To find the expression for \( A \) such that it satisfies the equation \( A = 5 - \frac{11}{3} \), we first need to simplify the right-hand side.
Starting with the calculation:
\[ 5 - \frac{11}{3} \]
First, we express 5 as a fraction with a denominator of 3:
\[ 5 = \frac{15}{3} \]
Now we can rewrite the equation:
\[ A = \frac{15}{3} - \frac{11}{3} \]
Next, subtract the fractions:
\[ A = \frac{15 - 11}{3} = \frac{4}{3} \]
So, \( A = \frac{4}{3} \).
Next, we evaluate each of the provided expressions to see which one equals \( \frac{4}{3} \).
- \( A = 1\frac{2}{3} + \frac{1}{3} \)
Convert \( 1\frac{2}{3} \) to an improper fraction:
\[ 1\frac{2}{3} = \frac{3 \cdot 1 + 2}{3} = \frac{5}{3} \]
Now calculate:
\[ A = \frac{5}{3} + \frac{1}{3} = \frac{6}{3} = 2 \quad (\text{not equal to } \frac{4}{3}) \]
- \( A = 1\frac{2}{3} - \frac{1}{3} \)
Using \( 1\frac{2}{3} = \frac{5}{3} \):
\[ A = \frac{5}{3} - \frac{1}{3} = \frac{4}{3} \quad (\text{this equals } \frac{4}{3}) \]
- \( A = \frac{15}{3} + \frac{1}{3} \)
Calculate:
\[ A = \frac{15}{3} + \frac{1}{3} = \frac{16}{3} \quad (\text{not equal to } \frac{4}{3}) \]
- \( A = -1\frac{2}{3} + \frac{1}{3} \)
Convert \( -1\frac{2}{3} \) to an improper fraction:
\[ -1\frac{2}{3} = -\frac{3 \cdot 1 + 2}{3} = -\frac{5}{3} \]
Now calculate:
\[ A = -\frac{5}{3} + \frac{1}{3} = -\frac{5}{3} + \frac{1}{3} = -\frac{4}{3} \quad (\text{not equal to } \frac{4}{3}) \]
The only expression that equals \( \frac{4}{3} \) is:
\[ A = 1\frac{2}{3} - \frac{1}{3} \]
Thus, the correct answer is:
\[ \boxed{1\frac{2}{3} - \frac{1}{3}} \]