Let's simplify the expression step by step:
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Convert mixed numbers into improper fractions: \(12 \frac{8}{15}\) can be converted by multiplying the whole number by the denominator and adding the numerator: \[ 12 \frac{8}{15} = \frac{12 \times 15 + 8}{15} = \frac{180 + 8}{15} = \frac{188}{15} \]
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Rewrite the full expression: Now substitute into the original expression: \[ \frac{188}{15} - 7 + \frac{7}{15} + 15 \]
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Convert whole numbers to 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 expression with fractions: Now the expression looks like: \[ \frac{188}{15} - \frac{105}{15} + \frac{7}{15} + \frac{225}{15} \]
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Combine the fractions: Combine the numerators: \[ \frac{188 - 105 + 7 + 225}{15} = \frac{188 - 105 + 7 + 225}{15} = \frac{188 - 105 + 7 + 225}{15} \] Calculate the numerator: \(188 - 105 = 83\) \(83 + 7 = 90\) \(90 + 225 = 315\)
Therefore, we have: \[ \frac{315}{15} \]
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Simplify the fraction: Divide both the numerator and denominator by 15: \[ \frac{315 \div 15}{15 \div 15} = \frac{21}{1} = 21 \]
So, the simplified answer is: \[ \boxed{21} \]