Question

Five friends each knit one part of a scarf that is 1 5/12
yards long.

Which shows the fractions of the scarf each friend could have knit?

(1 point)
Responses

1/12+2/12+3/12+8/12+4/12

1/12+6/12+3/12+2/12+4/12


2/12+3/12+3/12+2/12+5/12


5/12+1/12+4/12+2/12+5/12

Answer 1

To determine which response shows fractions that sum to the total length of the scarf (1 5/12 yards, or 1.41667 yards), we first need to convert that mixed number into an improper fraction.

1 5/12 as an improper fraction is calculated as follows:

1 * 12 + 5 = 12 + 5 = 17

So, 1 5/12 = 17/12.

Now, we need to check the sums of the fractions given in the responses.

1. **Response 1:**
\[
\frac{1}{12} + \frac{2}{12} + \frac{3}{12} + \frac{8}{12} + \frac{4}{12} = \frac{1 + 2 + 3 + 8 + 4}{12} = \frac{18}{12} = \frac{3}{2} \text{ (or 1.5, which is greater than } \frac{17}{12}\text{)}
\]

2. **Response 2:**
\[
\frac{1}{12} + \frac{6}{12} + \frac{3}{12} + \frac{2}{12} + \frac{4}{12} = \frac{1 + 6 + 3 + 2 + 4}{12} = \frac{16}{12} = \frac{4}{3} \text{ (or about 1.333, which is less than } \frac{17}{12}\text{)}
\]

3. **Response 3:**
\[
\frac{2}{12} + \frac{3}{12} + \frac{3}{12} + \frac{2}{12} + \frac{5}{12} = \frac{2 + 3 + 3 + 2 + 5}{12} = \frac{15}{12} = \frac{5}{4} \text{ (or 1.25, which is less than } \frac{17}{12}\text{)}
\]

4. **Response 4:**
\[
\frac{5}{12} + \frac{1}{12} + \frac{4}{12} + \frac{2}{12} + \frac{5}{12} = \frac{5 + 1 + 4 + 2 + 5}{12} = \frac{17}{12} \text{ (which is exactly } \frac{17}{12}\text{)}
\]

The response that shows the correct fractions summing to 1 5/12 (or 17/12) is **Response 4**:

\[
5/12 + 1/12 + 4/12 + 2/12 + 5/12
\]