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

Question

$A=1\frac {2}{3}+\frac {1}{3}$
$A=1\frac {2}{3}-\frac {1}{3}$
$A=\frac {15}{3}+\frac {1}{3}$
$A=-1\frac {2}{3}+\frac {1}{3}$

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

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