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Adding Subtracting Integers

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Adding Subtracting Integers

  1. 1. Interesting Integers!
  2. 2. What You Will Learn
  3. 3. What You Will Learn  Some definitions related to integers.
  4. 4. What You Will Learn  Some definitions related to integers.  Rules for adding and subtracting integers.
  5. 5. What You Will Learn  Some definitions related to integers.  Rules for adding and subtracting integers.  A method for proving that a rule is true.
  6. 6. What You Will Learn  Some definitions related to integers.  Rules for adding and subtracting integers.  A method for proving that a rule is true. Are you ready??
  7. 7. Definition 0
  8. 8. Definition  Positive number – a number greater than zero. 0
  9. 9. Definition  Positive number – a number greater than zero. 0 1
  10. 10. Definition  Positive number – a number greater than zero. 0 1 2
  11. 11. Definition  Positive number – a number greater than zero. 0 1 2 3
  12. 12. Definition  Positive number – a number greater than zero. 0 1 2 3 4
  13. 13. Definition  Positive number – a number greater than zero. 0 1 2 3 4 5
  14. 14. Definition  Positive number – a number greater than zero. 0 1 2 3 4 5 6
  15. 15. Definition  Positive number – a number greater than zero. 0 1 2 3 4 5 6
  16. 16. Definition 0 1 2 3 4 5 6
  17. 17. Definition  Negative number – a number less than zero. 0 1 2 3 4 5 6
  18. 18. Definition  Negative number – a number less than zero. -1 0 1 2 3 4 5 6
  19. 19. Definition  Negative number – a number less than zero. -2 -1 0 1 2 3 4 5 6
  20. 20. Definition  Negative number – a number less than zero. -3 -2 -1 0 1 2 3 4 5 6
  21. 21. Definition  Negative number – a number less than zero. -4 -3 -2 -1 0 1 2 3 4 5 6
  22. 22. Definition  Negative number – a number less than zero. -5 -4 -3 -2 -1 0 1 2 3 4 5 6
  23. 23. Definition  Negative number – a number less than zero. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
  24. 24. Definition  Negative number – a number less than zero. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
  25. 25. Definition -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
  26. 26. Definition  Opposite Numbers – 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
  27. 27. Definition  Opposite Numbers – 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
  28. 28. Definition  Opposite Numbers – 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
  29. 29. Definition
  30. 30. Definition  Integers – Integers are all the whole numbers and all of their opposites on the negative number line including zero.
  31. 31. Definition  Integers – Integers are all the whole numbers and all of their opposites on the negative number line including zero. 7 opposite -7
  32. 32. Definition The absolute value of 9 or of –9 is 9.
  33. 33. Definition  Absolute Value – The size of a number with or without the negative sign. The absolute value of 9 or of –9 is 9.
  34. 34. Negative Numbers Are Used to Measure Temperature
  35. 35. Negative Numbers Are Used to Measure Under Sea Level 30 20 10 0 -10 -20 -30 -40 -50
  36. 36. Negative Numbers Are Used to Show Debt
  37. 37. 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.
  38. 38. Hint
  39. 39. Hint  If you don’t see a negative or positive sign in front of a number it is positive.
  40. 40. Hint  If you don’t see a negative or positive sign in front of a number it is positive. 9
  41. 41. Hint  If you don’t see a negative or positive sign in front of a number it is positive. +9
  42. 42. Integer Addition Rules
  43. 43. Integer Addition Rules  Rule #1 – If the signs are the same, pretend the signs aren’t there. Add the numbers and then put the sign of the addends in front of your answer.
  44. 44. Integer Addition Rules  Rule #1 – If the signs are the same, pretend the signs aren’t there. Add the numbers and then put the sign of the addends in front of your answer. 9 + 5 = 14
  45. 45. Integer Addition Rules  Rule #1 – If the signs are the same, pretend the signs aren’t there. Add the numbers and then put the sign of the addends in front of your answer. 9 + 5 = 14 -9 + -5 = -14
  46. 46. Solve the Problems  -3 + -5 = 4 + 7 =  (+3) + (+4) =  -6 + -7 = 5 + 9 =  -9 + -9 =
  47. 47. Solve the Problems  -3 + -5 = -8 4 + 7 =  (+3) + (+4) =  -6 + -7 = 5 + 9 =  -9 + -9 =
  48. 48. Solve the Problems  -3 + -5 = -8 4 + 7 = 11  (+3) + (+4) =  -6 + -7 = 5 + 9 =  -9 + -9 =
  49. 49. Solve the Problems  -3 + -5 = -8 4 + 7 = 11  (+3) + (+4) = 7  -6 + -7 = 5 + 9 =  -9 + -9 =
  50. 50. Solve the Problems  -3 + -5 = -8 4 + 7 = 11  (+3) + (+4) = 7  -6 + -7 = -13 5 + 9 =  -9 + -9 =
  51. 51. Solve the Problems  -3 + -5 = -8 4 + 7 = 11  (+3) + (+4) = 7  -6 + -7 = -13  5 + 9 = 14  -9 + -9 =
  52. 52. Solve the Problems  -3 + -5 = -8 4 + 7 = 11  (+3) + (+4) = 7  -6 + -7 = -13  5 + 9 = 14  -9 + -9 = -18
  53. 53. Solve the problems on Part A of your worksheet now. Click to the next slide when done.
  54. 54. Check Your Answers 1. 8 + 13 = 21 2. –22 + -11 = -33 3. 55 + 17 = 72 4. –14 + -35 = -49
  55. 55. Integer Addition Rules
  56. 56. Integer Addition Rules  Rule #2 – If the signs are different pretend the signs aren’t there. Subtract the smaller from the larger one and put the sign of the one with the larger absolute value in front of your answer.
  57. 57. Integer Addition Rules  Rule #2 – If the signs are different pretend the signs aren’t there. Subtract the smaller from the larger one and put the sign of the one with the larger absolute value in front of your answer. -9 + +5 =
  58. 58. Integer Addition Rules  Rule #2 – If the signs are different pretend the signs aren’t there. Subtract the smaller from the larger one and put the sign of the one with the larger absolute value in front of your answer. -9 + +5 = 9-5=4
  59. 59. Integer Addition Rules  Rule #2 – If the signs are different pretend the signs aren’t there. Subtract the smaller from the larger one and put the sign of the one with the larger absolute value in front of your answer. Larger abs. value -9 + +5 = 9-5=4
  60. 60. Integer Addition Rules  Rule #2 – If the signs are different pretend the signs aren’t there. Subtract the smaller from the larger one and put the sign of the one with the larger absolute value in front of your answer. Larger abs. value -9 + +5 = 9-5=4
  61. 61. Integer Addition Rules  Rule #2 – If the signs are different pretend the signs aren’t there. Subtract the smaller from the larger one and put the sign of the one with the larger absolute value in front of your answer. -9 + +5 = Larger abs. value 9 - 5 = 4 Answer = - 4
  62. 62. Solve These Problems  3 + -5 =  -4 + 7 =  (+3) + (-4) =  -6 + 7 =  5 + -9 =  -9 + 9 =
  63. 63. Solve These Problems  3 + -5 = 5 – 3 = 2  -4 + 7 =  (+3) + (-4) =  -6 + 7 =  5 + -9 =  -9 + 9 =
  64. 64. Solve These Problems  3 + -5 = 5 – 3 = 2  -4 + 7 =  (+3) + (-4) =  -6 + 7 =  5 + -9 =  -9 + 9 =
  65. 65. Solve These Problems  3 + -5 = 5 – 3 = 2 -2  -4 + 7 =  (+3) + (-4) =  -6 + 7 =  5 + -9 =  -9 + 9 =
  66. 66. Solve These Problems  3 + -5 = 5 – 3 = 2 -2  -4 + 7 = 7 – 4 = 3  (+3) + (-4) =  -6 + 7 =  5 + -9 =  -9 + 9 =
  67. 67. Solve These Problems  3 + -5 = 5 – 3 = 2 -2  -4 + 7 = 7 – 4 = 3  (+3) + (-4) =  -6 + 7 =  5 + -9 =  -9 + 9 =
  68. 68. Solve These Problems  3 + -5 = 5 – 3 = 2 -2  -4 + 7 = 7 – 4 = 3 3  (+3) + (-4) =  -6 + 7 =  5 + -9 =  -9 + 9 =
  69. 69. Solve These Problems  3 + -5 = 5 – 3 = 2 -2  -4 + 7 = 7 – 4 = 3 3  (+3) + (-4) = 4–3=1  -6 + 7 =  5 + -9 =  -9 + 9 =
  70. 70. Solve These Problems  3 + -5 = 5 – 3 = 2 -2  -4 + 7 = 7 – 4 = 3 3  (+3) + (-4) = 4–3=1  -6 + 7 =  5 + -9 =  -9 + 9 =
  71. 71. Solve These Problems  3 + -5 = 5 – 3 = 2 -2  -4 + 7 = 7 – 4 = 3 3  (+3) + (-4) = 4–3=1 -1  -6 + 7 =  5 + -9 =  -9 + 9 =
  72. 72. Solve These Problems  3 + -5 = 5 – 3 = 2 -2  -4 + 7 = 7 – 4 = 3 3  (+3) + (-4) = 4–3=1 -1  -6 + 7 = 7–6=1  5 + -9 =  -9 + 9 =
  73. 73. Solve These Problems  3 + -5 = 5 – 3 = 2 -2  -4 + 7 = 7 – 4 = 3 3  (+3) + (-4) = 4–3=1 -1  -6 + 7 = 7–6=1  5 + -9 =  -9 + 9 =
  74. 74. Solve These Problems  3 + -5 = 5 – 3 = 2 -2  -4 + 7 = 7 – 4 = 3 3  (+3) + (-4) = 4–3=1 -1  -6 + 7 = 7–6=1 1  5 + -9 =  -9 + 9 =
  75. 75. Solve These Problems  3 + -5 = 5 – 3 = 2 -2  -4 + 7 = 7 – 4 = 3 3  (+3) + (-4) = 4–3=1 -1  -6 + 7 = 7–6=1 1  5 + -9 = 9–5=4  -9 + 9 =
  76. 76. Solve These Problems  3 + -5 = 5 – 3 = 2 -2  -4 + 7 = 7 – 4 = 3 3  (+3) + (-4) = 4–3=1 -1  -6 + 7 = 7–6=1 1  5 + -9 = 9–5=4  -9 + 9 =
  77. 77. Solve These Problems  3 + -5 = 5 – 3 = 2 -2  -4 + 7 = 7 – 4 = 3 3  (+3) + (-4) = 4–3=1 -1  -6 + 7 = 7–6=1 1  5 + -9 = 9 – 5 = 4 -4  -9 + 9 =
  78. 78. Solve These Problems  3 + -5 = 5 – 3 = 2 -2  -4 + 7 = 7 – 4 = 3 3  (+3) + (-4) = 4–3=1 -1  -6 + 7 = 7–6=1 1  5 + -9 = 9 – 5 = 4 -4  -9 + 9 = 9–9=0
  79. 79. Solve These Problems  3 + -5 = 5 – 3 = 2 -2  -4 + 7 = 7 – 4 = 3 3  (+3) + (-4) = 4–3=1 -1  -6 + 7 = 7–6=1 1  5 + -9 = 9 – 5 = 4 -4  -9 + 9 = 9–9=0
  80. 80. Solve These Problems  3 + -5 = 5 – 3 = 2 -2  -4 + 7 = 7 – 4 = 3 3  (+3) + (-4) = 4–3 =1 -1  -6 + 7 = 7–6=1 1  5 + -9 = 9–5=4 -4  -9 + 9 = 9–9=0 0
  81. 81. Solve the problems on Part B of your worksheet now. Click to the next slide when done.
  82. 82. Check Your Answers 1. –12 + 22 = 10 2. –20 + 5 = -15 3. 14 + (-7) = 7 4. –70 + 15 = -55
  83. 83. One Way to Add Integers Is With a Number Line -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
  84. 84. 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. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
  85. 85. 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. + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
  86. 86. 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. + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
  87. 87. 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. - + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
  88. 88. 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. - + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
  89. 89. One Way to Add Integers Is With a Number Line +3 + -5 = -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
  90. 90. One Way to Add Integers Is With a Number Line +3 + -5 = + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
  91. 91. One Way to Add Integers Is With a Number Line +3 + -5 = + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
  92. 92. One Way to Add Integers Is With a Number Line +3 + -5 = + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -
  93. 93. One Way to Add Integers Is With a Number Line +3 + -5 = + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -
  94. 94. One Way to Add Integers Is With a Number Line +3 + -5 = -2 + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -
  95. 95. One Way to Add Integers Is With a Number Line +6 + -4 = -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
  96. 96. One Way to Add Integers Is With a Number Line +6 + -4 = + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
  97. 97. One Way to Add Integers Is With a Number Line +6 + -4 = + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
  98. 98. One Way to Add Integers Is With a Number Line +6 + -4 = + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -
  99. 99. One Way to Add Integers Is With a Number Line +6 + -4 = + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -
  100. 100. One Way to Add Integers Is With a Number Line +6 + -4 = +2 + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -
  101. 101. One Way to Add Integers Is With a Number Line +3 + -7 = -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
  102. 102. One Way to Add Integers Is With a Number Line +3 + -7 = + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
  103. 103. One Way to Add Integers Is With a Number Line +3 + -7 = + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
  104. 104. One Way to Add Integers Is With a Number Line +3 + -7 = + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -
  105. 105. One Way to Add Integers Is With a Number Line +3 + -7 = + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -
  106. 106. One Way to Add Integers Is With a Number Line +3 + -7 = -4 + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -
  107. 107. One Way to Add Integers Is With a Number Line -3 + +7 = -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
  108. 108. One Way to Add Integers Is With a Number Line -3 + +7 = - -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
  109. 109. One Way to Add Integers Is With a Number Line -3 + +7 = - -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
  110. 110. One Way to Add Integers Is With a Number Line -3 + +7 = - -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 +
  111. 111. One Way to Add Integers Is With a Number Line -3 + +7 = - -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 +
  112. 112. One Way to Add Integers Is With a Number Line -3 + +7 = +4 - -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 +
  113. 113. Integer Subtraction Rule Subtracting a negative number is the same as adding a positive. Change the signs and add.
  114. 114. Integer Subtraction Rule Subtracting a negative number is the same as adding a positive. Change the signs and add. 2 – (-7)
  115. 115. 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
  116. 116. 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)
  117. 117. 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) 2 + 7 = 9!
  118. 118. Here are some more examples.
  119. 119. Here are some more examples. 12 – (-8)
  120. 120. Here are some more examples. 12 – (-8) 12 + (+8)
  121. 121. Here are some more examples. 12 – (-8) 12 + (+8) 12 + 8 = 20
  122. 122. Here are some more examples. 12 – (-8) -3 – (-11) 12 + (+8) 12 + 8 = 20
  123. 123. Here are some more examples. 12 – (-8) -3 – (-11) 12 + (+8) -3 + (+11) 12 + 8 = 20
  124. 124. Here are some more examples. 12 – (-8) -3 – (-11) 12 + (+8) -3 + (+11) 12 + 8 = 20 -3 + 11 = 8
  125. 125. Solve the problems on Part C of your worksheet now. Click to the next slide when done.
  126. 126. 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
  127. 127. How do we know that “Subtracting a negative number is the same as adding a positive” is true?
  128. 128. 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.
  129. 129. Suppose you subtract a – b and it equals c:
  130. 130. Suppose you subtract a – b and it equals c: a–b=c
  131. 131. Suppose you subtract a – b and it equals c: a–b=c 5–2=3
  132. 132. 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:
  133. 133. 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
  134. 134. 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
  135. 135. Here are some examples:
  136. 136. Here are some examples: a–b=c a=b+c
  137. 137. Here are some examples: a–b=c a=b+c 9–5=4 9=5+4
  138. 138. Here are some examples: a–b=c a=b+c 9–5=4 9=5+4 a–b=c a=b+c
  139. 139. Here are some examples: a–b=c a=b+c 9–5=4 9=5+4 a–b=c a=b+c 20 – 3 = 17 20 = 3 + 17
  140. 140. If the method for checking subtraction works, it should also work for subtracting negative numbers.
  141. 141. If a – b = c, and….
  142. 142. If a – b = c, and…. 2 – (-5) is the same as
  143. 143. If a – b = c, and…. 2 – (-5) is the same as 2 + (+5), which equals 7,
  144. 144. 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…
  145. 145. a–b=c a=b+c
  146. 146. a–b=c a=b+c 2 – (-5) = 7 2 = -5 + 7
  147. 147. a–b=c a=b+c 2 – (-5) = 7 2 = -5 + 7 It works!
  148. 148. a–b=c a=b+c 2 – (-5) = 7 2 = -5 + 7 It works! a–b=c a=b+c
  149. 149. a–b=c a=b+c 2 – (-5) = 7 2 = -5 + 7 It works! a–b=c a=b+c -11 – (-3) = -8 -11 = -3 + -8
  150. 150. a–b=c a=b+c 2 – (-5) = 7 2 = -5 + 7 It works! a–b=c a=b+c -11 – (-3) = -8 -11 = -3 + -8 YES!
  151. 151. Solve the problems on Part D of your worksheet now. Click to the next slide when done.
  152. 152. Check Your Answers Continued on next slide
  153. 153. Check Your Answers 1. Solve: 3 – 10 = 7 Check: 3 = 10 + (-7) Continued on next slide
  154. 154. Check Your Answers 1. Solve: 3 – 10 = 7 Check: 3 = 10 + (-7) 2. Solve: 17 – ( 12) = 29 Continued on next slide
  155. 155. Check Your Answers 1. Solve: 3 – 10 = 7 Check: 3 = 10 + (-7) 2. Solve: 17 – ( 12) = 29 Continued on next slide
  156. 156. Check Your Answers 1. Solve: 3 – 10 = 7 Check: 3 = 10 + (-7) 2. Solve: 17 – ( 12) = 29 Continued on next slide
  157. 157. Check Your Answers 1. Solve: 3 – 10 = 7 Check: 3 = 10 + (-7) 2. Solve: 17 – ( 12) = 29 Check: 17 = -12 + 29 Continued on next slide
  158. 158. Check Your Answers
  159. 159. Check Your Answers 1. Solve: 20 – ( 5) = 25
  160. 160. Check Your Answers 1. Solve: 20 – ( 5) = 25
  161. 161. Check Your Answers 1. Solve: 20 – ( 5) = 25
  162. 162. Check Your Answers 1. Solve: 20 – ( 5) = 25 Check: 20 = -5 + 25
  163. 163. Check Your Answers 1. Solve: 20 – ( 5) = 25 Check: 20 = -5 + 25 1. Solve: -7 – ( 2) = -5
  164. 164. Check Your Answers 1. Solve: 20 – ( 5) = 25 Check: 20 = -5 + 25 1. Solve: -7 – ( 2) = -5
  165. 165. Check Your Answers 1. Solve: 20 – ( 5) = 25 Check: 20 = -5 + 25 1. Solve: -7 – ( 2) = -5
  166. 166. Check Your Answers 1. Solve: 20 – ( 5) = 25 Check: 20 = -5 + 25 1. Solve: -7 – ( 2) = -5 Check: -7 = -2 + -5
  167. 167. You have learned lots of things About adding and subtracting Integers. Let’s review!
  168. 168. Integer Addition Rules
  169. 169. Integer Addition Rules  Rule #1 – If the signs are the same, pretend the signs aren’t there. Add the numbers and then put the sign of the addends in front of your answer.
  170. 170. Integer Addition Rules  Rule #1 – If the signs are the same, pretend the signs aren’t there. Add the numbers and then put the sign of the addends in front of your answer. 9 + 5 = 14
  171. 171. Integer Addition Rules  Rule #1 – If the signs are the same, pretend the signs aren’t there. Add the numbers and then put the sign of the addends in front of your answer. 9 + 5 = 14 -9 + -5 = -14
  172. 172. Integer Addition Rules
  173. 173. Integer Addition Rules  Rule #2 – If the signs are different pretend the signs aren’t there. Subtract the smaller from the larger one and put the sign of the one with the larger absolute value in front of your answer.
  174. 174. Integer Addition Rules  Rule #2 – If the signs are different pretend the signs aren’t there. Subtract the smaller from the larger one and put the sign of the one with the larger absolute value in front of your answer. -9 + +5 =
  175. 175. Integer Addition Rules  Rule #2 – If the signs are different pretend the signs aren’t there. Subtract the smaller from the larger one and put the sign of the one with the larger absolute value in front of your answer. -9 + +5 = 9-5=4
  176. 176. Integer Addition Rules  Rule #2 – If the signs are different pretend the signs aren’t there. Subtract the smaller from the larger one and put the sign of the one with the larger absolute value in front of your answer. Larger abs. value -9 + +5 = 9-5=4
  177. 177. Integer Addition Rules  Rule #2 – If the signs are different pretend the signs aren’t there. Subtract the smaller from the larger one and put the sign of the one with the larger absolute value in front of your answer. Larger abs. value -9 + +5 = 9-5=4
  178. 178. Integer Addition Rules  Rule #2 – If the signs are different pretend the signs aren’t there. Subtract the smaller from the larger one and put the sign of the one with the larger absolute value in front of your answer. -9 + +5 = Larger abs. value 9 - 5 = 4 Answer = - 4
  179. 179. One Way to Add Integers Is With a Number Line -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
  180. 180. 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. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
  181. 181. 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. + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
  182. 182. 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. + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
  183. 183. 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. - + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
  184. 184. 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. - + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
  185. 185. Integer Subtraction Rule Subtracting a negative number is the same as adding a positive. Change the signs and add.
  186. 186. Integer Subtraction Rule Subtracting a negative number is the same as adding a positive. Change the signs and add. 2 – (-7)
  187. 187. 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
  188. 188. 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)
  189. 189. 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) 2 + 7 = 9!
  190. 190. How do we know that “Subtracting a negative number is the same as adding a positive” is true?
  191. 191. 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.
  192. 192. a–b=c a=b+c
  193. 193. a–b=c a=b+c 2 – (-5) = 7 2 = -5 + 7
  194. 194. a–b=c a=b+c 2 – (-5) = 7 2 = -5 + 7 It works!
  195. 195. a–b=c a=b+c 2 – (-5) = 7 2 = -5 + 7 It works! a–b=c a=b+c
  196. 196. a–b=c a=b+c 2 – (-5) = 7 2 = -5 + 7 It works! a–b=c a=b+c -11 – (-3) = -8 -11 = -3 + -8
  197. 197. a–b=c a=b+c 2 – (-5) = 7 2 = -5 + 7 It works! a–b=c a=b+c -11 – (-3) = -8 -11 = -3 + -8 YES!
  198. 198. Discuss with a partner ways that you know that that is problem is solved correctly. 6 – (-9) = 15
  199. 199. Aren’t integers interesting?

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