To find the expression A that satisfies the equation \( A = 5 - \frac{11}{3} \), let's first simplify the right-hand side of the equation.
First, convert 5 to a fraction with a denominator of 3:
\[ 5 = \frac{15}{3} \]
Now we can rewrite the equation:
\[ A = \frac{15}{3} - \frac{11}{3} \]
Subtract the fractions:
\[ A = \frac{15 - 11}{3} = \frac{4}{3} \]
Now let's check the options to see which one is equal to \( \frac{4}{3} \):
- \( A = -\frac{1}{2} + \frac{1}{3} \)
Calculating:
- Find a common denominator (6):
\[ -\frac{1}{2} = -\frac{3}{6}, \quad \frac{1}{3} = \frac{2}{6} \]
So:
\[ -\frac{3}{6} + \frac{2}{6} = -\frac{1}{6} \quad (\text{Not equal to } \frac{4}{3}) \]
- \( A = \frac{1}{2} - \frac{1}{3} \)
Calculating:
- Again finding a common denominator (6):
\[ \frac{1}{2} = \frac{3}{6}, \quad -\frac{1}{3} = -\frac{2}{6} \]
So:
\[ \frac{3}{6} - \frac{2}{6} = \frac{1}{6} \quad (\text{Not equal to } \frac{4}{3}) \]
- \( A = \frac{1}{2} + \frac{1}{3} \)
Calculating:
\[ \frac{1}{2} = \frac{3}{6}, \quad \frac{1}{3} = \frac{2}{6} \]
So:
\[ \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \quad (\text{Not equal to } \frac{4}{3}) \]
- \( A = \frac{15}{3} + \frac{1}{3} \)
Calculating:
\[ \frac{15}{3} = 5, \quad \frac{1}{3} \text{ stays the same} \]
So:
\[ 5 + \frac{1}{3} = \frac{15}{3} + \frac{1}{3} = \frac{16}{3} \quad (\text{Not equal to } \frac{4}{3}) \]
None of the provided responses equal \( \frac{4}{3} \). Please double-check the original values or provide new options.