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Cross multiplication is a method used to solve equations that involve ratios or proportions. It's a powerful tool that can also be useful in verifying whether two ratios form a proportion. Understand that when you have a proportion, such as \( \frac{a}{b} = \frac{c}{d} \), the cross products (multiplying across the equality), which are \( a \times d \) and \( b \times c \), must be equal. This principle forms the basis of cross multiplication.

For example, let's consider the statement \( \frac{-8}{5} = \frac{32}{-20} \). To verify this using cross multiplication, you multiply the numerator of the first fraction by the denominator of the second fraction. In parallel, you multiply the numerator from the second fraction with the denominator of the first. If the results are equal, the two fractions constitute a proportion. Here's this concept in action: \( -8 \times -20 = 32 \times 5 \), both yield the same product, 160, confirming the proportion.

Ratios are a way to compare two quantities, expressing how many times one value contains another. In algebra, ratios are usually presented as fractions, but unlike typical fractions, they don't necessarily represent a part of a whole. Instead, they express a relationship between two quantities. When these ratios are equal, we say that they are in proportion, signifying that there is a constant scaling factor from one ratio to the other.

For instance, the algebraic expression \( \frac{-8}{5} \) represents a ratio, as does \( \frac{32}{-20} \). These express relationships between the quantities -8 and 5, and 32 and -20, respectively. Equality of such ratios indicates that multiplying -8 by the same factor that would multiply 5 to get -20, will result in 32. This is a foundational concept when dealing with problems of direct and inverse variation within algebra.

To verify whether a given statement is a proportion, you can employ the method of cross multiplication. However, there are other ways to check for proportional relationships as well. A common practice is to simplify each ratio to its lowest terms and see if they match. Additionally, you can divide the values of each ratio and compare the quotients. If the quotients are equal, the original statement represents a proportion.

Looking at the statement \( \frac{-8}{5} = \frac{32}{-20} \), one way to verify the proportion is to simplify the second ratio: \( \frac{32}{-20} \) simplifies to \( \frac{-8}{5} \), which is identical to the first ratio. Another approach is to calculate the quotients: \( \frac{-8}{5} \) and \( \frac{32}{-20} \) both result in the same value, -1.6, thus confirming that the original statement is indeed a proportion.