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← Adding integers with different signs

Adding integers with different signs

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Showing Revision 6 created 10/22/2013 by Hitoshi Yamauchi.

  1. Find the sum of 15 plus -46 plus 29.
  2. So lets just think about the first part over here
  3. We have 15 plus -46, we will worry about +29 later on.
  4. So lets do 15 plus -46. We will get a different color.
  5. We will do it orange. Plus -46.
  6. So we draw a number line here.
  7. Just we can properly visualize what is going on.
  8. That's my number line.
  9. We are starting 15. Let me put 0 over here and we're starting with 15.
  10. 15 could be right over here. So this is 15. Let me draw a big fat arrow to signify this is 15
  11. 15 has an absolute value of 15.
  12. So the length of this arrow would be 15.
  13. Now, we are adding -46 to that 15, that is the same thing...
  14. This is equaivalent to 15-46, which means we are going to move
  15. 46 spots to the left of 15.
  16. Negative sign or minus needs to be the left on the number line.
  17. So we are going to 46 to the left.
  18. So we are starting with 15 and we are going to move 46 to the left.
  19. The length of this arrow right here is going to be 46.
  20. We are moving to the left. This is the negative 46 we are adding to the 15.
  21. We are going to end up at some point over here.
  22. That point is clearly 0. We were 15 to the right. Now we are goig to move 46 to the left.
  23. So we are definitely going to be the left of 0.
  24. So it's definitely going to a negative number.
  25. We can even think about the absolute value of that negative number. We can just visualize it.
  26. This yellow arrow has the length of 15 and this orange arrow has the length of 46
  27. The blue arrow that I am going about to draw which is the sum of these two
  28. is going to be have this length, right over here.
  29. And just visually, how can we figure out the length of the blue part.
  30. If we know the length of this orange part and we know the length of this yellow part.
  31. Well, it's just going to be the difference.
  32. It's just going to be the difference of these two. So the absolute value of the sum is
  33. going to be the difference between this length 46 and 15.
  34. So this is 46... Let me just figure it out. 46 - 15. 6 - 5 is 1, 4 - 1 is 3.
  35. The length of this is going to be 31.
  36. and it's going to be 31 to the left of 0. This is going to be -31, right over here.
  37. So we know the first part over here is -31 and then to that
  38. we are going to add 29. Let me do that another color.
  39. So what does that mean. That means we start at -31.
  40. So we are gonna move 29 to the right. We are adding 29.
  41. So we are gonna to move 29 to the right. Maybe that is right about there. The arrow of length 29.
  42. I can draw a cleaner looking arrow than that. I'll do it right over here actually.
  43. So then we are going to 29 over to the right.
  44. That's the 29 part.
  45. So now this is the positive 29.
  46. So how do we figure out what this is.
  47. So this is going to land us... So this number, ... This is 29 right here that we are adding.
  48. This is going to land us right over here on the number line
  49. So how do we figure out that number that is?
  50. Well, once again we can just visualize it and eventually you want to draw a number line and the stuffs.
  51. I think it'll be useful here. The number we are going to do.
  52. We are starting from -31 and adding 29 to it.
  53. Since we are adding a number less than -31,
  54. we are not going to get all the way back to 0.
  55. So we are stilll going to have a negative number
  56. But how to figure out the absolute value of that negative number, it's distance.
  57. Once again, the little white part right there, that white part plus this 29 is going to equal to 31.
  58. If we just think of the absolute value.
  59. If we don't think about the signs, we just think about the length.
  60. Or another way to think about is, 31-29 will give us the length of the white part
  61. and of course it's going to be negative. Because the negative number here is larger than the positive number.
  62. We are adding the two.
  63. So, 31-29, you can borrow and all of that. But it's clearly just going to equal to 2. You could say, that's 11, this is 2.
  64. Subtract. This is equal to 2. Since it is -31 plus 29, it's going to be a negative 2.
  65. We are still going to stay negative. We haven't moved far to the right enough to pass 0.
  66. This right here is going to be negative 2.
  67. Or another way to think about is that the length of the white bar, the absolute value is going to be 2.
  68. 2 + 29 is 31. We are operating to left to 0. So it's negative 31. This is -2.
  69. Anyway, hopefully you found that useful.
  70. Oh anyway, I would like to make it clear.
  71. So our final answer is negative 2.