There is a common phrase that is associated with subtraction: "Subtraction is addition of the opposite." Integer chips and the number line can help to illuminate this concept. Consider the following diagram:
How would you describe the idea that and are "opposite" numbers? How well does this idea extend to other numbers?
2.
Describe how integer chips can be used to demonstrate the idea that "subtraction is addition of the opposite." (Hint: You may want to think about the physical manipulation of the chips when doing subtraction, and the relationship between a number and its opposite.)
3.
The more technical term of the "opposite" of a number is the "additive inverse" of a number. The additive inverse of a number is the number that has the property that \(a + b = 0\text{.}\) Using this definition, we can see that is the opposite of since \(1 + (-1) = 0\text{.}\) Use this definition to argue that the additive inverse of the additive inverse of a number is itself.
