We also think that math needs to be done the way it's taught to us in school, but in many cultures, arithmetic was done using completely different methods from the ones we use now.
That's all fine and dandy, but cutting a pizza into fifths is not so easy. What if we cut each pizza in half and give a half to everyone? Then we would have just one half left over. We could cut that half into five pieces (still tricky, but easier than cutting a whole pizza into fifths), and each piece would be 1/10 of the whole pizza. Then each person would have 1/2 and 1/10 pizza.
This was how Egyptians did fractions--they broke things into unit fractions, where the numerator (the top) was always 1. In a lot of practical situations, like dividing pizzas, it would make more sense to do fractions this way, but it could also make things more complicated. What if instead if cutting each pizza in half, we cut the first two pizzas into thirds and gave everyone 1/3 (with one left over), then we cut the third pizza into fifths and gave 1/5 to each person. Then we could cut that left over third into five pieces (each 1/15 of the whole pizza) and give each person one. Then everyone would have 1/3, 1/5 and 1/15 pizza.
I guess if we want to do math like ancient Egyptians, we should figure out why 1/3 + 1/5 + 1/15 = 1/2 + 1/10. And we should learn how to recognize when two sums of unit fractions are equal.
To learn more about the history of math, check out this great animated video on YouTube: History of Math