We can restate this problem as:
$13 is what percent of $52?
First, lets call the percent we are looking for "p" or p%p%.
"Percent" or "%" means "out of 100" or "per 100", Therefore p% can be written as p/100p100.
When dealing with percents the word "of" means "times" or "to multiply".
Putting this altogether we can write this equation and solve for pp while keeping the equation balanced:
$13 = p/100 xx $52$13=p100×$52
$13 = ($52p)/100$13=$52p100
$13 xx color(red)(100/($52)) = ($52p)/100 xx color(red)(100/($52))$13×100$52=$52p100×100$52
($1300)/($52) = ($52p)/100 xx 100/($52)$1300$52=$52p100×100$52
(color(green)(cancel(color(black)($)))1300)/(color(green)(cancel(color(black)($)))52) = (color(blue)(cancel(color(black)($52)))p)/color(red)(cancel(color(black)(100))) xx color(red)(cancel(color(black)(100)))/(color(blue)(cancel(color(black)($52))))
1300/52 = p
25 = p
