2. Definition Positive number: A number greater than zero. 0123456

3. Definition Negative number: A number less than zero. 0123456-2-3-4-5-6

4. Definition Opposite Numbers: Numbers that are the same distance from zero in the opposite direction 0123456-2-3-4-5-6

5. Definition Integers: Integers are all the whole numbers and all of their opposites on the negative number line including zero. -7 opposite 7

7. 0123456-2-3-4-5-6 When the number is positive count to the right. + - When the number is negative count to the left. One Way to Add Integers Is With a Number Line Always start at zero!

8. One Way to Add Integers Is With a Number Line 0123456-2-3-4-5-6 + - +3 + (-5) = -2

9. One Way to Add Integers Is With a Number Line 0123456-2-3-4-5-6 + - +6 + (-4) =+2

10. One Way to Add Integers Is With a Number Line 0123456-2-3-4-5-6 + - +3 + (-7) = -4

11. One Way to Add Integers Is With a Number Line 0123456-2-3-4-5-6 - + -3 + 7 =+4

12. One Way to Add Integers Is With a Number Line 0123456-2-3-4-5-6 - + -5 + 3 =-2

13. One Way to Add Integers Is With a Number Line 0123456-2-3-4-5-6 - + -2 + 8 =+6

14. One Way to Add Integers Is With a Number Line 0123456-2-3-4-5-6 - + -5 + 2 =-3

15. One Way to Add Integers Is With a Number Line 0123456-2-3-4-5-6 - - -4 + (-2) = -6

16. One Way to Add Integers Is With a Number Line 0123456-2-3-4-5-6 - - -2 + (-3) = -5

17. One Way to Add Integers Is With a Number Line 0123456-2-3-4-5-6 - - -1 + (-4) = -5

18. One Way to Add Integers Is With a Number Line 0123456-2-3-4-5-6 + + 4 + 1 =5

19. One Way to Add Integers Is With a Number Line 0123456-2-3-4-5-6 + + 1 + 5 =6

21. One Way to Subtract Integers Is With a Number Line Subtraction on the number line can become tricky without the introduction of some rules. Before we introduce the rules, let’s look at some scenarios that involve integer subtraction.

22. Accounting Say I borrow $5 from you and buy lunch since I forgot my wallet. I owe you $5 so on my balance sheet I have -5. Later I get my wallet and pay you the $5 back so I can subtract what I owe. So we have: -5 -(-5) = -5 +5 = 0

23. Driving You are driving with cruise control set at 65 mph, which we will call your reference speed. You see a sign stating that you are entering a 55 mph zone so you slow down 10 mph ( -10). After a few miles a new sign informs you that you are entering a 65 zone again so you resume your original speed, thus removing ( subtracting ) the -10 mph modification. We thus have: -10 - (-10) = 0 or no speed modification ( thus you are moving at the reference speed of 65 again ).

24. Books You borrow 3 books from a library. You thus owe three books (-3). You read one and discover it does not cover what you want, so you return ( subtract ) it ( a borrowed book is a minus, thus a -1 ) and thus you have subtracted one book you owe, and now owe only two. And we have: -3 -(-1) = -3 + 1 = -2

25. Behavior Johnny swears and fights a lot ( two negatives ). He feels he wants to get better so he decides to stop ( thus removing or subtracting ) fighting ( a negative ). Thus he now has: -2 - (-1) = -2 + 1 = -1 or 1 negative behavior he does a lot.

26. Integer Subtraction Rule Subtracting a negative number is the same as adding a positive. Change the signs and add. 2 - (-7) is the same as 2 + (+7) and 2 + 7 = 9!

27. How do we know that “Subtracting a negative number is the same as adding a positive” is true? We can use the same method we use to check our answers when we subtract.

28. Suppose you subtract a – b and it equals c: a – b = c 5 – 2 = 3 To check if your answer is correct, add b and c: a = b + c 5 = 2 + 3

29. Here are some examples: a – b = ca = b + c 9 – 5 = 49 = 5 + 4 a – b = ca = b + c 20 – 3 = 1720 = 3 + 17

30. If the method for checking subtraction works, it should also work for subtracting negative numbers.

31. If a – b = c, and…. 2 - (-5) is the same as 2 + (+5), which equals 7, Then let’s check with the negative numbers to see if it’s true…

32. a - b = c a = b + c 2 - (-5) = 7 2 = -5 + 7 It works! a - b = ca = b + c -11 - (-3) = -8 -11 = -3 + (-8) YES!