How to combine ratios? If $a:b$ is $2:5$, and $c:d$ is $5:2$, and $d:b$ is $3:2$, what is the ratio $a:c$? How would I go about solving this math problem?
if the ratio of $a:b$ is $2:5$ the ratio of $c:d$ is $5:2$ and the ratio of $d:b$ is $3:2$, what is the ratio of $a:c$?
I got $\frac{a}{c} = \frac{2}{5}$ but that is not a correct answer.

These ratios are just simple equations. For example $a:b=2:5$ is
$$a= \frac{2}{5}b$$
No need for confusing tricks here. Just substitutions :
$$ a = \frac{2}{5}b = \frac{2}{5}\frac{2}{3} d = \frac{2}{5}\frac{2}{3}\frac{2}{5} c = \frac{8}{75} c$$
So that 
$$ a:c = 8:75 $$
