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Math Help - The "Keep, change, flip" Method with Integers, how do I know when I have to use it

  1. #1
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    Question The "Keep, change, flip" Method with Integers, how do I know when I have to use it

    Please help.

    For example,
    -3+5-(-2)=
    (for some reason it had to change two of the signs that are bolded instead of using the minuses again.)
    2+(+2)
    answer:
    4

    In this other example I'm about to show you doesn't need to "keep, change, flip":
    9-5+(-4)+3=
    4+(-4)+3=
    0+3=
    3

    I just don't understand why some of these problems on Combining Integers use keepchangeflip but others don't. I wouldn't know whether I'd need to use it or not...do any of you know what I'm talking about? lol.
    Last edited by mr fantastic; September 11th 2009 at 05:19 AM. Reason: Deleted the dramatics.
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  2. #2
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    Quote Originally Posted by dandelionclockk View Post
    please help.

    For example,
    -3+5-(-2)=
    (for some reason it had to change two of the signs that are bolded instead of using the minuses again.)
    2+(+2)
    answer:
    4

    in this other example i'm about to show you doesn't need to "keep, change, flip":
    9-5+(-4)+3=
    4+(-4)+3=
    0+3=
    3

    i just don't understand why some of these problems on combining integers use keepchangeflip but others don't. I wouldn't know whether i'd need to use it or not...do any of you know what i'm talking about? Lol.
    -3+5-(-2) = -3+5+2 = 4.

    9-5+(-4)+3 = 9-5-4+3 = 3.
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  3. #3
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    I had never heard of "keep, change, flip" before! But basically, you are just talking about the fact that (-1)*(-1)= +1 or, more generally, that the product of two negative numbers is negative. And, you can always think of a "+" in front of a number as meaning "times +1" and a "-" in front of a number as meaning "times -1".

    In your first example, -3+ 5- (-2), that "-(-2)" is (-1)(-2)= +2. That's why it is the same as -3+ 5+ 2. -3+ 5= 2 and 2+ 2= 4. -3+ 5-(-2)= 4.

    The other example, 9-5+(-4)+3, doesn't have that "double negative": (+1)(-4)= -4 so it is 9- 5- 4+ 3. 9-5= 4, 4- 4= 0, and 0+ 3= 3. 9- 5- 4+ 3= 3.
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  4. #4
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    Quote Originally Posted by mr fantastic View Post
    -3+5-(-2) = -3+5+2 = 4.

    9-5+(-4)+3 = 9-5-4+3 = 3.
    You changed some of the signs; How do you know when you're allowed to?

    example, 9-5+(-4)+3=
    What of I change the signs to 9-5-(4)-3= How do I know when not to do that? I changed the signs without knowing what I actually needed to change. It's probably all wrong now. But because I didn't know what to change and why I had to change them.
    Am I making sense? lol.
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  5. #5
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    Here are the rules:

    When two negative signs exist next to one another they become positive:

    Example: 2--2 (notice the two negative signs) will simply become 2+2.

    When a negative sign and a positive sign sit next to one another they become negative:

    Example: 2-+2 (notice the conflicting signs) will simply become 2-2

    When a positive and a positive sign sit next to one another they remain positive:

    Example: 2++2 (notice the two plus signs) will simply become 2+2


    Note: These are the general rules, it's much easier to understand what's going on if you can visualize the number plane and grasp what influence the operator is having on a number.

    Have you been taught about the number plane and directed numbers?
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    Quote Originally Posted by Finley View Post
    Here are the rules:

    When two negative signs exist next to one another they become positive:

    Example: 2--2 (notice the two negative signs) will simply become 2+2.

    When a negative sign and a positive sign sit next to one another they become negative:

    Example: 2-+2 (notice the conflicting signs) will simply become 2-2

    When a positive and a positive sign sit next to one another they remain positive:

    Example: 2++2 (notice the two plus signs) will simply become 2+2


    Note: These are the general rules, it's much easier to understand what's going on if you can visualize the number plane and grasp what influence the director is having on a number.

    Have you been taught about the number plane and directed numbers?

    Thank youuuuuu. About time.
    And no I don't think I've ever heard of the number plane and directed numbers. What are they?
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  7. #7
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    Well, this is a section of the standard number plane, obviously it goes on for an infinite amount of numbers! It's comprised of both a negative and a positive region:

    http://img11.imageshack.us/i/34559785.jpg/

    Now, let's pose ourselves a question:
    What is 2--2? (Notice the two negative signs)!

    We can use the logic involved in a number plane to visualize what is actually happening, rather than blindly applying some rules.

    http://img15.imageshack.us/i/numberplane2.jpg/

    What this represents:

    The first minus sign after the first 2 tells us we're moving in a negative direction on the number plane, correct? If the question was simply 2-2 the resultant would be 0, which is left of 2 (or in the negative direction).

    However!!!!!!!!! The second minus sign (2--) yet again reverses our direction so we move in a positive direction.

    In other words, if we move backwards and then reverse (or minus) our movement, we'll be moving in the opposite direction (forwards).

    The same logic applies, we're initially moving in a negative direction (because of the first minus) but this reverses due to the second minus and we must head in the positive direction of the number plane.




    Alternatively, we could apply the rule which makes things quick and efficient:

    When two negative signs exist next to one another they become positive:

    Example: 2--2 (notice the two negative signs) will simply become 2+2.
    So 2--2 will become 2+2

    Is this making any sense?
    Last edited by Finley; September 12th 2009 at 05:47 PM.
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    Question

    Hmm interesting. Yes I think I understand.
    But here's one problem I don't get:
    9-5+(-4)+3=
    I change the signs by the rules you told me so=
    9-5-4+3= is 4 on google, but my teacher got 3.
    I changed the 5+(-4) because like you said since + and - are close together they become negative so I wrote - . Then I had +3 left so I wrote that down too.
    So, what did I do wrong if I did anything wrong?
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  9. #9
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    Google's wrong then?

    9-5-4+3=3 is 100% right

    9 - 5 is 4
    4 - 4 is 0
    0 + 3 is 3?
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  10. #10
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    Quote Originally Posted by dandelionclockk View Post
    9-5-4+3= is 4 on google, but my teacher got 3.
    9-5-4+3= - Google Search=

    By the way, you can get 3 by counting on your fingers and toes
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  11. #11
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    Quote Originally Posted by Wilmer View Post
    More to the point: 9-5+(-4)+3 - Google Search

    Quote Originally Posted by Wilmer View Post
    [snip]
    By the way, you can get 3 by counting on your fingers and toes
    Some people wear shoes.
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  12. #12
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    Quote Originally Posted by Finley View Post
    Google's wrong then?

    9-5-4+3=3 is 100% right

    9 - 5 is 4
    4 - 4 is 0
    0 + 3 is 3?
    2+-8-(-3)
    I did:
    2-8+3=
    6+3=9 But my teach got -3.
    I don't understand this one if she happened to get -3 and I got 9.
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  13. #13
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    Quote Originally Posted by dandelionclockk View Post
    2+-8-(-3)
    I did:
    2-8+3=
    6+3=9 But my teach got -3.
    I don't understand this one if she happened to get -3 and I got 9.
    2- 8 is -6 NOT 6. You need to take greater care.
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