Find the Opposite Number of 1⅖: Mixed Number Conversion

To solve the problem of finding the opposite number of $1\frac{2}{5}$, follow these steps:

• Step 1: Convert the mixed number $1\frac{2}{5}$ into an improper fraction.
• Step 2: Calculate the reciprocal of that improper fraction.

Let's work through each step:

Step 1: Convert the mixed number to an improper fraction. A mixed number like $1\frac{2}{5}$ can be expressed as $\frac{7}{5}$. Here's how:
- Multiply the whole number (1) by the denominator of the fractional part (5), giving $1 \times 5 = 5$.
- Add the numerator of the fractional part (2) to this result, resulting in $5 + 2 = 7$.
- The improper fraction is thus $\frac{7}{5}$.

Step 2: Determine the reciprocal of $\frac{7}{5}$.
- The reciprocal of a fraction is obtained by swapping its numerator and denominator.
- Therefore, the reciprocal of $\frac{7}{5}$ is $\frac{5}{7}$.

Comparing the result with the multiple-choice options, the correct choice is $\frac{5}{7}$, which is option 2.

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