To determine which expression for \( A \) makes the equation \( A = 5 - \frac{11}{3} \) true, we first need to simplify the right side of the equation.
Starting with \( 5 - \frac{11}{3} \):
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Convert \( 5 \) to a fraction with a denominator of 3: \[ 5 = \frac{15}{3} \]
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Subtract \( \frac{11}{3} \): \[ \frac{15}{3} - \frac{11}{3} = \frac{15 - 11}{3} = \frac{4}{3} \]
Now we have: \[ A = \frac{4}{3} \]
Next, let's evaluate each of the given expressions to see if any simplify to \( \frac{4}{3} \):
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\( A = -1 \frac{2}{3} + \frac{1}{3} \)
- Convert \( -1 \frac{2}{3} \) to an improper fraction: \[ -1 \frac{2}{3} = -\frac{5}{3} \]
- Now add: \[ -\frac{5}{3} + \frac{1}{3} = -\frac{5 - 1}{3} = -\frac{4}{3} \]
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\( A = 1 \frac{2}{3} - \frac{1}{3} \)
- Convert \( 1 \frac{2}{3} \): \[ 1 \frac{2}{3} = \frac{5}{3} \]
- Now subtract: \[ \frac{5}{3} - \frac{1}{3} = \frac{5 - 1}{3} = \frac{4}{3} \]
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\( A = \frac{15}{3} + 1/ \)
- This expression seems incomplete, but we can evaluate what's given: \[ A = \frac{15}{3} = 5 \]
- Assuming the \( +1/ \) was a typo or a misprint, we can't determine if it equals \( \frac{4}{3} \).
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\( A = 1 \frac{2}{3} + \frac{1}{3} \)
- Convert \( 1 \frac{2}{3} \): \[ 1 \frac{2}{3} = \frac{5}{3} \]
- Now add: \[ \frac{5}{3} + \frac{1}{3} = \frac{5 + 1}{3} = \frac{6}{3} = 2 \]
From the evaluations, the expression that gives \( A = \frac{4}{3} \) is:
\( A = 1 \frac{2}{3} - \frac{1}{3} \).