To determine which expression for \( A \) will make the equation \( A = 5 - \frac{1}{13} \) true, let's first simplify the right side of the equation:
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Find a common denominator to subtract \( \frac{1}{13} \) from 5.
Rewrite 5 with a denominator of 13: \[ 5 = \frac{65}{13} \]
Now, substituting into the equation: \[ A = \frac{65}{13} - \frac{1}{13} = \frac{65 - 1}{13} = \frac{64}{13} \]
Now, we need to check which of the provided responses is equivalent to \( \frac{64}{13} \):
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A = -\frac{2}{3} + \frac{1}{3}: \[ A = -\frac{2}{3} + \frac{1}{3} = -\frac{1}{3} \text{ (not equal to } \frac{64}{13}) \]
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A = \frac{2}{3} - \frac{1}{3}: \[ A = \frac{2}{3} - \frac{1}{3} = \frac{1}{3} \text{ (not equal to } \frac{64}{13}) \]
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A = \frac{2}{3} + \frac{1}{3}: \[ A = \frac{2}{3} + \frac{1}{3} = 1 \text{ (not equal to } \frac{64}{13}) \]
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A = \frac{15}{3} + \frac{1}{3}: \[ A = \frac{15}{3} + \frac{1}{3} = 5 + \frac{1}{3} = \frac{15 + 1}{3} = \frac{16}{3} \text{ (not equal to } \frac{64}{13}) \]
None of the provided expressions match \( \frac{64}{13} \).
Please check the response options for correctness or provide a correct option if \( A = 5 - \frac{1}{13} \).