2A. - Algebra 1

Question

Use cross products to determine whether each pair of ratios forms a proportion.

$\frac{0.2}{1.8},\frac{1}{0.9}$

Step-by-Step Solution

Answer

No, the pair of ratios $\frac{0.2}{1.8},\frac{1}{0.9}$ do not form the proportion.

Step-1. Define proportion.

If $\frac{a}{b}=\frac{c}{d}$, where a and d are extremes and b and c are the means, then in a proportion the product of the extremes is equal to the product of the means that is., $ad=bc,b,d\ne 0$.

Step-2. Determine the cross products.

Use cross products to determine whether two ratios form a proportion.

$\begin{array}{c}\frac{0.2}{1.8}\stackrel{?}{=}\frac{1}{0.9}\\ 0.9\times 0.2\stackrel{?}{=}1\times 1.8\\ 0.18\ne 1.8\end{array}$

Step-3. State the conclusion.

Since, the cross products are not equal, that is., $0.18\ne 1.8$, therefore the ratios do not form the proportion.