To solve the expression \( 12 \frac{8}{15} - 7 + \frac{7}{15} + 15 \), we can follow these steps:
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Convert the mixed number to an improper fraction: \[ 12 \frac{8}{15} = \frac{12 \times 15 + 8}{15} = \frac{180 + 8}{15} = \frac{188}{15} \]
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Convert the whole numbers to fractions with a common denominator: \( 7 \) and \( 15 \) can be expressed as: \[ 7 = \frac{7 \times 15}{15} = \frac{105}{15} \] \[ 15 = \frac{15 \times 15}{15} = \frac{225}{15} \]
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Now rewrite the expression with fractions: \[ \frac{188}{15} - \frac{105}{15} + \frac{7}{15} + \frac{225}{15} \]
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Combine the fractions: \[ \frac{188 - 105 + 7 + 225}{15} = \frac{188 - 105 + 7 + 225}{15} \] \[ = \frac{188 - 105 + 7 + 225}{15} = \frac{83 + 7 + 225}{15} = \frac{90 + 225}{15} = \frac{315}{15} \]
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Simplify the result: \[ \frac{315}{15} = 21 \]
Thus, the simplified result of \( 12 \frac{8}{15} - 7 + \frac{7}{15} + 15 \) is \( \boxed{21} \).
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