Which expression is A, in order to have a true equation A=5−11/3 ?(1 point)

Question

Responses

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

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

A=15/3 + 1/3
Start Fraction 15 over 3 End Fraction plus Start Fraction 1 over 3 End Fraction

A=1 2/3 − 1/3

Answer 1

To determine which expression for \( A \) is true such that \( A = 5 - \frac{11}{3} \), we first need to calculate \( 5 - \frac{11}{3} \).

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

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

This gives us \( A = \frac{4}{3} \), which can also be expressed as \( 1\frac{1}{3} \).

Now let's analyze the provided expressions:

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

   • This equals \( \frac{5}{3} + \frac{1}{3} = \frac{6}{3} = 2\) (not equal to \( \frac{4}{3} \)).

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

   • This equals \( -\frac{5}{3} - \frac{1}{3} = -\frac{6}{3} = -2\) (not equal to \( \frac{4}{3} \)).

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

   • This equals \( -\frac{5}{3} + \frac{1}{3} = -\frac{4}{3}\) (not equal to \( \frac{4}{3} \)).

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

   • This equals \( \frac{15 + 1}{3} = \frac{16}{3} \) (not equal to \( \frac{4}{3} \)).

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

   • This equals \( \frac{5}{3} - \frac{1}{3} = \frac{4}{3} \) (this is equal to \( \frac{4}{3} \)).

Thus, the expression for \( A \) that satisfies \( A = 5 - \frac{11}{3} \) is:

\[ A = 1 \frac{2}{3} - \frac{1}{3} \]