Math Lair Home > Topics > Adding Apples and Oranges

An apple and an orange. Despite what your teacher told you, they can be added together. In this case, the result is 2 fruit.

Perhaps one of your mathematics teachers once told you that "you can't add apples and oranges." Probably this was done to drive home the point that two quantities with different units may not be added together. This isn't a good example, though, because you can add apples and oranges together.

Let's say that you wanted to add

3 apples + 4 oranges

Now, apples and oranges are physical objects, not measurements, so they don't have intrinsic units associated with them. To add unlike things, we just need to find a category broad enough to include both. Instead of calling the apples "apples" and the oranges "oranges," we can call each of them "fruit." If we do so, we can add them together; the answer is

7 fruit

We could go further. If we wanted to add 2 hamburgers to our 3 apples and 4 oranges, the result would be "9 food items." If we add 5 books to that, the result might be "14 things."