1. Let's restate the question: You want to know if for any equation where both sides have the same denominator, you can multiply both sides by that denominator (for example, 10) to eliminate the fraction. 2. The answer is generally yes, as long as the denominator is not zero. Multiplying both sides of the equation by the same nonzero number preserves the equality. 3. For example, if you have $$\frac{a}{10} = \frac{b}{10}$$, multiplying both sides by 10 gives: $$10 \times \frac{a}{10} = 10 \times \frac{b}{10}$$ which simplifies to: $$a = b$$ 4. This is a valid step because we are applying the multiplication property of equality, which states that you can multiply both sides of an equation by the same nonzero number without changing the equation. 5. Just ensure that the denominator you're multiplying by is not zero to avoid division by zero errors. Final takeaway: Yes, multiplying both sides by the common denominator eliminates the fractions correctly.