### Theory:

Let's look for the steps to compare the ratios.
Step $$1$$: First write the given ratios in the form of fractions.

Step $$2$$: Compare the fractions by converting them 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.
Applying the equivalent ratio method, we can determine whether the given ratios are equivalent or not.
Example:
Check whether the ratios 1:4 and 4:8 are equivalent?

Step $$1$$: Write the given ratios in the form of fractions $$=$$ $\frac{1}{4}$ and $\phantom{\rule{0.147em}{0ex}}\frac{4}{8}$.

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

That is LCM of 4 and 8 is $$16$$.

Then we get:

$\frac{1×4}{4×4}\phantom{\rule{0.147em}{0ex}}$ and $\phantom{\rule{0.147em}{0ex}}\frac{4×2}{8×2}$

$\frac{4}{16}$ and $\phantom{\rule{0.147em}{0ex}}\frac{8}{16}$.

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

Step $$3$$: Now check the like fractions are equal or not.

We know that $\phantom{\rule{0.147em}{0ex}}\frac{4}{16}\phantom{\rule{0.147em}{0ex}}\prec \phantom{\rule{0.147em}{0ex}}\frac{8}{16}\phantom{\rule{0.147em}{0ex}}$

That is $\frac{4}{16}$ is lesser than $\phantom{\rule{0.147em}{0ex}}\frac{8}{16}$ as the numerator is lesser. Thus, the like fraction form of the given ratios are not equal.

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