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Adding fractions with different signs

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    Find the sum 3 1/8 + 3/4 + ( -2 1/6)
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    Let's just do the first part first,
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    This is pretty straightforward.
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    We have two positive numbers, let me draw a
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    number line , we are going to start with 3 1/8,
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    this is 0, then we have 1, 2, 3 and then you have 4.
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    3 1/8 is going to be right about there
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    so let me just draw its absolute value
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    3 1/8, is going to be 3 1/8ths to the right of 0
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    So it is going to be exactly that distance
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    from 0 to the right.
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    The length of this arrow, you could view it as 3 1/8th.
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    Now, whenever I like to deal with fractions
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    especially when I have different denominators
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    i like to deal them with improper fractions,
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    it makes the addition, and the subtraction,
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    and actually the multiplication and divison a lot easier.
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    So 3 1/8 is the same thing as
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    8 times 3 is 24 plus one is 25 over 8.
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    which is the same thing as 3 1/8.
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    Another way to think about it,
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    3 is 24 over 8,
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    and then add 1/8 to that,
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    so that you get 25/8.
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    So this is our starting point.
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    To that we are going to add 3/4,
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    we are going to move another 3/4
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    to the right, this length of this is 3/4
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    So plus 3/4.
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    Where does this put us,
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    so both of these are positive intergers,
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    so we can just add them,
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    we just have to find the like denominators
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    we have 25/8 + 3/4. That's the same thing as,
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    we have to find the common denominator here,
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    the common denominator, or the least common multiple
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    of 4 and 8 is 8, so it's going to be something over 8.
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    To get from 4 to 8, we multiplied by 2,
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    so we have to multiply 3 by 2 as well.
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    So we get 6,
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    so 3/4 is the same thing as 6/8.
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    So we have 25/8, and we're adding 6/8 to that,
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    that gives us 25 plus 6 is
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    31, over 8.
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    So this number right over here is 31/8
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    And it makes sense, because 32/8 will be 4,
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    so it should be a litte bit less than 4
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    So this number right over here is 31/8
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    or the length of this arrow,
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    the absolute value of that number
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    is 31/8.
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    If you want to write it as a mixed number, it would be
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    3 7/8.
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    Now to that we want to add a -2 1/6.
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    So we're going to add a negative number.
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    So think about what -2 1/6 is going to be like.
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    Let me do this in a new color, do it in pink.
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    -2 1/6. So we're gonna subtract, or,
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    I guess we should say we are going to add a -1,
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    add a -2, and then a -1/6.
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    So -2 1/6, we can literally draw it like this.
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    -2 1/6, we can draw it with an arrow
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    that looks something like that,
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    so this is -2 1/6.
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    There are a couple of ways to think about it,
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    we could just say,
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    when you add this arrow, this thing is moving to the left.
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    We could put it over here
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    and you would get straight to -2 1/6.
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    But we're adding this -2 1/6,
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    it is same thing as subtracting a 2 1/6;
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    we're moving 2 1/6 to the left.
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    And we're going to end up with a number
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    whose absolute value is going to
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    look something like that.
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    It is actually going to be to the right,
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    so it's not only going to be its absolute value,
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    the absolute value is going to be the number,
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    since it's going to be a positive number.
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    So let's just think about what it is.
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    This value right here,
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    which is going to be the answer to our problem,
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    is going to be the difference of 31/8 and 2 1/6.
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    And it's a positive difference,
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    because we're dealing with a positive number.
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    So we just take 31/8, and
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    from that, we will subtract 2 1/6.
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    So this orange value is going to be 31/8
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    minus 2 1/6.
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    So 2 1/6 is the same thing as
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    6 times 2 is 12 plus 1 is 13.
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    -13/6, and this is equal to --
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    the common denominator over here -
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    once again we're going to get
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    and it looks like 24 will be the common denominator.
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    This is the 31/8, and this is the 2 1/6.
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    So 31/8, over 24, you have to multiply by 3
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    to get the 24 over here,
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    so we multiply by 3 on the 31,
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    that gives us 93.
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    And then to go from 6 to 24,
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    you have to multiply by 4,
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    I'll do that in another color,
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    so you have to multiply by 4 up here as well.
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    So 4 times 13, let's see.
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    4 times 10 is 40, 4 times 3 is 12,
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    so that's 52.
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    So this is going to be equal to
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    93 minus 52 over 24, and that is,
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    3 minus 2 is 1, 9 minus 5 is 4.
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    So it is 41/24, positive.
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    You can see that here,
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    just by looking at the number line.
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    This right here is 41/24, and it should be
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    a little bit less than 2,
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    because 2 would be 48/24.
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    So this would be 48/24, and it makes sense
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    because we're are a little bit less than that.
Title:
Adding fractions with different signs
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Video Language:
English
Duration:
06:22

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