Question

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

$\frac{39.68}{60.14},\frac{6.4}{9.7}$

Short answer

Yes, the pair of ratios $\frac{39.68}{60.14},\frac{6.4}{9.7}$are equivalent ratios.

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.

$$\begin{gathered} \frac{39.68}{60.14}=\frac{3968}{6014} \\ =\frac{4\times 4\times 4\times \cancel{2}\times \cancel{31}}{\cancel{2}\times \cancel{31}\times 97} \\ =\frac{64}{97} \end{gathered}$$

And,

$\frac{6.4}{9.7}=\frac{64}{97}$

Step-3. State the conclusion.

As, both the results are equal, that is., $\frac{64}{97}=\frac{64}{97}$, therefore, yes, the given ratios are equivalent.