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