Question

Which expression is A, in order to have a true equation A=5-\frac{11}{3}?(1 point) Responses A=1\frac{2}{3}+\frac{1}{3} negative 1 Start Fraction 2 over 3 End Fraction minus Start Fraction 1 over 3 End Fraction A=1\frac{2}{3}-\frac{1}{3} 1 Start Fraction 2 over 3 End Fraction minus Start Fraction 1 over 3 End Fraction A=\frac{15}{3}+\frac{1}{3} Start Fraction 15 over 3 End Fraction plus Start Fraction 1 over 3 End Fraction A=-1\frac{2}{3}+\frac{1}{3}

Answer 1

To find the value of \( A \) that makes the equation \( A = 5 - \frac{11}{3} \) true, we first need to calculate the right side.

1. Convert 5 to a fraction with a denominator of 3:
\[
5 = \frac{15}{3}
\]

2. Substitute this into the equation:
\[
A = \frac{15}{3} - \frac{11}{3}
\]

3. Combine the fractions:
\[
A = \frac{15 - 11}{3} = \frac{4}{3}
\]

Next, we can analyze each of the responses provided to see which one equals \( \frac{4}{3} \):

1. **Response A: \( 1\frac{2}{3} + \frac{1}{3} \)**:
- Convert \( 1\frac{2}{3} \) into an improper fraction:
\[
1\frac{2}{3} = \frac{5}{3}
\]
- Now add \( \frac{5}{3} + \frac{1}{3} = \frac{6}{3} = 2 \) (not equal).

2. **Response B: \( 1\frac{2}{3} - \frac{1}{3} \)**:
- Convert \( 1\frac{2}{3} \):
\[
1\frac{2}{3} = \frac{5}{3}
\]
- Now subtract \( \frac{5}{3} - \frac{1}{3} = \frac{4}{3} \) (equal).

3. **Response C: \( \frac{15}{3} + \frac{1}{3} \)**:
- Calculate:
\[
\frac{15}{3} + \frac{1}{3} = \frac{16}{3} \) (not equal).

4. **Response D: \( -1\frac{2}{3} + \frac{1}{3} \)**:
- Convert \( -1\frac{2}{3} \):
\[
-1\frac{2}{3} = -\frac{5}{3}
\]
- Now add:
\[
-\frac{5}{3} + \frac{1}{3} = -\frac{4}{3} \) (not equal).

Thus, the correct response that makes \( A = 5 - \frac{11}{3} \) true is:

**Response B: \( A = 1\frac{2}{3} - \frac{1}{3} \)**.