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Adding integers with different signs

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    Find the sum 15 plus
    negative 46 plus 29.
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    Let's just think about
    this first part over here
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    where we have 15
    plus negative 46.
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    And we'll worry about
    the plus 29 later on.
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    So let's just do
    15-- let me do that
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    in a different color--
    plus negative 46.
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    I'll do it in that orange.
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    Let me draw a number line
    here, just so we can properly
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    visualize what is going on.
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    That's my number line.
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    And we're starting at 15.
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    So let's draw a 0 over here.
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    And so we're starting at 15.
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    15 could be right over here.
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    So this is 15.
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    Let me draw a big fat arrow
    to signify this is 15.
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    15 has an absolute value of
    15, so the length of this arrow
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    would be 15.
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    Now we're adding
    negative 46 to that 15.
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    This is equivalent
    to 15 minus 46,
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    which means we are going to
    move 46 spots to the left of 15.
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    A negative sign or
    a minus means we're
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    moving to the left
    on the number line.
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    So we're going to
    move 46 to the left.
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    We're starting at 15, and we are
    going to move 46 to the left.
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    So the length of this arrow
    right here is going to be 46,
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    and we're moving to the left.
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    This is the negative 46
    that we're adding to the 15.
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    We're going to end up
    at some point over here.
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    That point is clearly 0.
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    Because we were 15 to the right.
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    Now we're going to
    move 46 to the left.
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    So we're definitely going
    to be to the left of 0.
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    It's definitely going
    to be a negative number.
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    And we can even think
    about the absolute value
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    of that negative number.
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    We can just visualize it.
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    This yellow arrow
    has a length of 15.
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    This orange arrow
    has a length of 46.
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    The blue arrow that
    I'm about to draw,
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    which is the sum
    of these two, is
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    going to have this
    length right over here.
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    And just visually,
    how can we figure out
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    the length of this
    blue part if we
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    know the length of
    this orange part
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    and we know the length
    of this yellow part?
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    Well, it's just going
    to be the difference.
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    It's just going to be the
    difference of these two.
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    So the absolute
    value of the sum is
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    going to be the difference
    between this length, 46,
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    and 15.
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    Let me just figure
    that out, 46 minus 15.
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    6 minus 5 is 1.
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    4 minus 1 is 3.
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    So the length of this
    is going to be 31,
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    and it's going to be
    31 to the left of 0.
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    So this is going to be
    negative 31 right over here.
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    We know that this first part
    over here is negative 31,
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    and then to that we
    are going to add 29.
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    So we're going to add 29.
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    Let me do that in another color.
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    What does that mean?
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    That means that we're going
    to start at negative 31,
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    and we're going to
    move 29 to the right.
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    We're adding 29, so we're
    going to move 29 to the right.
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    So maybe that gets
    us right about there.
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    I'm trying to draw an
    arrow of length 29.
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    I can draw a cleaner
    looking arrow than that.
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    I'll do it right
    over here, actually.
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    So then we're going to
    move 29 over to the right.
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    That's the 29 part.
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    Now this is a positive
    29, and so how
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    do we figure out what this is?
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    This is 29 right here
    that we're adding.
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    This is going to land us right
    over here on the number line.
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    So how do we figure out
    what number that is?
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    Well, once again, we
    can just visualize it.
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    And eventually you won't have
    to draw number lines and stuff,
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    but I think it'll
    be useful here.
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    We're starting at negative 31.
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    We're adding 29 to it, so it's
    going to make it less negative.
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    But we're still
    adding less than 31,
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    so we're not going to get
    all the way back to 0.
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    We're still going to
    have a negative number.
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    But how could we figure
    out the absolute value
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    of that negative
    number, its distance?
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    Well, once again, that little
    white part right there,
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    that white part plus
    this 29, is going
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    to equal 31, if you just
    think of absolute value,
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    if we don't think
    about the signs,
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    if we just think
    about the length.
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    Or another way to think
    about it, 31 minus 29
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    will give us the length
    of that white part.
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    And of course, it's
    going to be negative,
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    because the negative
    number here is
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    larger than the positive number.
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    And we're adding the 2.
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    If we do 31 minus 29, you
    could borrow and all of that,
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    but that's clearly just
    going to be equal to 2.
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    You could say that's 11.
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    This is a 2.
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    You subtract, this
    is equal to 2.
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    But since it's
    negative 31 plus 29,
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    it's going to be a negative 2.
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    We're still going
    to stay negative.
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    We haven't moved far to
    the right enough to pass 0.
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    So this right here is
    going to be negative 2.
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    Or another way to
    think about it,
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    the length of this white
    bar, the absolute value,
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    is going to be 2.
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    2 plus 29 is 31.
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    But we're operating to the
    left of 0, so it's negative 31.
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    This is negative 2.
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    Anyway, hopefully you
    found that useful.
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    And let me make it clear.
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    Our final answer is negative 2.
Title:
Adding integers with different signs
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Video Language:
English
Duration:
05:32

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