To determine which expression for A makes the equation \( A = 5 - \frac{11}{3} \) true, we first need to calculate the right side of the equation.
First, we convert 5 into a fraction with a denominator of 3:
\[ 5 = \frac{15}{3} \]
Now we can compute \( 5 - \frac{11}{3} \):
\[ A = \frac{15}{3} - \frac{11}{3} = \frac{15 - 11}{3} = \frac{4}{3} \]
Now we can convert \( \frac{4}{3} \) to a mixed number or check the expressions provided:
- \( A = \frac{15}{3} + \frac{1}{3} = \frac{16}{3} \) (not equal to \( \frac{4}{3} \))
- \( A = 1 \frac{2}{3} + \frac{1}{3} = \frac{5}{3} \) (not equal to \( \frac{4}{3} \))
- \( A = 1 \frac{2}{3} - \frac{1}{3} = \frac{5}{3} - \frac{1}{3} = \frac{4}{3} \) (this is equal to \( \frac{4}{3} \))
- \( A = - 1 \frac{2}{3} + \frac{1}{3} = -\frac{5}{3} + \frac{1}{3} = -\frac{4}{3} \) (not equal to \( \frac{4}{3} \))
The only correct expression that makes the equation true is:
A = 1 \frac{2}{3} - \frac{1}{3}.