Chris eats 3 slices of a pizza that is cut into 8 equal slices. What percentage of the pizza does he eat?

Well, he ate 3/8 of the pizza. To convert a fraction into a percentage ("by hand method") you need to multiply the denominator by something to get it to 100. To do this you just simply take 100 and divide it by the denominator and this is the number that you need to multiply to the denominator to get it to 100. Whatever you multiply to the denominator you must multiply to the numerator. Hence:

100 / 8 = 12.5

3/8 * 12.5/12.5 = 37.5/100

Now whatever number that is over 100 is that percentage. So, Chris ate 37.5% of the pizza.