We will begin our look at the various meanings for each of the operations and the laws that govern the operations by examining addition.
Addition is the simplest of the four operations. The operation, however, may look quite different depending on whether a problem has an unknown result, starting point, or change. We can describe addition as a merger or joining of two or more things; we can also describe it as combining parts of a whole, with the whole or one of the parts unknown.
The following table gives an example of each kind of addition problem:
The merger or joining concept always requires some sort of combining action, whereas the parts-of-a-whole concept is static. Note 2
One of the most important facts about addition is that no two quantities can be added unless they are measured or reported in the same units. For example, you cannot add 2 tens and 3 ones, or 2 halves and 3 fourths, and expect to get 5 of anything. These quantities can only be combined if we can somehow find a common unit with which to measure or label them. Note 3