To determine which expression for \( A \) makes the equation \( A = 5 - \frac{1}{13} \) true, we first need to simplify the right side of the equation:
- Calculate \( 5 - \frac{1}{13} \):
- First, convert \( 5 \) to a fraction with a denominator of \( 13 \): \[ 5 = \frac{65}{13} \]
- Now, subtract \( \frac{1}{13} \) from \( \frac{65}{13} \): \[ \frac{65}{13} - \frac{1}{13} = \frac{65 - 1}{13} = \frac{64}{13} \]
So, \( A = \frac{64}{13} \).
Now, let's evaluate the given expressions one by one to see which equals \( A \):
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\( A = -\frac{2}{3} + \frac{1}{3} \): \[ -\frac{2}{3} + \frac{1}{3} = -\frac{2 - 1}{3} = -\frac{1}{3} \quad \text{(NOT equal to } \frac{64}{13}) \]
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\( A = \frac{2}{3} - \frac{1}{3} \): \[ \frac{2}{3} - \frac{1}{3} = \frac{2 - 1}{3} = \frac{1}{3} \quad \text{(NOT equal to } \frac{64}{13}) \]
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\( A = \frac{2}{3} + \frac{1}{3} \): \[ \frac{2}{3} + \frac{1}{3} = \frac{2 + 1}{3} = \frac{3}{3} = 1 \quad \text{(NOT equal to } \frac{64}{13}) \]
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\( A = \frac{15}{3} + \frac{1}{3} \): \[ \frac{15}{3} + \frac{1}{3} = 5 + \frac{1}{3} = \frac{15 + 1}{3} = \frac{16}{3} \quad \text{(NOT equal to } \frac{64}{13}) \]
None of the provided expressions evaluate to \( \frac{64}{13} \). It appears there has been a misunderstanding since none of the responses given are equal to \( A \) based on the calculated value.
If more expressions were provided, we could check those as well. However, from the roles presented, none satisfy \( A = \frac{64}{13} \).