Solve Fraction Division: 4/5 ÷ 2⁴⁄₅ Step by Step

To solve this problem, we'll break it down into manageable steps:

• Step 1: Convert the mixed number $2\frac{4}{5}$ into an improper fraction.
• Step 2: Divide the fraction $\frac{4}{5}$ by the improper fraction obtained in Step 1.
• Step 3: Multiply by the reciprocal to perform the division.

Let's work through each step:

Step 1: Convert the mixed number to an improper fraction.
The mixed number $2\frac{4}{5}$ can be converted as follows:

$2\frac{4}{5} = \frac{2 \times 5 + 4}{5} = \frac{10 + 4}{5} = \frac{14}{5}$

Step 2: Change the division into multiplication by using the reciprocal of $\frac{14}{5}$.
The reciprocal of $\frac{14}{5}$ is $\frac{5}{14}$.

Step 3: Multiply $\frac{4}{5}$ by $\frac{5}{14}$:

$\frac{4}{5} \times \frac{5}{14} = \frac{4 \times 5}{5 \times 14}$

Simplify the expression:

$= \frac{20}{70}$

Reduce $\frac{20}{70}$ by dividing the numerator and the denominator by their greatest common divisor, which is 10:

$= \frac{2}{7}$

Therefore, the solution to the problem is $\boxed{\frac{2}{7}}$, which corresponds to choice 2.