Integers

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Integers

  1. 1. INTEGERSINTEGERS
  2. 2. What is anInteger?
  3. 3. • An integer is a positive ornegative whole number,including 0.…-3, -2, -1, 0, 1, 2, 3…
  4. 4. There are“4”IntegerOperations
  5. 5. 4 Integer Operations• Addition +• Subtraction -• Multiplication x• Division ÷
  6. 6. Rule #1 forAdding Integers (+)• The sum of two positive integers isalways positive.5 + 1 = 6
  7. 7. Rule #2 forAdding Integers (+)• The sum of two negative integers isalways negative.-5 + (-1) = -6
  8. 8. Rule #3 forAdding Integers (+)• The sum of a positive and a negativeinteger could be positive, negative, orzero.
  9. 9. Rule #3 forAdding Integers Continued• When you add a positive and negativeinteger, you are really subtracting. Then,you give the answer the sign of thegreater absolute value.5 + (-1) = -4-5 + 1 = 4-5 + (-5) = 0
  10. 10. Let’s Practice “Addition”1) 5 + 6 =2) -3 + (-2) =3) -6 + 5 =4) 8 + (-7) =5) -9 + 9 =
  11. 11.  Let’s Check1) 5 + 6 = 112) -3 + (-2) = -53) -6 + 5 = -14) 8 + (-7) = 15) -9 + 9 = 0
  12. 12. Rules forSubtracting Integers (-)• To subtract an integer, add itsopposite.• You will need to correctly change allsubtraction problems into additionproblems!
  13. 13. How do youchange asubtractionproblem into anaddition problem?
  14. 14. There are three steps:1. Keep the first integer the same.(Same)2. Change the subtraction sign into anaddition sign. (Change)3. Take the opposite of the number thatimmediately follows the newly placedaddition sign. (Change)
  15. 15. Examples:5 – (-2) = 5 + 2 = 7-5 – 2 = -5 + (-2) = -7Think …Same, Change, Change
  16. 16. Let’s Practice “Subtraction”1) 5 – 2 =2) -3 – 4 =3) -1 – (-2) =4) -5 – (-3) =5) 7 – (-6) =
  17. 17.  Let’s Check1) 5 – 2 = 5 + (-2) = 32) -3 – 4 = -3 + (-4) = -73) -1 – (-2) = -1 + 2 = 14) -5 – (-3) = -5 + 3 = -25) 7 – (-6) = 7+ 6 = 13
  18. 18. Rules forMultiplying Integers (x)• The product of two integers with thesame signs is POSITIVE.• The product of two integers withdifferent signs is NEGATIVE.
  19. 19. Rules Summary forMultiplication• Positive x Positive = Positive• Negative x Negative = Positive• Positive x Negative= Negative• Negative x Positive = Negative
  20. 20. Let’s Practice “Multiplication”1) 6 x (-3) =2) 3 x 3 =3) -4 x 5 =4) -6 x (-2) =5) -7 x (-8) =
  21. 21.  Let’s Check1) 6 x (-3) = -182) 3 x 3 = 93) -4 x 5 = -204) -6 x (-2) = 125) -7 x (-8) = 56
  22. 22. Did you know thatthe rules formultiplication anddivision are thesame?
  23. 23. Guess what….They are!
  24. 24. The rules for division are exactlythe same as those for multiplication.If we were to take the rules formultiplication and change themultiplication signs to division signs,we would have an accurate set ofrules for division.
  25. 25. Rules forDividing Integers (÷)• The quotient of two integers withthe same signs is POSITIVE.• The quotient of two integers withdifferent signs is NEGATIVE.
  26. 26. Rules Summary forDivision• Positive ÷ Positive = Positive• Negative ÷ Negative = Positive• Positive ÷ Negative= Negative• Negative ÷ Positive = Negative
  27. 27. Let’s Practice “Division”1) 18 ÷ (-2) =2) -48 ÷ (-6) =3) -27 ÷ 9 =4) 64 ÷ 8 =5) 30 ÷ (-5) =
  28. 28.  Let’s Check1) 18 ÷ (-2) = -92) -48 ÷ (-6) = 83) -27 ÷ 9 = -34) 64 ÷ 8 = 85) 30 ÷ (-5) = -6
  29. 29. Let’s Review…
  30. 30. What is an integer?
  31. 31. ANSWER• An integer is a positive ornegative whole number,including 0.
  32. 32. Can you give an exampleof an integer?
  33. 33. ANSWER• …-3, -2, -1, 0, 1, 2, 3…
  34. 34. What are the fouroperations?
  35. 35. ANSWER• The four operations are:addition, subtraction,multiplication, and division.
  36. 36. How do you addintegers?
  37. 37. ANSWER• The sum of two positive integers is alwayspositive.• The sum of two negative integers is alwaysnegative.• When you add a positive and negativeinteger, you are really subtracting. Then, yougive the answer the sign of the greaterabsolute value.
  38. 38. How do yousubtract integers?
  39. 39. ANSWER• To subtract an integer, add itsopposite.• Same, Change, Change
  40. 40. How do you multiplyintegers?
  41. 41. ANSWER• If the signs are the same, your answeris always positive.• If the signs are different, your answeris always negative.
  42. 42. How do you divideintegers?
  43. 43. ANSWER• If the signs are the same, your answer isalways positive.• If the signs are different, your answer isalways negative.*Multiplication and Division Rules are thesame!

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