Which expression is A, in order to have a true equation A=5−113

?(1 point)
Responses

A=−12/3+13
negative 1 Start Fraction 2 over 3 End Fraction plus Start Fraction 1 over 3 End Fraction

A=12/3+13
negative 1 Start Fraction 2 over 3 End Fraction minus Start Fraction 1 over 3 End Fraction

A=12/3−13
1 Start Fraction 2 over 3 End Fraction minus Start Fraction 1 over 3 End Fraction

A=15/3+13

1 answer

To find which expression for \( A \) makes the equation \( A = 5 - 1 \frac{1}{3} \) true, we first need to simplify the right side of the equation.

  1. Convert \( 1 \frac{1}{3} \) to an improper fraction: \[ 1 \frac{1}{3} = \frac{4}{3} \]

  2. Substitute this back into the equation: \[ A = 5 - \frac{4}{3} \]

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

  4. Now, subtract \( \frac{4}{3} \) from \( \frac{15}{3} \): \[ A = \frac{15}{3} - \frac{4}{3} = \frac{15 - 4}{3} = \frac{11}{3} \]

Now we must evaluate the given responses to find which one equals \( \frac{11}{3} \).

  1. \( A = -\frac{12}{3} + \frac{1}{3} \) \[ = -4 + \frac{1}{3} = -4 + 0.33 \approx -3.67 \quad (\text{not } \frac{11}{3}) \]

  2. \( A = \frac{12}{3} + \frac{1}{3} \) \[ = 4 + \frac{1}{3} = 4.33 \quad (\text{not } \frac{11}{3}) \]

  3. \( A = \frac{12}{3} - \frac{1}{3} \) \[ = 4 - \frac{1}{3} = 4 - 0.33 \approx 3.67 \quad (\text{not } \frac{11}{3}) \]

  4. \( A = \frac{15}{3} + \frac{1}{3} \) \[ = 5 + \frac{1}{3} = 5.33 \quad (\text{not } \frac{11}{3}) \]

None of the provided option values equal \( \frac{11}{3} \).

However, based on calculations, the correct lineup or choices might not be reflected in the responses you provided. Can you please verify the options again, or provide any additional information?