 1 = 4 cars. The answer is 4.

  3. A line plot shows the lengths of 9 pencils: 1/4, 1/2, 3/4, 1/2, 1/4, 1/2, 3/4, 1/4, 1/2. What fraction appears most often? Answer: 1/2 Solution: List all the pencil lengths: 1/4, 1/2, 3/4, 1/2, 1/4, 1/2, 3/4, 1/4, 1/2 Count how many times 1/4 appears: It appears in positions 1, 5, and 8, so 3 times Count how many times 1/2 appears: It appears in positions 2, 4, 6, and 9, so 4 times Count how many times 3/4 appears: It appears in…
    Full step-by-step solution

    Step 1: List all the pencil lengths: 1/4, 1/2, 3/4, 1/2, 1/4, 1/2, 3/4, 1/4, 1/2 Step 2: Count how many times 1/4 appears: It appears in positions 1, 5, and 8, so 3 times Step 3: Count how many times 1/2 appears: It appears in positions 2, 4, 6, and 9, so 4 times Step 4: Count how many times 3/4 appears: It appears in positions 3 and 7, so 2 times Step 5: Compare the counts: 1/2 appears 4 times, which is more than 1/4 (3 times) and 3/4 (2 times) The fraction that appears most often is 1/2.

  4. Noah is collecting data for his science project on the lengths of different sticks he found in the forest. He measures each stick to the nearest eighth of a foot and records the data on a line plot. The lengths are: 7 1/4 ft, 7 5/8 ft, 7 3/8 ft, 7 1/4 ft, 7 1/2 ft, 7 5/8 ft, 7 1/4 ft, 7 3/8 ft, 7 1/2 ft, 7 5/8 ft, 7 1/4 ft, and 7 1/2 ft. Which stick length appears most often on Noah's line plot? Answer: 7 1/4 feet Solution: List all the stick lengths: 7 1/4 ft, 7 5/8 ft, 7 3/8 ft, 7 1/4 ft, 7 1/2 ft, 7 5/8 ft, 7 1/4 ft, 7 3/8 ft, 7 1/2 ft, 7 5/8 ft, 7 1/4 ft, 7 1/2 ft.
    Full step-by-step solution

    Step 1: List all the stick lengths: 7 1/4 ft, 7 5/8 ft, 7 3/8 ft, 7 1/4 ft, 7 1/2 ft, 7 5/8 ft, 7 1/4 ft, 7 3/8 ft, 7 1/2 ft, 7 5/8 ft, 7 1/4 ft, 7 1/2 ft. Step 2: Count how many times each length appears: - 7 1/4 ft appears 4 times - 7 3/8 ft appears 2 times - 7 1/2 ft appears 3 times - 7 5/8 ft appears 3 times Step 3: The length with the highest count is 7 1/4 ft, which appears 4 times. The answer is 7 1/4 feet.

  5. A line plot shows the lengths of 9 ribbons: 1/8, 1/4, 3/8, 1/2, 1/4, 5/8, 3/8, 1/8, 3/8. What fraction appears most often? Answer: 3/8 Solution: List all the ribbon lengths: 1/8, 1/4, 3/8, 1/2, 1/4, 5/8, 3/8, 1/8, 3/8 Count how many times 1/8 appears: It appears in positions 1, 7, and 8, so 3 times Count how many times 1/4 appears: It appears in positions 2 and 5, so 2 times Count how many times 3/8 appears: It appears in positions 3, 7,…
    Full step-by-step solution

    Step 1: List all the ribbon lengths: 1/8, 1/4, 3/8, 1/2, 1/4, 5/8, 3/8, 1/8, 3/8 Step 2: Count how many times 1/8 appears: It appears in positions 1, 7, and 8, so 3 times Step 3: Count how many times 1/4 appears: It appears in positions 2 and 5, so 2 times Step 4: Count how many times 3/8 appears: It appears in positions 3, 7, and 9, so 3 times Step 5: Count how many times 1/2 appears: It appears in position 4, so 1 time Step 6: Count how many times 5/8 appears: It appears in position 6, so 1 time Step 7: Compare the counts: 1/8 appears 3 times, 1/4 appears 2 times, 3/8 appears 3 times, 1/2 appears 1 time, 5/8 appears 1 time Step 8: Both 1/8 and 3/8 appear 3 times, which is more than any other fraction Step 9: Since both have the same frequency, we look at the data set order. 3/8 appears more consistently throughout the data set. The fraction that appears most often is 3/8.

  6. A line plot shows the lengths of 10 pencils: 1/8, 1/4, 3/8, 1/2, 5/8, 1/8, 1/4, 3/8, 1/8, 5/8. What is the most common pencil length? Answer: 1/8 Solution: List all the pencil lengths: 1/8, 1/4, 3/8, 1/2, 5/8, 1/8, 1/4, 3/8, 1/8, 5/8 Count how many times 1/8 appears: It appears in positions 1, 6, and 9, so 3 times Count how many times 1/4 appears: It appears in positions 2 and 7, so 2 times Count how many times 3/8 appears: It appears in positions…
    Full step-by-step solution

    Step 1: List all the pencil lengths: 1/8, 1/4, 3/8, 1/2, 5/8, 1/8, 1/4, 3/8, 1/8, 5/8 Step 2: Count how many times 1/8 appears: It appears in positions 1, 6, and 9, so 3 times Step 3: Count how many times 1/4 appears: It appears in positions 2 and 7, so 2 times Step 4: Count how many times 3/8 appears: It appears in positions 3 and 8, so 2 times Step 5: Count how many times 1/2 appears: It appears in position 4, so 1 time Step 6: Count how many times 5/8 appears: It appears in positions 5 and 10, so 2 times Step 7: Compare the counts: 1/8 appears 3 times, which is more than 1/4 (2 times), 3/8 (2 times), 1/2 (1 time), and 5/8 (2 times) The most common pencil length is 1/8.

  7. Liam measured the lengths of different colored pencils for his art class and recorded them on a line plot. The line plot shows these measurements in inches: 4 1/4, 4 1/2, 4 1/2, 4 3/4, 4 1/2, 4 1/4, 4 3/4, and 4 1/2. What is the total length of all the colored pencils combined? Answer: 36 1/2 inches Solution: Count how many colored pencils are at each measurement: - 4 1/4 inches: 2 pencils - 4 1/2 inches: 4 pencils - 4 3/4 inches: 2 pencils - 4 1/4 × 2 = 8 2/4 = 8 1/2 inches - 4 1/2 × 4 = 18 inches - 4 3/4 × 2 = 9 2/4 = 9 1/2 inches 8 1/2 + 18 + 9 1/2 = (8 1/2 + 9 1/2) + 18 = 18 + 18 = 36 inches The…
    Full step-by-step solution

    Step 1: Count how many colored pencils are at each measurement: - 4 1/4 inches: 2 pencils - 4 1/2 inches: 4 pencils - 4 3/4 inches: 2 pencils Step 2: Calculate the total for each measurement: - 4 1/4 × 2 = 8 2/4 = 8 1/2 inches - 4 1/2 × 4 = 18 inches - 4 3/4 × 2 = 9 2/4 = 9 1/2 inches Step 3: Add all the totals together: 8 1/2 + 18 + 9 1/2 = (8 1/2 + 9 1/2) + 18 = 18 + 18 = 36 inches The answer is 36 inches.