Express $x=0.overline{31}_5$ as a fraction in lowest terms

Given $x=0.\overline{31}_5$, find the value of $x$, expressed as a fraction in lowest terms.

I tried to change it into base $10$, but I don't think it's possible with fractions. So please help I'll appreciate it. Also I'm in 7th grade (easy solutions please) and no copying other people's answer (I've seen it in other problems).

Answer

$$x=.\overline{31}_5$$
$$100_5x=31.\overline{31}_5$$
subtracting the top from the bottom we get
$44_5x=31_5$ (comment if you dont understand why $100_5-1_5=44_5$)

Solving for $x$ we get $x=\frac{31}{44}$ as a base $5$ fraction. To simplify, we convert to base 10
$$x=\frac{16}{24}=\frac{2}{3}$$

This works like converting base-10 recurring fractions (practice -- it's a good tool to have).