Question

claire had $5\frac{1}{7}$ feet of string. she used some string to hang party decorations. now she has $1\frac{5}{7}$ feet of string left.
part a
choose the model that shows how much string claire used.
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$$\begin{array}{c}\ \\text{ }5\\frac{1}{7}\\text{ feet }\\\ \\boxed{n}\\quad\\boxed{1\\frac{5}{7}}\\\ \\end{array}$$

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$$\begin{array}{c}\ \\text{ }1\\frac{5}{7}\\text{ feet }\\\ \\boxed{5\\frac{1}{7}}\\quad\\boxed{n}\\\ \\end{array}$$

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$$\begin{array}{c}\ \\text{ }n\\text{ feet }\\\ \\boxed{5\\frac{1}{7}}\\quad\\boxed{1\\frac{5}{7}}\\\ \\end{array}$$

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$$\begin{array}{c}\ \\text{ }n\\text{ feet }\\\ \\boxed{\\frac{51}{7}}\\quad\\boxed{\\frac{15}{7}}\\\ \\end{array}$$

Explanation:

To determine the correct model, we analyze the relationship between the total string, the used string, and the remaining string. The total string Claire had is \( 5\frac{1}{7} \) feet, the remaining string is \( 1\frac{5}{7} \) feet, and the used string is \( n \). The correct model should represent the total as the sum of the used (\( n \)) and the remaining (\( 1\frac{5}{7} \)). So the first model, with \( 5\frac{1}{7} \) as the total, \( n \) as used, and \( 1\frac{5}{7} \) as remaining, is correct. The other models incorrectly represent the total or the parts (e.g., the second model has the remaining as total, the third and fourth misalign the total - part relationship).

Answer:

The first option (the model with \( 5\frac{1}{7} \) feet as the total, \( n \) in one box, and \( 1\frac{5}{7} \) in the other box)