Line Plots with Fractions

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Answer Key & Explanations

Line Plots with Fractions · Grade 4 · Worksheet 3

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

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

2. A line plot shows the lengths of 7 pencils: 1/4, 1/2, 3/4, 1/2, 1/4, 1/2, 3/4. What is the most common pencil length? Answer: 1/2 Solution: List all the pencil lengths: 1/4, 1/2, 3/4, 1/2, 1/4, 1/2, 3/4 Count how many times 1/4 appears: It appears in positions 1 and 5, so 2 times Count how many times 1/2 appears: It appears in positions 2, 4, and 6, so 3 times Count how many times 3/4 appears: It appears in positions 3 and 7, so 2…
   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 Step 2: Count how many times 1/4 appears: It appears in positions 1 and 5, so 2 times Step 3: Count how many times 1/2 appears: It appears in positions 2, 4, and 6, so 3 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 3 times, which is more than 1/4 (2 times) and 3/4 (2 times) The most common pencil length is 1/2.

3. A rectangular field measures 150 meters long and 80 meters wide. A farmer plants corn in rows that run the full length of the field, with each row spaced 2 meters apart. How many complete rows of corn can the farmer plant across the width of the field? Answer: 40 Solution: The field width is 80 meters. Rows are spaced 2 meters apart. To find how many rows fit, divide the total width by the spacing: 80 ÷ 2 = 40.
   Full step-by-step solution

   Step 1: The field width is 80 meters. Step 2: Rows are spaced 2 meters apart. Step 3: To find how many rows fit, divide the total width by the spacing: 80 ÷ 2 = 40. Step 4: Since the rows run the full length, we can plant 40 complete rows. The answer is 40.

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

   Step 1: List all the ribbon lengths: 1/4, 1/2, 3/4, 1/4, 1/2, 3/4, 1/2, 3/4 Step 2: Count how many times 1/4 appears: It appears in positions 1 and 4, so 2 times Step 3: Count how many times 1/2 appears: It appears in positions 2, 5, and 7, so 3 times Step 4: Count how many times 3/4 appears: It appears in positions 3, 6, and 8, so 3 times Step 5: Compare the counts: Both 1/2 and 3/4 appear 3 times, which is more than 1/4 Step 6: Since both have equal frequency, we look at which fraction appears later in the data set. 3/4 appears at position 8, while 1/2 appears at position 7. Therefore, 3/4 appears more frequently in the later positions. The fraction that appears most often is 3/4.

5. A farmer plants corn in a rectangular field that measures 125 meters long and 80 meters wide. She plants 4 rows of corn along the length and 3 rows along the width. What is the total number of corn plants if each plant is spaced equally in this grid pattern? Answer: 12 Solution: The field is 125 m long and 80 m wide. - 4 rows along the length means there are 4 rows running parallel to the width. - 3 rows along the width means there are 3 rows running parallel to the length.
   Full step-by-step solution

   Let's go step-by-step. --- **Step 1: Understand the problem** The field is 125 m long and 80 m wide. Corn is planted in a grid: - 4 rows along the length means there are 4 rows running parallel to the width. - 3 rows along the width means there are 3 rows running parallel to the length. --- **Step 2: Interpret the grid arrangement** "4 rows along the length" means if you stand along the length, you see 4 rows of corn plants in the width direction. Similarly, "3 rows along the width" means if you stand along the width, you see 3 rows of corn plants in the length direction. This means the corn plants are arranged in a grid with: - Number of rows in the length direction = 3 - Number of rows in the width direction = 4 --- **Step 3: Find total number of plants** The plants are at the intersections of these rows. So it's like a grid with 3 rows along length × 4 rows along width. Number of plants = (rows along length) × (rows along width) = 3 × 4 = 12 --- **Step 4: Verify reasoning** The field dimensions (125 m and 80 m) are not needed for the total number of plants here because the problem already gives the number of rows in each direction directly. The spacing is equal, so the plants are at the intersections of these perpendicular rows. --- **Final Answer:** 12