To solve the equation \( A = 5 - \frac{11}{3} \), we first need to simplify the right-hand side.
Let's convert \( 5 \) into a fraction with a denominator of \( 3 \). We can do this as follows:
\[ 5 = \frac{15}{3} \]
Now, substituting that into the equation, we have:
\[ A = \frac{15}{3} - \frac{11}{3} \]
Now, we can subtract the fractions:
\[ A = \frac{15 - 11}{3} = \frac{4}{3} \]
So, \( A = \frac{4}{3} \).
Now, we need to find which of the given expressions equals \( \frac{4}{3} \).
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\( \frac{15}{3} + \frac{1}{3} \) \[ = \frac{15 + 1}{3} = \frac{16}{3} \quad \text{(not equal to \( \frac{4}{3} \))} \]
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\( 1 \frac{2}{3} + \frac{1}{3} \) \[ = \frac{3}{3} + \frac{2}{3} + \frac{1}{3} = \frac{3 + 2 + 1}{3} = \frac{6}{3} = 2 \quad \text{(not equal to \( \frac{4}{3} \))} \]
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\( -1 \frac{2}{3} + \frac{1}{3} \) \[ = -\frac{3}{3} - \frac{2}{3} + \frac{1}{3} = -\frac{3 + 2 - 1}{3} = -\frac{4}{3} \quad \text{(not equal to \( \frac{4}{3} \))} \]
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\( \frac{12}{3} - \frac{1}{3} \) \[ = \frac{12 - 1}{3} = \frac{11}{3} \quad \text{(not equal to \( \frac{4}{3} \))} \]
None of the above options actually equal \( \frac{4}{3} \), meaning the correct choice must be one that was not properly simplifiable, as the expressions provided seem not sufficient to meet the solution.
Upon reevaluation, the correct substitution to match with \( A = \frac{4}{3} \) should actually be made from proper compound numbers or different fractions. Among the responses, it appears clear that the only fitting choice might reflect the last preferred \( 1\frac{1}{3} = \frac{4}{3} \) in the forms unlisted.
Thus an adjustment or clarification on available options could be needed for confirmation.