To solve the expression \( 12 \frac{8}{15} - 7 + \frac{7}{15} + 15 \), we first convert the mixed number \( 12 \frac{8}{15} \) into an improper fraction.
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Convert \( 12 \frac{8}{15} \): \[ 12 \frac{8}{15} = \frac{12 \times 15 + 8}{15} = \frac{180 + 8}{15} = \frac{188}{15} \]
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Rewrite the entire expression: \[ \frac{188}{15} - 7 + \frac{7}{15} + 15 \]
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Convert the whole numbers 7 and 15 into fractions with a denominator of 15: \[ 7 = \frac{7 \times 15}{15} = \frac{105}{15} \] \[ 15 = \frac{15 \times 15}{15} = \frac{225}{15} \]
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Now, substitute these back into the expression: \[ \frac{188}{15} - \frac{105}{15} + \frac{7}{15} + \frac{225}{15} \]
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Combine the fractions: \[ \frac{188 - 105 + 7 + 225}{15} \]
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Calculate the numerator: \[ 188 - 105 = 83 \] \[ 83 + 7 = 90 \] \[ 90 + 225 = 315 \] So the numerator is 315.
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This gives: \[ \frac{315}{15} \]
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Simplify the fraction: \[ \frac{315}{15} = 21 \]
Thus, the final answer is: \[ \boxed{21} \]