Question

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

$\frac{3}{7},\frac{9}{14}$

Short answer

No, the pair of ratios $\frac{3}{7},\frac{9}{14}$are not equivalent ratios because $\frac{3}{7}\ne \frac{9}{14}$.

Step-by-step solution

Step-1. Define equivalent ratios.

Equivalent ratios are two ratios which have same relationship between the numbers.

Step-2. Simplify the ratios.

Simplify both the ratios by dividing them with the common factor, if there is any.

$\begin{array}{c}\frac{3}{7}=\frac{3\times 1}{7\times 1}\\ =\frac{3}{7}\end{array}$

And,

role="math" localid="1642697328129" $$\begin{gathered} \frac{9}{14}=\frac{3\times 3}{7\times 2}\left(\text{\hspace{0.17em}nocommonfactor}\right) \\ =\frac{9}{14} \end{gathered}$$

Step-3. State the conclusion.

As, both the results are not equal, that is., $\frac{3}{7}\ne \frac{9}{14}$, therefore, no, the given ratios are not equivalent ratios.