To find the fractions of the scarf each friend could have knit, we need to determine how the total length of the scarf (1512 yards) is divided among the five friends.
Since there are 5 friends, we can divide the total length by 5 to figure out how much each should ideally knit if the scarf is evenly distributed.
1512 yards divided by 5 equals 302.4 yards.
To represent the lengths knitted by each friend as fractions, we can express them as a portion of the total length. However, the given options present fractions that sum to 1 whole when combined, indicating how much of the scarf each contributed as a fraction.
Let’s evaluate the options:
-
Option 1: \( \frac{1}{12} + \frac{2}{12} + \frac{3}{12} + \frac{8}{12} + \frac{4}{12} \)
- This sums to \( \frac{1 + 2 + 3 + 8 + 4}{12} = \frac{18}{12} \) which is greater than 1.
-
Option 2: \( \frac{1}{12} + \frac{6}{12} + \frac{3}{12} + \frac{2}{12} + \frac{4}{12} \)
- This sums to \( \frac{1 + 6 + 3 + 2 + 4}{12} = \frac{16}{12} \) which is greater than 1.
-
Option 3: \( \frac{2}{12} + \frac{3}{12} + \frac{3}{12} + \frac{2}{12} + \frac{5}{12} \)
- This sums to \( \frac{2 + 3 + 3 + 2 + 5}{12} = \frac{15}{12} \) which is greater than 1.
-
Option 4: \( \frac{5}{12} + \frac{1}{12} + \frac{4}{12} + \frac{2}{12} + \frac{5}{12} \)
- This sums to \( \frac{5 + 1 + 4 + 2 + 5}{12} = \frac{17}{12} \) which is greater than 1.
None of the options provided lead to a sum of fractions that equals exactly 1. Thus, it seems like there is an inconsistency or error in the provided selections. Ideally, we would be looking for five fractions that, when added together, total 1.
If we divide the scarf equally, each friend would knit \( \frac{1}{5} \) of the scarf, or \( \frac{12}{60} \) which does not match any of the options given.
Please check the answer options again for correctness, as none are valid fractions that sum to 1.
1 answer