1. **State the problem:** You want to understand how to decide which number to divide both sides of an equation by when solving for a variable. 2. **General rule:** When you have an equation like $a = b \times x$ and you want to solve for $x$, you need to isolate $x$ on one side. 3. **Isolating the variable:** To isolate $x$, divide both sides of the equation by the coefficient multiplying $x$, which is $b$ in this case. 4. **Why divide by $b$?:** Dividing by $b$ cancels out the multiplication by $b$ on the right side because $\frac{b}{b} = 1$. 5. **Example:** From $15.5 = \frac{x}{100} \times 77.5$, rewrite as $15.5 = x \times \frac{77.5}{100}$. 6. **Multiply both sides by 100:** $15.5 \times 100 = x \times 77.5$. 7. **Divide both sides by 77.5 to isolate $x$:** $$x = \frac{15.5 \times 100}{77.5}$$ 8. **Summary:** You divide both sides by the number that is multiplied by the variable to cancel it out and isolate the variable. This is a fundamental algebraic principle used to solve for unknowns.