The Rule of Change of Addends

The rule of change of the addends is a manifestation of the associativity of addition:

When one of the addends changes by a certain amount, the sum changes by the same amount.

The applet below illustrates that rule. In this applet, you may click on either of the two addends. Clicking a little to the right of the number's vertical central line will increase it by one. Clicking a little to the left of the central line decreases the number by 1. You start with the common fact 1 + 1 = 2 which simply says that 2 denotes the number of elements in a group that is counted as "one and one", or which consists of two smaller groups each having 1 element. If you add an element to either of the smaller groups, the number on the right changes by the same amount. (To change numbers faster, you can drag the mouse on the left or right of their central line.)

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