To find the quotient of \(-59 \div 15\), we can start by performing the division:
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Divide \(59\) by \(15\). \[ 59 \div 15 = 3 \quad \text{(since \(15 \times 3 = 45\))} \] The remainder is: \[ 59 - 45 = 14 \]
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Since we are dealing with \(-59\), the quotient will be negative. Therefore, the quotient is: \[ -3 \text{ with a remainder of } 14 \]
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Now, we express this as a mixed number. The value of the quotient as a mixed number can be expressed as: \[ -3 \frac{14}{15} \]
Thus, the final answer as a mixed number is: \[ \boxed{-3 \frac{14}{15}} \]