To find the quotient of \(-4 \frac{1}{3}\) divided by \(-\frac{3}{4}\), we start by converting the mixed number \(-4 \frac{1}{3}\) into an improper fraction.
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Convert \(-4 \frac{1}{3}\) to an improper fraction: \[ -4 \frac{1}{3} = -\left(4 \times 3 + 1\right)/3 = -\left(12 + 1\right)/3 = -\frac{13}{3} \]
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Now we need to divide by \(-\frac{3}{4}\): \[ \text{To divide by a fraction, we multiply by its reciprocal:} \] \[ -\frac{13}{3} \div -\frac{3}{4} = -\frac{13}{3} \times -\frac{4}{3} \]
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Multiply the fractions: \[ = \frac{13 \times 4}{3 \times 3} = \frac{52}{9} \]
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Convert \(\frac{52}{9}\) to a mixed number: \[ 52 \div 9 = 5 \quad \text{(whole number part, since } 9 \times 5 = 45\text{)} \] \[ \text{Remainder: } 52 - 45 = 7 \] \[ \therefore \frac{52}{9} = 5 \frac{7}{9} \]
So, the quotient is \(5 \frac{7}{9}\).