I would like to be more fancy, since you all seem fancy, but I taught adult literacy for a few years. Adults with 1st - 5th grade math level coming in to try and get their GED.
Cut up a circular pizza into 1/2$1/2$ and 1/3$1/3$ each, and then have them cut up a pizza into 1/5$1/5$. They will then intuitively get that 1/2 + 1/3 != 1/5$1/2 + 1/3 \,=' 1/5$, because that's way less pizza.
Then you can do the same with the numerator to show that 2/5 + 3/5 = 5/5$2/5 + 3/5 = 5/5$ a whole pizza.
In two years of teaching that class, my most powerful techniques bar none were pizzas and dollars. Even the most self-proclaimed math illiterate will learn percentages when there's a sale going on.