Integers

1. Integers

3. Definition • Positive integer – a number greater than zero. 0 1 2 3 4 5 6

4. Definition • Negative number – a number less than zero. -6 -5 -4 -3 -2 -1 0 1 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 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

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

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 30 20 10 0 -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: -8 • -3 + -5 = • 4 + 7 = • (+3) + (+4) = • -6 + -7 = • 5 + 9 = • -9 + -9 = +11 +7 -13 14 -18

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 = Larger absolute value: Answer = - 4 9 - 5 = 4

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

21. Solve the following: • 1. –12 + 22 = • –20 + 5 = • 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. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 One Way to Add Integers Is With a Number Line When the number is positive, count to the right. When the number is negative, count to the left. - +

24. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 One Way to Add Integers Is With a Number Line - +

25. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 One Way to Add Integers Is With a Number Line Answer: +3 + -5 = -2 - +

26. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 One Way to Add Integers Is With a Number Line - +

27. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 One Way to Add Integers Is With a Number Line Answer: +6 + -4 = +2 - +

28. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 One Way to Add Integers Is With a Number Line - +

29. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 One Way to Add Integers Is With a Number Line Answer: +3 + -7 = -4 - +

30. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 One Way to Add Integers Is With a Number Line + -

31. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 One Way to Add Integers Is With a Number Line 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 #2 When multiplying two integers with different signs, the product is always negative. • Rule #3 If the number of negative signs is even, the product is always positive. • Rule #4 If 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 #2 When 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. -486 n - 6

46. Aren’t integers interesting?