To determine which expression for \( A \) would make the equation \( A = 5 - \frac{1}{13} \) true, we first need to evaluate \( 5 - \frac{1}{13} \).
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Convert 5 to a fraction with a denominator of 13: \[ 5 = \frac{65}{13} \]
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Now perform the subtraction: \[ A = \frac{65}{13} - \frac{1}{13} = \frac{65 - 1}{13} = \frac{64}{13} \]
Now, let's evaluate each of the given expressions to see which one equals \( \frac{64}{13} \).
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For \( A = \frac{15}{3} + \frac{1}{3} \): \[ A = 5 + \frac{1}{3} = 5 + 0.333 \approx 5.333 \text{(not correct)} \]
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For \( A = -\frac{2}{3} - \frac{1}{3} \): \[ A = -\frac{2}{3} - \frac{1}{3} = -1 \text{(not correct)} \]
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For \( A = -\frac{2}{3} + \frac{1}{3} \): \[ A = -\frac{2}{3} + \frac{1}{3} = -\frac{1}{3} \text{(not correct)} \]
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For \( A = \frac{12}{3} - \frac{1}{3} \): \[ A = 4 - \frac{1}{3} = \frac{12}{3} - \frac{1}{3} = \frac{12 - 1}{3} = \frac{11}{3} \text{(not correct)} \]
It seems that none of the answer choices gives the value \( \frac{64}{13} \).
Hence, there may be an error in the provided answers, or \( A = 5 - \frac{1}{13} \) could have been intended to be matched with a different representation not listed.
Based on current analysis:
- None of the expressions provided match \( A = \frac{64}{13} \).
If you have any specific choices that might be rewritten or clarified, please let me know for further analysis!