What is the equation showing two ratios to be equal called?

The equation that shows two ratios to be equal is called a proportion. A proportion illustrates the relationship between two ratios, indicating that they are equivalent. For example, if you have the ratios ( \frac{a}{b} ) and ( \frac{c}{d} ), the equation ( \frac{a}{b} = \frac{c}{d} ) is considered a proportion. This concept is fundamental in various mathematical applications, including solving for unknowns in equations that involve ratios, and is particularly useful in scaling, comparing measurements, and in geometric relationships.

Understanding proportions allows for cross-multiplying to check equality or resolve unknowns. For instance, if you know that ( \frac{2}{3} = \frac{x}{6} ), you can cross-multiply to find that ( 2 \times 6 = 3 \times x ), leading to a straightforward solution for ( x ).

In contrast, terms like ratio and rate have different meanings. A ratio is simply a comparison of two quantities, while a rate specifically relates two quantities of different units. An expression, on the other hand, is any mathematical phrase that can represent a number but does not make a statement of equality.