To determine which of the responses correctly shows the fractions of the scarf that each of the five friends could have knit, we need to consider that the total length of the scarf is 1512 yards and it is divided among five friends.
When each friend knits a portion of the scarf, the sum of the fractions representing what each friend knit should equal 1 (or 12/12) because they collectively knit the entire scarf.
Now, let's evaluate each response to see if their fractions sum to 12/12:
-
112 + 212 + 312 + 812 + 412
- Convert to a common denominator (assuming common denominator of 12):
- \(1/12 + 2/12 + 3/12 + 8/12 + 4/12 = (1 + 2 + 3 + 8 + 4)/12 = 18/12\) (which does not equal 12/12)
-
1/12 + 2/12 + 3/12 + 8/12 + 4/12
- Same calculation as above:
- \(1/12 + 2/12 + 3/12 + 8/12 + 4/12 = 18/12\) (which does not equal 12/12)
-
212 + 312 + 312 + 212 + 512
- Convert to common denominator:
- \(2/12 + 3/12 + 3/12 + 2/12 + 5/12 = (2 + 3 + 3 + 2 + 5)/12 = 15/12\) (which does not equal 12/12)
-
512 + 112 + 412 + 212 + 512
- Convert to common denominator:
- \(5/12 + 1/12 + 4/12 + 2/12 + 5/12 = (5 + 1 + 4 + 2 + 5)/12 = 17/12\) (which does not equal 12/12)
None of the options provided correctly sum to equal 1 (12/12).
If we assume that there might be an error in the options, we typically would aim for fractions that simplify altogether into 12/12.
For five friends, a reasonable distribution could be something like 1/12, 2/12, 2/12, 3/12, 4/12 (or other combinations that equal 12/12). Could you please confirm if there's a specific set of numbers in mind?