To find the quotient of \(-59 \div 15\) and express it as a mixed number, we can divide the numbers:
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First, find how many whole times 15 goes into -59:
- \(-59 \div 15\) gives approximately -3.9333.
- This means 15 goes into -59 a total of -4 whole times, because we're looking for the greatest integer less than -3.9333.
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Now we calculate the product of -4 and 15:
- \(-4 \times 15 = -60\).
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Next, we find the remainder:
- Remainder = -59 - (-60) = -59 + 60 = 1.
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Thus, \(-59\) can be expressed as: \[ -59 = -4 \cdot 15 + 1 \]
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The mixed number form of this calculation will be: \[ -4 \frac{1}{15} \]
Therefore, the quotient of \(-59 \div 15\) as a mixed number is \(-4 \frac{1}{15}\).