1. Let's start by stating the problem: You want to understand how to "move" the numerator and denominator in fractions to isolate variables or expressions. 2. The key formula to remember is that multiplying both sides of an equation by the same nonzero number keeps the equation balanced. For example, if you have $$\frac{a}{b} = c$$, multiplying both sides by $$b$$ gives $$a = bc$$. 3. Moving the denominator: If you want to "move" the denominator from the left side to the right side, you multiply both sides by the denominator. For example, from $$\frac{a}{b} = c$$, multiply both sides by $$b$$ to get $$a = bc$$. 4. Moving the numerator: If you want to isolate the denominator, you can divide both sides by the numerator. Starting from $$\frac{a}{b} = c$$, multiply both sides by $$b$$ to get $$a = bc$$, then divide both sides by $$c$$ to isolate $$b$$: $$b = \frac{a}{c}$$. 5. Important rules: - You can only multiply or divide both sides of an equation by the same nonzero number. - "Moving" terms across the equals sign is really multiplying or dividing both sides by that term. 6. Summary: - To move the denominator to the other side, multiply both sides by the denominator. - To isolate the denominator, multiply both sides by the denominator, then divide both sides by the other term. This way, you keep the equation balanced and correctly isolate the variable or expression you want.