To simplify the expression \( 12 \frac{8}{15} - 7 + \frac{7}{15} + 15 \), we'll follow the steps below:
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First, convert the mixed number \( 12 \frac{8}{15} \) into 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 \( -7 \) 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 values back into the expression: \[ \frac{188}{15} - \frac{105}{15} + \frac{7}{15} + \frac{225}{15} \]
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Combine the fractions: \[ \frac{188 - 105 + 7 + 225}{15} = \frac{188 + 7 - 105 + 225}{15} \] Calculate the numerator: \[ 188 + 7 = 195 \] \[ 195 - 105 = 90 \] \[ 90 + 225 = 315 \] Thus, the combined fraction becomes: \[ \frac{315}{15} \]
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Finally, simplify \( \frac{315}{15} \): \[ 315 \div 15 = 21 \]
So the final answer is \( 21 \), which corresponds to option: A. 21