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.
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Convert \( 1 \frac{1}{3} \) to an improper fraction: \[ 1 \frac{1}{3} = \frac{4}{3} \]
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Substitute this back into the equation: \[ A = 5 - \frac{4}{3} \]
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Convert 5 into a fraction with a common denominator of 3: \[ 5 = \frac{15}{3} \]
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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 \( \frac{11}{3} \).
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\( A = -\frac{12}{3} + \frac{1}{3} \) \[ = -4 + \frac{1}{3} = -4 + 0.33 \approx -3.67 \quad (\text{not } \frac{11}{3}) \]
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\( A = \frac{12}{3} + \frac{1}{3} \) \[ = 4 + \frac{1}{3} = 4.33 \quad (\text{not } \frac{11}{3}) \]
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\( A = \frac{12}{3} - \frac{1}{3} \) \[ = 4 - \frac{1}{3} = 4 - 0.33 \approx 3.67 \quad (\text{not } \frac{11}{3}) \]
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\( A = \frac{15}{3} + \frac{1}{3} \) \[ = 5 + \frac{1}{3} = 5.33 \quad (\text{not } \frac{11}{3}) \]
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?