1. Integers Grade 9 Applied Mathematics M. M. Couturier

2. Integers An integer is a whole number that can be either greater than 0, called positive, or less than 0, called negative. Zero is neither positive nor negative.

3. Adding or Subtracting Integers Throughout your academic career you have been given questions that resemble: 4 – 3 = 1 10 - 2 = 8

4. Adding or Subtracting Integers In this lesson, we will rearrange the numbers such that we get questions that look like: – 3 + 4 = 1 - 2 + 10 = 8

5. Adding or Subtracting Integers Let us compare the first example: Initially, we had, 4 – 3 = 1 Then we rearranged the order to get: – 3 + 4 = 1 What do you notice?

6. Adding or Subtracting Integers In the other example, we had: 10 - 2 = 8 Then we rearranged the order to get: - 2 + 10 = 8 Again, what do you notice?

7. Using Number Lines Let us look at how number lines work: http://nlvm.usu.edu/en/nav/frame s_asid_156_g_1_t_1.html?open=a ctivities http://nlvm.usu.edu/en/nav/frame s_asid_156_g_1_t_1.html?open=a ctivities

8. Using Number Lines Let us look at how number lines work with negatives: http://www.funbrain.com/cgi- bin/nl.cgi?A1=s&A2=3 http://www.funbrain.com/cgi- bin/nl.cgi?A1=s&A2=3

9. The Darth Vader Luke Skywalker Method If number lines are not your thing, there is a different way to look at this.

10. The Darth Vader Luke Skywalker Method

11. Imagine that numbers that are positive are Luke Skywalkers and negative numbers are Darth Vaders. There are four possible outcomes to these situations.

12. The Darth Vader Luke Skywalker Method In this example, we will look at all four possibilities with the numbers 3 and 4. They are: 3 + 4 3 – 4 -3 + 4 -3 – 4

13. The Darth Vader Luke Skywalker Method In the example, 3 + 4, we have a positive 3 and a positive 4 (another way to look at it is: +3+4). This means that we have three Luke’s who will meet another four Luke’s. Since they are on the same side, they will join forces, hence, there will be …

14. 3 + 4 = 7

15. The Darth Vader Luke Skywalker Method In the example, 3 - 4, we have a positive 3 and a negative 4 (another way to look at it is:+3-4). This means that we have three Luke’s who will run into four Vader’s.

16. The Darth Vader Luke Skywalker Method Since they are on opposite sides, they will fight, but who will win? There are more Vader’s than Luke’s so the answer will be negative. Now how many more Vader’s are there?

17. 3 - 4 = -1

19. The Darth Vader Luke Skywalker Method In the example, -3+4, we have a negative 3 and a positive 4. This means that we have three Vader’s who will run into four Luke’s.

20. The Darth Vader Luke Skywalker Method Since they are on opposite sides, they will fight, but who will win? There are more Luke’s than Vader’s so the answer will be positive. Now how many more Luke’s?

21. -3+4 =1

23. The Darth Vader Luke Skywalker Method In the example, -3-4, we have a negative 3 and a negative 4. This means that we have three Vader’s who will meet another four Vader’s. Since they are on the same side, they will join forces, hence, there will be …

24. -3 - 4 = -7

25. A financial aspect? We can also look at integers as dollar values. Negative numbers imply debts and/or liabilities (things that take away money). Positive numbers imply earnings and/or assets (things that increase your worth).

26. A financial aspect? Going back to the examples used previously: 3+4 Think of someone giving you $3 and then getting another $4. You now have $7.

27. A financial aspect? Going back to the examples used previously: 3-4 Think of someone giving you $3 and then having to pay a bill worth $4. You are now in debt $1, hence $–1.

28. A financial aspect? Going back to the examples used previously: -3+4 Think of a situation where you pay a bill that costs $3 and then finding $4. You now have $1.

29. A financial aspect? Going back to the examples used previously: -3-4 Think of a situation where you owe $3 and then you pay another bill costing $4. You are now in debt $7, hence $-7.