Solve: Dividing 2⅝ by ⅘ - Mixed Number and Fraction Division

To solve the problem of dividing the mixed number $2\frac{5}{7}$ by the fraction $\frac{4}{5}$, we will follow the outlined steps:

• Step 1: Convert the mixed number to an improper fraction.
• For $2\frac{5}{7}$: Multiply the whole number $2$ by the denominator $7$, giving $2 \times 7 = 14$.
• Add the numerator $5$ to this result, giving $14 + 5 = 19$. Thus, $2\frac{5}{7} = \frac{19}{7}$.
• Step 2: Divide the improper fraction by $\frac{4}{5}$ by multiplying by the reciprocal of $\frac{4}{5}$, which is $\frac{5}{4}$.
• Perform the multiplication: $\frac{19}{7} \times \frac{5}{4} = \frac{19 \times 5}{7 \times 4} = \frac{95}{28}$.
• Step 3: Convert the result back to a mixed number if needed.
• Divide $95$ by $28$ to find the whole part; $28$ goes into $95$ three times, with a remainder.
• The remainder is $95 - (28 \times 3) = 95 - 84 = 11$.
• Therefore, $\frac{95}{28}$ is written as the mixed number $3\frac{11}{28}$.

Therefore, the solution is $3\frac{11}{28}$.