Adding & Subtracting Fractions

You ate ½ of a pizza. Your friend ate ¼ of the same pizza. How much is gone? You'd love to just add the numbers — but 1 + 1 = 2 and 2 + 4 = 6, and 2/6 is clearly wrong (that's a third, less than your half alone). The problem is that your slices are different sizes. A 'half' slice and a 'quarter' slice can't be counted together until you redraw the lines so every slice is the same size.