To find an expression for \( A \) that makes the equation \( A = 5 - \frac{11}{3} \) true, we first calculate \( 5 - \frac{11}{3} \).
First, convert 5 into a fraction with a denominator of 3: \[ 5 = \frac{15}{3} \]
Now replace 5 in the equation: \[ A = \frac{15}{3} - \frac{11}{3} \]
Now we can combine the fractions: \[ A = \frac{15 - 11}{3} = \frac{4}{3} \]
Now we check which of the given responses can be simplified or calculated to equal \( \frac{4}{3} \).
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\( A = 1 \frac{2}{3} + \frac{1}{3} \):
Convert \( 1 \frac{2}{3} \) to an improper fraction:
\( 1 \frac{2}{3} = \frac{5}{3} \)
Adding:
\[ \frac{5}{3} + \frac{1}{3} = \frac{6}{3} = 2 \quad \text{(not equal to } \frac{4}{3}\text{)} \] -
\( A = -\frac{2}{3} - \frac{1}{3} \):
Adding:
\[ -\frac{2}{3} - \frac{1}{3} = -\frac{3}{3} = -1 \quad \text{(not equal to } \frac{4}{3}\text{)} \] -
\( A = -\frac{1}{2} + \frac{1}{3} \):
Convert \( -\frac{1}{2} \) to have a common denominator of 6:
\[ -\frac{1}{2} = -\frac{3}{6}, \quad \frac{1}{3} = \frac{2}{6} \] Adding:
\[ -\frac{3}{6} + \frac{2}{6} = -\frac{1}{6} \quad \text{(not equal to } \frac{4}{3}\text{)} \] -
\( A = \frac{15}{3} + \frac{1}{3} \):
Adding:
\[ \frac{15}{3} + \frac{1}{3} = \frac{16}{3} \quad \text{(not equal to } \frac{4}{3}\text{)} \] -
\( A = \frac{2}{3} - \frac{1}{3} \):
Subtracting:
\[ \frac{2}{3} - \frac{1}{3} = \frac{1}{3} \quad \text{(not equal to } \frac{4}{3}\text{)} \]
None of the given options equal \( \frac{4}{3} \). Since we've not successfully matched an expression, I will confirm the calculations are done correctly:
From \( A = 5 - \frac{11}{3} \), we calculated: \[ A = \frac{15}{3} - \frac{11}{3} = \frac{4}{3} \]
Among the options listed, it appears none of them yields \( \frac{4}{3} \). Please double-check the question or options for possible errors or omissions.