Question

Which expression is A, in order to have a true equation A=5−113
?(1 point)
Responses

A=−123+13
negative 1 Start Fraction 2 over 3 End Fraction plus Start Fraction 1 over 3 End Fraction

A=123−13
1 Start Fraction 2 over 3 End Fraction minus Start Fraction 1 over 3 End Fraction

A=123+13
negative 1 Start Fraction 2 over 3 End Fraction minus Start Fraction 1 over 3 End Fraction

A=153+13

Answer 1

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

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

Calculating:

- Find a common denominator (6):

\[
-\frac{1}{2} = -\frac{3}{6}, \quad \frac{1}{3} = \frac{2}{6}
\]

So:

\[
-\frac{3}{6} + \frac{2}{6} = -\frac{1}{6} \quad (\text{Not equal to } \frac{4}{3})
\]

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

Calculating:

- Again finding a common denominator (6):

\[
\frac{1}{2} = \frac{3}{6}, \quad -\frac{1}{3} = -\frac{2}{6}
\]

So:

\[
\frac{3}{6} - \frac{2}{6} = \frac{1}{6} \quad (\text{Not equal to } \frac{4}{3})
\]

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

Calculating:

\[
\frac{1}{2} = \frac{3}{6}, \quad \frac{1}{3} = \frac{2}{6}
\]

So:

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

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

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.