1. The problem is to solve the equation $\frac{1}{4} = 8 \times x$ for $x$. 2. The equation states that one quarter equals eight times some number $x$. 3. To isolate $x$, divide both sides of the equation by 8: $$x = \frac{\frac{1}{4}}{8}$$ 4. Simplify the right side by multiplying the denominator: $$x = \frac{1}{4} \times \frac{1}{8} = \frac{1}{32}$$ 5. Therefore, the solution is $x = \frac{1}{32}$. This means that when $x$ is $\frac{1}{32}$, multiplying it by 8 gives $\frac{1}{4}$, which satisfies the original equation.