Chapter 6.3, Problem 3E

To determine

To identify: whether the ratios $\frac{5}{8},\frac{10}{16}$ form a proportion or not.

Answer to Problem 3E

Yes. The ratios $\frac{5}{8},\frac{10}{16}$ form a proportion.

Explanation of Solution

Given information: The provided ratios are $\frac{5}{8},\frac{10}{16}$ .

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 or not. If the cross products are equal, then the ratios form a proportion.

  $\begin{array}{l}\frac{5}{8}=\frac{10}{16}\text{ [Write the proportion}\text{.]}\\ 5\times 16=8\times 10\text{}\text{}\text{ [Form cross products}\text{.]}\\ 80=80\text{ [Multiply}\text{.]}\end{array}$

Since the cross products of the ratios $\frac{5}{8},\frac{10}{16}$ are equal, the ratios form a proportion.