The Problem:
The problem states that the product of two numbers is -1, and one of the numbers is given as -17/8. We are required to find the other number.

Solution:
To find the other number, let's denote it as 'x'. We can set up an equation using the given information.

Let's assume that the other number, x, is a rational number. A rational number is any number that can be expressed as a fraction, where the numerator and denominator are both integers.

Setting up the equation:
We are given that the product of the two numbers is -1. So, we can write the equation as:
(-17/8) * x = -1

Solving the equation:
To solve the equation, we need to isolate 'x' on one side of the equation. We can do this by multiplying both sides of the equation by the reciprocal of (-17/8), which is (-8/17).

Multiplying both sides of the equation by (-8/17), we get:
(-8/17) * (-17/8) * x = (-8/17) * (-1)

Simplifying the equation, we have:
x = 8/17

Answer:
The other rational number is 8/17.

Explanation:
To find the other number, we set up an equation using the given information. By solving the equation, we find that the other rational number is 8/17. The rational number -17/8 is multiplied by the unknown number x to give a product of -1. By multiplying both sides of the equation by the reciprocal of -17/8, we isolate x and find that x = 8/17.