To find the value of \( A \) that makes the equation \( A = 5 - \frac{11}{3} \) true, we first need to calculate the right side.
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Convert 5 to a fraction with a denominator of 3: \[ 5 = \frac{15}{3} \]
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Substitute this into the equation: \[ A = \frac{15}{3} - \frac{11}{3} \]
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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 \( \frac{4}{3} \):
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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).
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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).
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Response C: \( \frac{15}{3} + \frac{1}{3} \):
- Calculate: \[ \frac{15}{3} + \frac{1}{3} = \frac{16}{3} ) (not equal).
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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: \( A = 1\frac{2}{3} - \frac{1}{3} \).