Solve Mixed Number Division: 2⅐ ÷ ⅝ Step-by-Step

To solve the problem $2\frac{1}{7} : \frac{5}{7}$, we proceed as follows:

• Step 1: Convert the mixed number $2\frac{1}{7}$ to an improper fraction.

To do this, multiply the whole number part by the denominator and add the numerator: $(2 \times 7) + 1 = 14 + 1 = 15$. Therefore, $2\frac{1}{7} = \frac{15}{7}$.

• Step 2: Find the reciprocal of the fraction $\frac{5}{7}$.

The reciprocal of $\frac{5}{7}$ is $\frac{7}{5}$.

• Step 3: Multiply $\frac{15}{7}$ by $\frac{7}{5}$.

The multiplication is: $\frac{15}{7} \times \frac{7}{5} = \frac{15 \times 7}{7 \times 5} = \frac{105}{35}$.

• Step 4: Simplify $\frac{105}{35}$.

To simplify, divide both the numerator and the denominator by their greatest common factor, which is 35: $\frac{105 \div 35}{35 \div 35} = \frac{3}{1} = 3$.

Thus, the solution to the problem $2\frac{1}{7} : \frac{5}{7}$ is $3$.