To find the quotient of \( 11 \frac{2}{3} \div 2 \frac{1}{3} \), we first need to convert both mixed numbers into improper fractions.
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Convert \( 11 \frac{2}{3} \): \[ 11 \frac{2}{3} = 11 \times 3 + 2 = 33 + 2 = 35 \] So, \( 11 \frac{2}{3} = \frac{35}{3} \).
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Convert \( 2 \frac{1}{3} \): \[ 2 \frac{1}{3} = 2 \times 3 + 1 = 6 + 1 = 7 \] So, \( 2 \frac{1}{3} = \frac{7}{3} \).
Now we can perform the division of the two improper fractions: \[ \frac{35}{3} \div \frac{7}{3} = \frac{35}{3} \times \frac{3}{7} \]
The 3’s cancel out: \[ = \frac{35}{7} \]
Now simplify: \[ = 5 \]
The quotient of \( 11 \frac{2}{3} \div 2 \frac{1}{3} \) is \( 5 \).
The answer, simplified, is: \[ \boxed{5} \]