The product of two rational numbers is `2/5`. If one of them is `-8/25` , find the other.

Answer

To find the other rational number when the product of two rational numbers is \( \frac{2}{5} \) and one of them is \( -\frac{8}{25} \), we can follow these steps:

### Step 1: Set up the equation
Let the unknown rational number be \( x \). According to the problem, we have:
\[ x \times -\frac{8}{25} = \frac{2}{5} \]

### Step 2: Isolate \( x \)
To find \( x \), we can rearrange the equation:
\[ x = \frac{2}{5} \div -\frac{8}{25} \]
Dividing by a fraction is the same as multiplying by its reciprocal, so we can rewrite this as:
\[ x = \frac{2}{5} \times -\frac{25}{8} \]

### Step 3: Perform the multiplication
Now, we multiply the fractions:
\[ x = \frac{2 \times -25}{5 \times 8} \]

### Step 4: Simplify the expression
Calculating the numerator and the denominator:
\[ x = \frac{-50}{40} \]
Now, we can simplify \( \frac{-50}{40} \):
\[ x = \frac{-5}{4} \]

### Conclusion
Thus, the other rational number is:
\[ \boxed{-\frac{5}{4}} \]