Question

Which expression is A, in order to have a true equation $A=5-\frac {11}{3}$ ? (1 point)
$A=1\frac {2}{3}+\frac {1}{3}$
$A=1\frac {2}{3}-\frac {1}{3}$
$A=\frac {15}{3}+\frac {1}{3}$
$A=-1\frac {2}{3}+\frac {1}{3}$

Answer 1

To find the expression for \( A \) that makes the equation \( A = 5 - \frac{11}{3} \) true, we first need to simplify \( 5 - \frac{11}{3} \).

First, we express \( 5 \) as a fraction with a denominator of \( 3 \):

\[
5 = \frac{15}{3}
\]

Now we can rewrite our equation as follows:

\[
A = \frac{15}{3} - \frac{11}{3}
\]

Next, we perform the subtraction:

\[
A = \frac{15 - 11}{3} = \frac{4}{3}
\]

Now we have \( A = \frac{4}{3} \). To find which expression corresponds to \( A = \frac{4}{3} \), we can simplify the given options:

1. **Option 1:** \( A = 1\frac{2}{3} + \frac{1}{3} \)
- \( 1\frac{2}{3} = \frac{5}{3} \)
- \( \frac{5}{3} + \frac{1}{3} = \frac{5 + 1}{3} = \frac{6}{3} = 2 \)

2. **Option 2:** \( A = 1\frac{2}{3} - \frac{1}{3} \)
- \( 1\frac{2}{3} = \frac{5}{3} \)
- \( \frac{5}{3} - \frac{1}{3} = \frac{5 - 1}{3} = \frac{4}{3} \)

3. **Option 3:** \( A = \frac{15}{3} + \frac{1}{3} \)
- \( \frac{15}{3} + \frac{1}{3} = \frac{15 + 1}{3} = \frac{16}{3} \)

4. **Option 4:** \( A = -1\frac{2}{3} + \frac{1}{3} \)
- \( -1\frac{2}{3} = -\frac{5}{3} \)
- \( -\frac{5}{3} + \frac{1}{3} = -\frac{5 - 1}{3} = -\frac{4}{3} \)

Now we compare our calculated \( A = \frac{4}{3} \) with the evaluated options. The only option that gives \( A = \frac{4}{3} \) is:

\[
\text{Option 2: } A = 1\frac{2}{3} - \frac{1}{3}
\]

Thus, the answer is

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