1. Integers

3. Definition Positive integer – a number greater than zero. 0123456

4. Definition Negative number – a number less than zero. 0123456-2-3-4-5-6

5. Place the following integers in order from least to greatest: 297 -56 39 -125 78 0

6. Place the following integers in order from least to greatest: 297 -56 39 -125 78 0 -125 -56 0 39 78 297

7. Definition Opposite Numbers OR Additive Inverse – numbers that are the same distance from zero in the opposite direction 0123456-2-3-4-5-6

8. Definition Integers – all whole numbers and their opposites on the number line, including zero. 7 opposite -7

9. Definition Absolute Value – The distance a number is from zero on the number line The absolute value of 9 or of –9 is 9.

10. Negative Numbers Are Used to Measure Temperature

11. Negative Numbers Are Used to Measure Below Sea Level 0 10 20 30 -10 -20 -30 -40 -50

12. Negative Numbers Are Used to Show Debt Let’s say your parents bought a car but had to get a loan from the bank for $5,000. When counting all their money they add in -$5,000 to show they still owe the bank.

13. Hint If you don’t see a negative or positive sign in front of a number, it is ALWAYS positive. 9 +

14. Integer Addition Rules Rule #1 – When adding two integers with the same sign, ADD the numbers and keep the sign. 9 + 5 = 14 -9 + -5 = -14

15. Solve the Following Problems: -3 + -5 = 4 + 7 = (+3) + (+4) = -6 + -7 = 5 + 9 = -9 + -9 =

16. Check Your Answers : -3 + -5 = 4 + 7 = (+3) + (+4) = -6 + -7 = 5 + 9 = -9 + -9 = -8 -18 14 -13 +7 +11

17. Solve the following: 1. 8 + 13 = 2. –22 + -11 = 3. 55 + 17 = 4. –14 + -35 =

18. Check Your Answers 1. 8 + 13 = +21 2. –22 + -11 = -33 3. 55 + 17 = +72 4. –14 + -35 = -49

19. Integer Addition Rules Rule #2 – When adding two integers with different signs, find the difference (SUBTRACT) and take the sign of the larger number. -9 + +5 = 9 - 5 = 4 Larger absolute value: Answer = - 4

20. Solve These Problems 3 + -5 = -4 + 7 = (+3) + (-4) = -6 + 7 = 5 + -9 = -9 + 9 = -2 5 – 3 = 2 0 -4 +1 +3 9 – 9 = 0 9 – 5 = 4 7 – 6 = 1 4 – 3 = 1 7 – 4 = 3

21. Solve the following: 1. –12 + 22 = 2. –20 + 5 = 3. 14 + (-7) = 4. –70 + 15 =

22. Check Your Answers 1. –12 + 22 = +10 2. –20 + 5 = -15 3. 14 + (-7) = +7 4. –70 + 15 = -55

23. One Way to Add Integers Is With a Number Line 0123456-2-3-4-5-6 When the number is positive, count to the right. When the number is negative, count to the left. +-

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

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

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

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

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

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

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

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

32. Integer Subtraction Rule Subtracting a negative number is the same as adding a positive one. Change the sign and add. “Keep, change, change.” 2 – (-7) is the same as 2 + (+7) 2 + 7 = 9

33. Here are some more examples. 12 – (-8) 12 + (+8) 12 + 8 = 20 -3 – (-11) -3 + (+11) -3 + 11 = 8

34. Solve the following: 1. 8 – (-12) = 2. 22 – (-30) = 3. – 17 – (-3) = 4. –52 – 5 =

35. Check Your Answers 1. 8 – (-12) = 8 + 12 = +20 2. 22 – (-30) = 22 + 30 = +52 3. – 17 – (-3) = -17 + 3 = -14 4. –52 – 5 = -52 + (-5) = -57

36. Integer Multiplication Rules Rule #1 When multiplying two integers with the same sign, the product is always positive. Rule #2When multiplying two integers with different signs, the product is always negative. Rule #3If the number of negative signs is even, the product is always positive. Rule #4If the number of negative signs is odd, the product is always negative.

37. Solve the following: 1. +8 x (-12) = 2. -20 x +30 = 3. – 17 x (-3) = 4. +50 x +5 =

38. Check Your Answers: 1. +8 x (-12) = -96 2. -20 x +30 = -600 3. – 17 x (-3) = +51 4. +50 x +5 = +250

39. Integer Division Rules Rule #1 When dividing two integers with the same sign, the quotient is always positive. Rule #2When dividing two integers with different signs, the quotient is always negative.

40. Solve the following: 1. (-36) ÷ 4 = 2. 200 ÷ -5 = 3. – 18 ÷ (-9) = 4. +50 ÷ +5 =

41. Check Your Work: 1. (-36) ÷ 4 = -9 2. 200 ÷ -5 = -40 3. – 18 ÷ (-9) = +2 4. +50 ÷ +5 = +10

42. Evaluate the following: 1. -45 + 10 3² - 2 2. 7 + -4(9 – 4) = 3. -50 ÷ 5² + (3 - 6) =

43. Check Your Work: 1. -45 + 10-35 = -5 3² - 2 7 2. 7 + -4(9 – 4) = -13 3. -50 ÷ 5² + (3 - 7) = -6

44. Evaluate the following if n = -2 : 1. -5 (2n – 2)² 2. -48 n - 6

45. Check Your Work: 1. -5 (2n – 2)²-180 2. -48 6 n - 6

46. Aren’t integers interesting?