Chapter 6.3, Problem 4E

To determine

To identify: whether the ratios $\frac{9}{32},\frac{3}{8}$ form a proportion or not.

Answer to Problem 4E

No. The ratios $\frac{9}{32},\frac{3}{8}$ do not form a proportion.

Explanation of Solution

Given information: The provided ratios are $\frac{9}{32},\frac{3}{8}$ .

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.

  $\begin{array}{l}\frac{9}{32}=\frac{3}{8}\text{ [Write proportion}\text{.]}\\ 9\times 8=32\times 3\text{}\text{}\text{ [Form cross products}\text{.]}\\ 72=96\text{ [Multiply}\text{.]}\end{array}$

Since the cross products of the ratios $\frac{9}{32},\frac{3}{8}$ are not equal, the ratios do not form a proportion.