What method is used to find the value of x in a ratio problem?

When solving ratio problems that involve two fractions set equal to each other, cross-multiplication is the method used to find the value of the unknown variable, such as x. For example, if you have a ratio expressed as a fraction, say ( \frac{a}{b} = \frac{c}{x} ), you can eliminate the fractions by cross-multiplying. This means you multiply the numerator of one fraction by the denominator of the other fraction: ( a \cdot x = b \cdot c ). Following cross-multiplication, you can then solve for x by isolating it on one side of the equation.

This method is particularly effective because it provides a straightforward way to work with proportions, allowing you to reduce the problem to a simpler algebraic equation. The other methods mentioned, while useful in different contexts, do not directly address the relationship between the parts of the ratio in this specific way. Thus, cross-multiplication stands out as the most appropriate technique for solving ratio problems involving unknowns.