To solve the division of mixed numbers 4 1/3 ÷ -1 1/5, we first convert the mixed numbers into improper fractions.
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Convert 4 1/3: \[ 4 \frac{1}{3} = \frac{4 \times 3 + 1}{3} = \frac{12 + 1}{3} = \frac{13}{3} \]
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Convert -1 1/5: \[ -1 \frac{1}{5} = -\left(\frac{1 \times 5 + 1}{5}\right) = -\left(\frac{5 + 1}{5}\right) = -\frac{6}{5} \]
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Now we perform the division of these fractions: \[ \frac{13}{3} \div -\frac{6}{5} = \frac{13}{3} \times -\frac{5}{6} \]
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Multiply the fractions: \[ = \frac{13 \times -5}{3 \times 6} = \frac{-65}{18} \]
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Convert \(-\frac{65}{18}\) to a mixed number:
- Divide 65 by 18. The quotient is 3 and the remainder is 11: \[ 65 \div 18 = 3 \quad \text{with a remainder of} , 11 \] So, \[ -\frac{65}{18} = -3 \frac{11}{18} \]
Thus, the quotient of \(4 \frac{1}{3} ÷ -1 \frac{1}{5}\) is \(-3 \frac{11}{18}\).
From the provided options, the correct response is: −31118 (negative 3 and 11 over 18).