To find the other rational number, we can use the given information that the product of two rational numbers is 5/18 and one of the numbers is -3/20. Let's solve this step by step.

Step 1: Understanding the problem
We are given that the product of two rational numbers is 5/18. We need to find the other rational number when one of them is -3/20.

Step 2: Formulating the problem mathematically
Let's assume the other rational number as "x". We know that the product of -3/20 and "x" is equal to 5/18. So we can write it as:

(-3/20) * x = 5/18

Step 3: Solving the equation
To solve the equation, we can cross-multiply:

(-3/20) * x = 5/18
-3x = (5/18) * 20
-3x = 100/18

Now, let's simplify the right side of the equation:

-3x = 100/18
-3x = 50/9

To solve for "x," we can divide both sides of the equation by -3:

x = (50/9) / -3
x = (50/9) * (-1/3)
x = -50/27

Step 4: Answer
The other rational number is -50/27.

Explanation
We started by understanding the problem and formulating it mathematically. Then, we solved the equation by cross-multiplying and simplifying the right side. Finally, we divided both sides by -3 to find the value of "x." The other rational number is -50/27.