Line Plots

lessonbunny.com

Answer Key & Explanations

Line Plots · Grade 5 · Worksheet 1

1. A line plot shows the lengths of 8 pencils measured by students: 5 1/4 inches, 5 1/2 inches, 5 1/2 inches, 5 3/4 inches, 5 3/4 inches, 5 3/4 inches, 6 inches, and 6 1/4 inches. What is the total length of all pencils that measure exactly 5 3/4 inches? Answer: 17 1/4 Solution: Identify how many pencils measure exactly 5 3/4 inches From the data: 5 3/4 inches appears 3 times 3 × 5 3/4 = 3 × 23/4 = 69/4 69 ÷ 4 = 17 with remainder 1, so 69/4 = 17 1/4 The total length of all pencils measuring 5 3/4 inches is 17 1/4 inches.
   Full step-by-step solution

   Step 1: Identify how many pencils measure exactly 5 3/4 inches From the data: 5 3/4 inches appears 3 times Step 2: Multiply the number of pencils by their length 3 × 5 3/4 = 3 × 23/4 = 69/4 Step 3: Convert the improper fraction to a mixed number 69 ÷ 4 = 17 with remainder 1, so 69/4 = 17 1/4 Step 4: State the final answer The total length of all pencils measuring 5 3/4 inches is 17 1/4 inches.

2. A line plot shows the lengths of 5 ribbons in inches: 6 3/8, 6 7/16, 6 1/2, 6 11/16, 6 5/8. What is the difference between the longest and shortest ribbon? Answer: 5/16 Solution: Convert all measurements to sixteenths of an inch: 6 3/8 = 6 + 6/16 = 6 6/16 6 7/16 = 6 + 7/16 = 6 7/16 6 1/2 = 6 + 8/16 = 6 8/16 6 11/16 = 6 + 11/16 = 6 11/16 6 5/8 = 6 + 10/16 = 6 10/16 Longest: 6 11/16 Shortest: 6 6/16 (6 3/8) 6 11/16 - 6 6/16 = (11/16 - 6/16) = 5/16 Check if 5/16 can be…
   Full step-by-step solution

   Step 1: Convert all measurements to sixteenths of an inch: 6 3/8 = 6 + 6/16 = 6 6/16 6 7/16 = 6 + 7/16 = 6 7/16 6 1/2 = 6 + 8/16 = 6 8/16 6 11/16 = 6 + 11/16 = 6 11/16 6 5/8 = 6 + 10/16 = 6 10/16 Step 2: Identify the longest and shortest ribbons: Longest: 6 11/16 Shortest: 6 6/16 (6 3/8) Step 3: Find the difference: 6 11/16 - 6 6/16 = (11/16 - 6/16) = 5/16 Step 4: Check if 5/16 can be simplified. Since 5 and 16 share no common factors other than 1, the fraction is already in simplest form. The answer is 5/16 inch.

3. A line plot shows the lengths of 5 pencils in inches: 6 1/4, 6 5/8, 6 3/16, 6 11/16, 6 7/8. What is the difference between the longest and shortest pencil? Answer: 11/16 Solution: Convert all measurements to sixteenths of an inch: 6 1/4 = 6 + 4/16 = 6 4/16 6 5/8 = 6 + 10/16 = 6 10/16 6 3/16 = 6 + 3/16 = 6 3/16 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 3/16 6 14/16 - 6 3/16 = (14/16 - 3/16) = 11/16 Check if 11/16 can be…
   Full step-by-step solution

   Step 1: Convert all measurements to sixteenths of an inch: 6 1/4 = 6 + 4/16 = 6 4/16 6 5/8 = 6 + 10/16 = 6 10/16 6 3/16 = 6 + 3/16 = 6 3/16 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 pencils: Longest: 6 14/16 (6 7/8) Shortest: 6 3/16 Step 3: Find the difference: 6 14/16 - 6 3/16 = (14/16 - 3/16) = 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.

4. A line plot shows the lengths of 5 pencils in inches: 5 1/8, 5 3/16, 5 1/4, 5 7/16, 5 1/2. What is the difference between the longest and shortest pencil? Answer: 3/8 Solution: Convert all measurements to sixteenths to compare them. 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 1/2 = 5 + 8/16 = 5 8/16 Identify the longest and shortest pencils.
   Full step-by-step solution

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

5. Emma is tracking how much water her plants need each week. She recorded the amounts in cups on a line plot: 3/4, 1/2, 3/4, 1/4, 1/2, 3/4, 1/4, 1/2, 3/4, 1/4. What is the total amount of water recorded for all measurements? Answer: 5 1/4 Solution: - 1/4 cup: 3 measurements - 1/2 cup: 3 measurements - 3/4 cup: 4 measurements - 1/4 cup: 3 × 1/4 = 3/4 cup - 1/2 cup: 3 × 1/2 = 3/2 = 1 1/2 cups - 3/4 cup: 4 × 3/4 = 12/4 = 3 cups 3/4 + 1 1/2 + 3 = 3/4 + 6/4 + 12/4 = 21/4 = 5 1/4 cups The total amount of water recorded is 5 1/4 cups.
   Full step-by-step solution

   Step 1: Count how many of each measurement there are: - 1/4 cup: 3 measurements - 1/2 cup: 3 measurements - 3/4 cup: 4 measurements Step 2: Calculate the total for each measurement: - 1/4 cup: 3 × 1/4 = 3/4 cup - 1/2 cup: 3 × 1/2 = 3/2 = 1 1/2 cups - 3/4 cup: 4 × 3/4 = 12/4 = 3 cups Step 3: Add all the totals together: 3/4 + 1 1/2 + 3 = 3/4 + 6/4 + 12/4 = 21/4 = 5 1/4 cups The total amount of water recorded is 5 1/4 cups.

6. 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.

7. The line plot shows the lengths of 8 caterpillars measured in inches: 1 1/8, 1 3/16, 1 1/4, 1 5/16, 1 3/8, 1 1/2, 1 9/16, 1 5/8. What is the difference between the longest and shortest caterpillar? Answer: 1/2 Solution: Identify the longest and shortest caterpillars. The measurements are: 1 1/8, 1 3/16, 1 1/4, 1 5/16, 1 3/8, 1 1/2, 1 9/16, 1 5/8.
   Full step-by-step solution

   Step 1: Identify the longest and shortest caterpillars. The measurements are: 1 1/8, 1 3/16, 1 1/4, 1 5/16, 1 3/8, 1 1/2, 1 9/16, 1 5/8. Step 2: Convert all measurements to sixteenths for easy comparison: - 1 1/8 = 1 2/16 - 1 3/16 = 1 3/16 - 1 1/4 = 1 4/16 - 1 5/16 = 1 5/16 - 1 3/8 = 1 6/16 - 1 1/2 = 1 8/16 - 1 9/16 = 1 9/16 - 1 5/8 = 1 10/16 Step 3: The smallest measurement is 1 2/16 (1 1/8). The largest measurement is 1 10/16 (1 5/8). Step 4: Find the difference: 1 10/16 - 1 2/16 = 8/16 Step 5: Simplify 8/16 to 1/2. The answer is 1/2.

8. A line plot shows the lengths of 5 ribbons in inches: 6 1/8, 6 3/16, 6 5/8, 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: 6 1/8 = 6 + 2/16 = 6 2/16 6 3/16 = 6 + 3/16 = 6 3/16 6 5/8 = 6 + 10/16 = 6 10/16 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…
   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 3/16 = 6 + 3/16 = 6 3/16 6 5/8 = 6 + 10/16 = 6 10/16 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.

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

   Step 1: Convert all measurements to sixteenths for easy comparison: - 4 3/16 = 4 + 3/16 = 4 3/16 - 4 1/4 = 4 + 4/16 = 4 4/16 - 4 5/16 = 4 + 5/16 = 4 5/16 - 4 3/8 = 4 + 6/16 = 4 6/16 - 4 7/16 = 4 + 7/16 = 4 7/16 - 4 1/2 = 4 + 8/16 = 4 8/16 Step 2: Identify the longest and shortest bookmarks: Longest: 4 8/16 (4 1/2) Shortest: 4 3/16 Step 3: Find the difference: 4 8/16 - 4 3/16 = (8/16 - 3/16) = 5/16 The answer is 5/16.