Chapter 6.3, Problem 2E

To determine

To explain: the way of using cross products in order to determine if two ratios are equal.

Explanation of Solution

Given information: Using cross products to determine if two ratios are equal.

The product of the numerator of one ratio and of the denominator of the other is known as a cross product. Cross products can be used to determine whether the ratios form a proportion. If the cross products are equal, then the ratios form a proportion. Given below is an example to explain how cross products can determine if two ratios are equal.

  $\begin{array}{l}\frac{42}{21}=\frac{4}{2}\text{ [Write the proportion}\text{.]}\\ 42\times 2=21\times 4\text{}\text{}\text{ [Form cross products}\text{.]}\\ 84=84\text{ [Multiply}\text{.]}\end{array}$

In the given example, both sides of the ratio are equal. Hence, you can determine if two ratios are equal or not by first forming cross products and then multiply them.