Did you know that fractions used to be a form of ancient torture? Actually, no—but the Babylonians used base-60, not base-10, which is why we have 60 minutes in an hour and 360 degrees in a circle. They were obsessed with fractions. They’d have loved your ½ + ⅓ problem.
Also, in Japan, schoolchildren learn fractions by folding origami paper. So if you mess up your measuring, just blame the paper crane you didn’t make. Another fun fact: the word “denominator” comes from the Latin for “naming thing” while “numerator” means “counting thing.” So the bottom names the size of the piece, and the top counts them. Now you know.