Which expression is A, in order to have a true equation $A=5-\frac {11}{3}$ ? (1 pc

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 \( \frac{4}{3} \).

1. \( A = 1\frac{2}{3} + \frac{1}{3} \)

Convert \( 1\frac{2}{3} \) to an improper fraction:

\[
1\frac{2}{3} = \frac{3 \cdot 1 + 2}{3} = \frac{5}{3}
\]

Now calculate:

\[
A = \frac{5}{3} + \frac{1}{3} = \frac{6}{3} = 2 \quad (\text{not equal to } \frac{4}{3})
\]

2. \( A = 1\frac{2}{3} - \frac{1}{3} \)

Using \( 1\frac{2}{3} = \frac{5}{3} \):

\[
A = \frac{5}{3} - \frac{1}{3} = \frac{4}{3} \quad (\text{this equals } \frac{4}{3})
\]

3. \( A = \frac{15}{3} + \frac{1}{3} \)

Calculate:

\[
A = \frac{15}{3} + \frac{1}{3} = \frac{16}{3} \quad (\text{not equal to } \frac{4}{3})
\]

4. \( A = -1\frac{2}{3} + \frac{1}{3} \)

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:

\[
\boxed{1\frac{2}{3} - \frac{1}{3}}
\]