To divide the mixed numbers \(5 \frac{2}{3}\) and \(3 \frac{4}{7}\), we can follow these steps:
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Convert the mixed numbers to improper fractions.
For \(5 \frac{2}{3}\): \[ 5 \times 3 + 2 = 15 + 2 = 17 \quad \Rightarrow \quad \frac{17}{3} \]
For \(3 \frac{4}{7}\): \[ 3 \times 7 + 4 = 21 + 4 = 25 \quad \Rightarrow \quad \frac{25}{7} \]
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Set up the division of the fractions. To divide by a fraction, we multiply by its reciprocal: \[ \frac{17}{3} \div \frac{25}{7} = \frac{17}{3} \times \frac{7}{25} \]
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Multiply the fractions. \[ \frac{17 \times 7}{3 \times 25} = \frac{119}{75} \]
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Convert the improper fraction to a mixed number (if needed). To convert \(\frac{119}{75}\):
- Divide 119 by 75, which gives 1 with a remainder of 44. \[ 119 \div 75 = 1 \quad \text{(whole number)} \] Thus, \[ 119 = 75 \times 1 + 44 \] Therefore, \[ \frac{119}{75} = 1 \frac{44}{75} \]
So, the result of \(5 \frac{2}{3} \div 3 \frac{4}{7}\) is \(1 \frac{44}{75}\).