Question

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

$\frac{1}{6},\frac{5}{30}$

Short answer

Yes, the pair of ratios$\frac{1}{6},\frac{5}{30}$ are equivalent ratios because $\frac{1}{6}=\frac{5}{30}$.

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.

$$\begin{gathered} \frac{1}{6}=\frac{1\times 1}{6\times 1} \\ =\frac{1}{6} \end{gathered}$$

And,

$$\begin{gathered} \frac{5}{30}=\frac{\cancel{5}}{\cancel{5}\times 6} \\ =\frac{1}{6} \end{gathered}$$

Step-3. State the conclusion.

As, both the results are equal, that is., $\frac{1}{6}=\frac{1}{6}$, therefore, yes, the given ratios are equivalent ratios.