### Theory:

Applying the equivalent ratio method, we can determine whether the given ratios are equivalent or not.

Let's see a few steps to understand this concept.
Equivalent ratios:

Step 1: First write the given ratios in the form of fractions.

Step 2: Compare the fractions by converting into like fractions. (Take LCM if needed)

Step 3: Now if the fractions are equal, then the ratios are said to be equivalent otherwise not.
Check whether the ratios 1:4 and 4:8 are equivalent?

Step 1: Write the given ratios in the form of fractions.

$\frac{1}{4}\mathit{and}\phantom{\rule{0.147em}{0ex}}\frac{4}{8}$

Step 2: Hence the denominators 4 and 8 is not equal. We should take LCM for 4 and 8.

That is LCM of 4 and 8 is $$16$$.

Then we get,

$\begin{array}{l}\frac{1×4}{4×4}\phantom{\rule{0.147em}{0ex}}\mathit{and}\phantom{\rule{0.147em}{0ex}}\frac{4×2}{8×2}\\ \\ \frac{4}{16}\phantom{\rule{0.147em}{0ex}}\mathit{and}\phantom{\rule{0.147em}{0ex}}\frac{8}{16}\end{array}$

Now we can compare the ratios $\frac{4}{16}\phantom{\rule{0.147em}{0ex}}\mathit{and}\phantom{\rule{0.147em}{0ex}}\frac{8}{16}$.

$\mathit{Since}\phantom{\rule{0.147em}{0ex}}\frac{4}{16}\phantom{\rule{0.147em}{0ex}}\prec \phantom{\rule{0.147em}{0ex}}\frac{8}{16}\phantom{\rule{0.147em}{0ex}}$

That is $$4$$$$/$$16 is lesser than 8$$/$$16.

Therefore the given ratios 1:4 and 4:8 are not equivalent.