Line Plots with Fractions

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Answer Key & Explanations

Line Plots with Fractions · Grade 4 · Worksheet 2

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

   Step 1: List all the ribbon lengths: 1/2, 3/8, 1/4, 3/8, 1/2, 5/8, 1/4 Step 2: Count how many times 1/2 appears: It appears in positions 1 and 5, so 2 times Step 3: Count how many times 3/8 appears: It appears in positions 2 and 4, so 2 times Step 4: Count how many times 1/4 appears: It appears in positions 3 and 7, so 2 times Step 5: Count how many times 5/8 appears: It appears in position 6, so 1 time Step 6: Compare the counts: 1/2, 3/8, and 1/4 all appear 2 times, which is more than 5/8 (1 time) Step 7: Since 1/2 appears first in the data set, it is considered the most common length The fraction that appears most often is 1/2.

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

   Step 1: List all the ribbon lengths: 1/8, 1/4, 3/8, 1/2, 1/4, 5/8, 1/4 Step 2: Count how many times 1/8 appears: It appears once (position 1) Step 3: Count how many times 1/4 appears: It appears three times (positions 2, 5, and 7) Step 4: Count how many times 3/8 appears: It appears once (position 3) Step 5: Count how many times 1/2 appears: It appears once (position 4) Step 6: Count how many times 5/8 appears: It appears once (position 6) Step 7: Compare the counts: 1/4 appears 3 times, which is more than any other fraction Step 8: The fraction that appears most often is 1/4.

3. A line plot shows the weights of 7 packages: 1/2, 3/4, 1/4, 1/2, 3/4, 1/2, 1/4. What is the most common weight? Answer: 1/2 Solution: List all the package weights: 1/2, 3/4, 1/4, 1/2, 3/4, 1/2, 1/4 Count how many times 1/2 appears: It appears in positions 1, 4, and 6, so 3 times Count how many times 3/4 appears: It appears in positions 2 and 5, so 2 times Count how many times 1/4 appears: It appears in positions 3 and 7, so 2…
   Full step-by-step solution

   Step 1: List all the package weights: 1/2, 3/4, 1/4, 1/2, 3/4, 1/2, 1/4 Step 2: Count how many times 1/2 appears: It appears in positions 1, 4, and 6, so 3 times Step 3: Count how many times 3/4 appears: It appears in positions 2 and 5, so 2 times Step 4: Count how many times 1/4 appears: It appears in positions 3 and 7, so 2 times Step 5: Compare the counts: 1/2 appears 3 times, which is more than 3/4 (2 times) and 1/4 (2 times) The most common weight is 1/2.

4. A rectangular garden is divided into 12 equal sections. The gardener plants beans in 4 sections, corn in 5 sections, and squash in the remaining sections. Create a line plot to represent this data where each X represents one section. How many sections have squash? Answer: 3 Solution: The garden has 12 equal sections total. Beans are planted in 4 sections. Corn is planted in 5 sections.
   Full step-by-step solution

   Step 1: The garden has 12 equal sections total. Step 2: Beans are planted in 4 sections. Step 3: Corn is planted in 5 sections. Step 4: Add the bean and corn sections: 4 + 5 = 9 sections. Step 5: Subtract from the total to find squash sections: 12 - 9 = 3 sections. The answer is 3.

5. Ava is helping her science class collect data on the lengths of 10 different leaves from a maple tree. She measures each leaf to the nearest eighth of an inch and records the lengths on a line plot. The lengths are: 3 1/8 in, 3 1/2 in, 3 3/8 in, 3 1/8 in, 3 5/8 in, 3 1/2 in, 3 1/8 in, 3 3/8 in, 3 1/2 in, and 3 1/8 in. Which leaf length appears most often on Ava's line plot? Answer: 3 1/8 inches Solution: List all the leaf lengths: 3 1/8, 3 1/2, 3 3/8, 3 1/8, 3 5/8, 3 1/2, 3 1/8, 3 3/8, 3 1/2, 3 1/8.
   Full step-by-step solution

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

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

   Step 1: List all the ribbon lengths: 1/8, 1/4, 3/8, 1/2, 1/8, 1/4, 3/8 Step 2: Count how many times 1/8 appears: It appears in positions 1 and 5, so 2 times Step 3: Count how many times 1/4 appears: It appears in positions 2 and 6, so 2 times Step 4: Count how many times 3/8 appears: It appears in positions 3 and 7, so 2 times Step 5: Count how many times 1/2 appears: It appears in position 4, so 1 time Step 6: Compare the counts: 1/8, 1/4, and 3/8 all appear 2 times, which is more than 1/2 (1 time) Step 7: Since 1/8 appears first in the data set, it is considered the most common length The most common ribbon length is 1/8.

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

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

8. A rectangular classroom floor is covered with square tiles. The floor is 12 tiles long and 9 tiles wide. If 1/4 of the tiles are blue, 1/3 are green, and the rest are yellow, create a line plot to represent the fraction of each color tile. What fraction of the tiles are yellow? Answer: 5/12 Solution: Find the total number of tiles. The floor is 12 tiles by 9 tiles, so total tiles = 12 × 9 = 108 tiles. Find how many tiles are blue.
   Full step-by-step solution

   Step 1: Find the total number of tiles. The floor is 12 tiles by 9 tiles, so total tiles = 12 × 9 = 108 tiles. Step 2: Find how many tiles are blue. Blue tiles = 1/4 of 108 = 108 ÷ 4 = 27 tiles. Step 3: Find how many tiles are green. Green tiles = 1/3 of 108 = 108 ÷ 3 = 36 tiles. Step 4: Find how many tiles are yellow. Yellow tiles = total tiles - blue tiles - green tiles = 108 - 27 - 36 = 45 tiles. Step 5: Find the fraction of yellow tiles. Fraction = yellow tiles ÷ total tiles = 45/108. Step 6: Simplify the fraction. Both 45 and 108 can be divided by 9: 45 ÷ 9 = 5, 108 ÷ 9 = 12, so 45/108 = 5/12. The answer is 5/12.