1. **Stating the problem:** We are given examples of rational numbers: $-\frac{5.6}{9}$, $0.25$, and $x \times 8$. We need to calculate the value of $x$ such that $x \times 8$ is a rational number. 2. **Understanding rational numbers:** A rational number is any number that can be expressed as $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$. 3. **Given values:** - $-\frac{5.6}{9}$ is rational because it is a fraction of two numbers. - $0.25$ is rational because it equals $\frac{1}{4}$. - $x \times 8$ must also be rational. 4. **Finding $x$:** Since $8$ is rational, for $x \times 8$ to be rational, $x$ must be rational. 5. **Calculating $x$:** If $x \times 8$ equals one of the given rational numbers, for example $0.25$, then: $$x \times 8 = 0.25$$ $$x = \frac{0.25}{8}$$ $$x = 0.03125$$ 6. **Conclusion:** The value of $x$ is $0.03125$ to make $x \times 8$ equal to $0.25$, a rational number. **Final answer:** $x = 0.03125$