Solve Mixed Number Division: 1⅔ ÷ ¾ Step-by-Step

To solve the division of the mixed fraction $1\frac{2}{7}$ by the fraction $\frac{3}{4}$, follow these steps:

• Step 1: Convert the mixed fraction to an improper fraction: $1\frac{2}{7} = \frac{9}{7}$.
• Step 2: Determine the reciprocal of the divisor fraction: $\text{Reciprocal of } \frac{3}{4} = \frac{4}{3}$.
• Step 3: Multiply the improper fraction by the reciprocal of the divisor: $\frac{9}{7} \times \frac{4}{3} = \frac{36}{21}$.
• Step 4: Simplify the resulting fraction: The greatest common divisor of 36 and 21 is 3. Thus, $\frac{36}{21} = \frac{12}{7}$.
• Step 5: Convert back to a mixed number: The improper fraction $\frac{12}{7} = 1\frac{5}{7}$.

Therefore, the solution to the problem is $1\frac{5}{7}$.