Solve Mixed Number Division: 2⅙ Divided by ⅔

To solve the problem of dividing the mixed number $2\frac{1}{6}$ by the fraction $\frac{2}{3}$, follow these steps:

• Step 1: Convert the mixed number $2\frac{1}{6}$ into an improper fraction.
  This is done by multiplying the whole number 2 by the denominator 6, then adding the numerator 1. Therefore, $2 \times 6 + 1 = 13$. The improper fraction is $\frac{13}{6}$.
• Step 2: Convert the division into multiplication by using the reciprocal of $\frac{2}{3}$.
  The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$.
• Step 3: Multiply the improper fraction $\frac{13}{6}$ by the reciprocal $\frac{3}{2}$.
  Performing the multiplication gives $\frac{13}{6} \times \frac{3}{2} = \frac{13 \times 3}{6 \times 2} = \frac{39}{12}$.
• Step 4: Simplify the resulting fraction $\frac{39}{12}$.
  This fraction simplifies by dividing both the numerator and denominator by their greatest common divisor, which is 3. Thus $\frac{39 \div 3}{12 \div 3} = \frac{13}{4}$.
• Step 5: Convert the improper fraction $\frac{13}{4}$ back to a mixed number.
  By dividing 13 by 4, we get 3 with a remainder of 1. This results in the mixed number $3\frac{1}{4}$.

Therefore, the solution to the problem is $3\frac{1}{4}$.