To simplify the expression \( 12 \frac{8}{15} - 7 + \frac{7}{15} + 15 \):
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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 \( 7 \) and \( 15 \) into fractions with a common 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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Rewrite the entire expression using common denominators: \[ \frac{188}{15} - \frac{105}{15} + \frac{7}{15} + \frac{225}{15} \]
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Combine the fractions: \[ \frac{188 - 105 + 7 + 225}{15} = \frac{188 - 105 + 7 + 225}{15} = \frac{188 - 105 + 7 + 225}{15} = \frac{188 - 105 + 7 + 225}{15} = \frac{188 + 225 - 105 + 7}{15} \] Calculating the numerator: \[ = \frac{188 + 225 = 413} \] \[ = 413 - 105 + 7 = 413 - 105 = 208 + 7 = 215 \] Final numerator: \[ = 215 \]
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This gives us: \[ = \frac{215}{15} \]
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Now, simplify \( \frac{215}{15} \):
- \( 215 \div 15 = 14 \) with a remainder of \( 5 \), so: \[ = 14 \frac{5}{15} = 14 \frac{1}{3} \]
Therefore, the simplified answer is:
14 \(\frac{1}{3}\) or \( 14.33 \).
None of the provided options matches this answer directly. Please check the problem statement or the answer choices again.