Q3. - Algebra 1

Question

Determine whether each pair of ratios are equivalent ratios. Write yes or no. Justify your answer.

$\frac{2.8}{4.4},\frac{1.4}{2.1}$

Step-by-Step Solution

Answer

No, the pair of ratios $\frac{2.8}{4.4},\frac{1.4}{2.1}$ are not equivalent ratios because $\frac{2.8}{4.4}\ne \frac{1.4}{2.1}$.

Step-1. Define equivalent ratios.

Equivalent ratios are two ratios which have same relationship between the numbers. 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., $ad=bc,b,d\ne 0$.

If two ratios are in proportion then they are equivalent ratios.

Step-2. Determine the cross products.

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

$\begin{array}{c}\frac{2.8}{4.4}\stackrel{?}{=}\frac{1.4}{2.1}\\ 2.8\times 2.1\stackrel{?}{=}1.4\times 4.4\\ \text{5.88}\ne \text{6.16}\end{array}$

Step-3. State the conclusion.

Since, the cross products are not equal, that is., $\text{5.88}\ne \text{6.16}$, therefore the ratios do not form the proportion and so they are not equivalent ratios.