1. Integer Representations History

2. Integer Representations Taken together, these chips add to zero. Think of a red chip as positive one and a blue chip as negative one. Example +1 -1 Red Blue

3. Represent a positive three:

4. Representation There are many ways to represent any integer. But the representation below will be referred to as the Distinguished Representation.

5. Representation This is an example of a Distinguished Representation. This is not an example of a Distinguished Representation.

6. Representation Example Non Example What is the definition of a Distinguished Representation?

8. Addition of Integers

9. Addition of Integers To add 3 + 4. To add two numbers, model each number and take the union of the models. Then find the distinguished representation.

10. Addition of Integers To add two numbers, model each number and take the union of the models. Then find the distinguished representation. To add 3 + -4. -1

12. Addition of integers 5 + -3 = ?? 2 + 3 + -3 = ?? How can we approach addition of integers by their symbols? For example: What are two numbers that add to 5? 2 + 0 = 2 2 2

14. Subtraction of Integers

15. Subtraction of Integers To subtract two numbers, model the first number and take-away the second number. Then find the distinguished representation. To subtract 5 - 3.

16. Subtraction of Integers 2 To subtract two numbers, model the first number and take-away the second number. Then find the distinguished representation. To subtract 5 - 3.

17. Subtraction of Integers To subtract two numbers, model the first number and take-away the second number. Then find the distinguished representation. Example: 5 - - 3. But there are no blue chips to take-away! What is another representation for 5?

18. Subtraction of Integers 8 To subtract two numbers, model the first number and take-away the second number. Then find the distinguished representation. Example: 5 - -3.