Chapter 6.3, Problem 15E

To determine

To identify: whether the ratios $\frac{45}{35},\frac{9}{21}$ form a proportion or not.

Answer to Problem 15E

No. The ratios $\frac{45}{35},\frac{9}{21}$ do not form a proportion.

Explanation of Solution

Given information: The provided ratios are $\frac{45}{35},\frac{9}{21}$ .

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.

  $\begin{array}{l}\frac{45}{35}=\frac{9}{21}\text{ [Write the proportion}\text{.]}\\ 45\times 21=35\times 9\text{}\text{}\text{ [Form cross products}\text{.]}\\ 945=315\text{ [Multiply}\text{.]}\end{array}$

Since the cross products of the ratios $\frac{45}{35},\frac{9}{21}$ are not equal, the ratios do not form a proportion.