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← Alternate mental subtraction method

How I subtract in my head

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Showing Revision 20 created 11/19/2011 by Напуснал потребител.

  1. I want to show you a way that,
    at least, I find more useful to

  2. subtract numbers in my head.
  3. And I do it this way-- it's
    not necessarily faster on
  4. paper, but it allows you to
    remember what you're doing.
  5. Because if you start borrowing
    and stuff it becomes very hard
  6. to remember what's
    actually going on.
  7. So let's try out a
    couple of problems.
  8. Let's have nine thousand four hundred fifty-six minus seven thousand five hundred eighty-nine.
  9. So the way I do
    this in my head.
  10. I say that nine thousand four hundred fifty-six minus
    seven thousand five hundred eighty-nine-- you have to
  11. remember the two numbers.
  12. So the first thing I do is
    I say, well, what's nine thousand four hundred fifty-six
  13. minus just seven thousand?
  14. That's pretty easy because I
    just take nine thousand minus seven thousand.
  15. So what I can do is I'll
    cross out this and I'll
  16. subtract seven thousand from it.
  17. And I'm going to get two thousand four hundred fifty six.
  18. So in my head I tell myself
    that nine thousand four hundred fifty-six minus seven thousand five hundred eighty-nine is the
  19. same thing as-- if I just
    subtract out the seven thousand--
  20. as two thousand four hundred fifty-six minus five hundred eighty-nine.
  21. I took the seven thousand out
    of the picture.
  22. I essentially subtracted it
    from both of these numbers.
  23. Now, if I want to do two thousand four hundred fifty-six
    minus five hundred eighty-nine what I do is I
  24. subtract five hundred from both
    of these numbers.
  25. So if I subtract five hundred from
    this bottom number,
  26. this five will go away.
  27. And if I subtract five hundred from this
    top number, what happens?
  28. What's two thousand four hundred fifty-six minus five hundred?
  29. Or an easier way to
    think about it?
  30. What's twenty-four minus five?
  31. Well, that's nineteen.
  32. So it's going to be one thousand nine hundred fifty-six.
  33. Let me scroll up a little bit.
  34. So it's one thousand nine hundred fifty six.
  35. So my original problem has now
    been reduced to one thousand nine hundred fifty-six minus eighty-nine.
  36. Now I can subtract eighty from both
    that number and that number.
  37. So if I subtract eighty from this
    bottom number the eight disappears.
  38. Eighty-nine minus eighty is just nine.
  39. And I subtract eighty from this top
    number, I can just think of,
  40. well, what's one hundred ninety-five minus eight?
  41. Well, one hundred ninety-five minus eight, let's see.
  42. Fifteen minus eight is seventeen.
  43. So one hundred ninety-five minus eight is going
    to be one hundred eighty-seven and then you
  44. still have the six there.
  45. So essentially I said,
    one thousand nine hundred fifty-six minus eighty is one thousand eight hundred seventy-six.
  46. And now my problem has been
    reduced to one thousand eight hundred seventy-six minus nine.
  47. And then we can do
    that in our head.
  48. What's seventy-six minus nine?
  49. That's what?
  50. Sixty-seven.
  51. So our final answer is one thousand eight hundred sixty-seven.
  52. And as you can see this isn't
    necessarily faster than the way
  53. we've done it in other videos.
  54. But the reason why I like it
    is that at any stage, I just
  55. have to remember two numbers.
  56. I have to remember my
    new top number and my
  57. new bottom number.
  58. My new bottom number is always
    just some of the leftover
  59. digits of the original
    bottom number.
  60. So that's how I like to
    do things in my head.
  61. Now, just to make sure that we
    got the right answer and maybe
  62. to compare and contrast
    a little bit.
  63. Let's do it the
    traditional way.
  64. Nine thousand four hundred fifty-six minus seven thousand five hundred eighty-nine.
  65. So the standard way of doing
    it, I like to do all my
  66. borrowing before I do any of my
    subtraction so that I can stay
  67. in my borrowing mode, or you
    can think of it as regrouping.
  68. So I look at all of my numbers
    on top and see, are they all
  69. larger than the numbers
    on the bottom?
  70. And I start here at the right.
  71. Six is definitely not larger
    than nine, so I have to borrow.
  72. So I'll borrow ten or I'll
    borrow one from the tens place,
  73. which ends up being ten.
  74. So the six becomes a sixteen and
    then the five becomes a four.
  75. Then I go to the tens place.
  76. Four needs to be larger than
    eight, so let me borrow one
  77. from the hundreds place.
  78. So then that four becomes a fourteen
    or fourteen tens because
  79. we're in the tens place.
  80. And then this four becomes a three.
  81. Now these two columns or places
    look good, but right here I
  82. have a three, which is
    less than a five.
  83. Not cool, so I have
    to borrow again.
  84. That three becomes a thirteen and
    then that nine becomes an eight.
  85. And now I'm ready to subtract.
  86. So you get sixteen minus nine is seven.
  87. Fourteen minus eight is six.
  88. Thirteen minus five is eight.
  89. Eight minus seven is one.
  90. And lucky for us, we
    got the right answer.
  91. I want to make it very clear.
  92. There's no better
    way to do this.
  93. This way is actually kind of
    longer and it takes up more
  94. space on your paper than this
    way was, but this for me,
  95. is very hard to remember.
  96. It's very hard for me to keep
    track of what I borrowed and
  97. what the other number
    is and et cetera.
  98. But here, at any point
    in time, I just have to
  99. remember two numbers.
  100. And the two numbers get
    simpler every step that I
  101. go through this process.
  102. So this is why I think
    that this is a little
  103. bit easier in my head.
  104. But this might be, depending on
    the context, easier on paper.
  105. But at least here you didn't
    have to borrow or regroup.
  106. Well, hopefully you find
    that a little bit useful.