Results 1 to 14 of 14

Math Help - help! how to deal with negative fractions?

  1. #1
    Member
    Joined
    Sep 2006
    Posts
    99

    help! how to deal with negative fractions?

    This problem completely confuses me as it had negative fractions. The answer that I worked out is different from the answer key.

    Simplify:

    (3a/-b) (b^2/6b) (b/-a)

    = (3/6) (a/-a) (b^3/-b^2)

    = (1/2) (-a^0) (-b^1)

    = (1/2) (1) (-b)

    = -b/2

    The answer key gives +b/2 as the answer.

    Should the negative sign in (3a/-b) be applied to 3 as well, such that step 2 would be:

    (-3/6) (a/-a) (b^3/-b^2)

    By having a -3, I could simplify the expression to +b/2. Does this mean that the negative sign in -b should be applied to 3 as well?

    Please help, I can't find any resource that discusses simplifying negative fractions. Thanks in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Quick's Avatar
    Joined
    May 2006
    From
    New England
    Posts
    1,024
    -a^0 does not equal 1, it equals -1

    remember it really says: -1a^0

    thus: -1(a^0)

    then: -1(1)

    finally: -1
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2006
    Posts
    99
    That was quick. Thanks!

    I didn't know what -a^0 is. So I put in something like -22^0 in the calculator and it gives me a 1, so I thought -a^0 is 1. Your proof of -a^0 is equal -1 certainly helps.

    (3a/-b) (b^2/6b) (b/-a)

    = (3/6) (a/-a) (b^3/-b^2)

    I'm not good in math, my head is still spinning about negative fractions. Since the mistake is in -a^0, I think the (3/6) in the second step is correct. It should not be (-3/6). It sounds silly to ask this, I'm thinking in terms of other questions, Is that right? Thanks again.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member classicstrings's Avatar
    Joined
    Mar 2006
    Posts
    175
    Awards
    1
    Quote Originally Posted by shenton View Post
    That was quick. Thanks!

    I didn't know what -a^0 is. So I put in something like -22^0 in the calculator and it gives me a 1,
    That should not be the case.....-22^0 = -1 too

    Maybe the calculator thinks (-22)^0 = 1
    but -22^0 = -1
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Sep 2006
    Posts
    99
    Quote Originally Posted by classicstrings View Post
    Maybe the calculator thinks (-22)^0 = 1
    but -22^0 = -1

    I am at loss now.

    My calculator, Casio fx-550s computes -22^0 = 1

    This web based exponent calculator, Exponential Expression Calculator computes -22^0 = 1

    It is hard to imagine this one as it is in the negative sign.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member classicstrings's Avatar
    Joined
    Mar 2006
    Posts
    175
    Awards
    1
    Quote Originally Posted by shenton View Post
    I am at loss now.

    My calculator, Casio fx-550s computes -22^0 = 1

    This web based exponent calculator, Exponential Expression Calculator computes -22^0 = 1

    It is hard to imagine this one as it is in the negative sign.
    I'm not sure...

    See picture... top on is TI-84 Plus, bottom CASIO fx-82MS

    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member Glaysher's Avatar
    Joined
    Aug 2006
    From
    Newton-le-Willows
    Posts
    224
    Quote Originally Posted by shenton View Post
    I am at loss now.

    My calculator, Casio fx-550s computes -22^0 = 1

    This web based exponent calculator, Exponential Expression Calculator computes -22^0 = 1

    It is hard to imagine this one as it is in the negative sign.
    The web based calculator should get 1 as it is really calculating (-22)^0

    Your calculator should require brackets to get 1 and get -1 without them
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor Quick's Avatar
    Joined
    May 2006
    From
    New England
    Posts
    1,024
    Quote Originally Posted by shenton View Post
    I'm not good in math, my head is still spinning about negative fractions. Since the mistake is in -a^0, I think the (3/6) in the second step is correct. It should not be (-3/6). It sounds silly to ask this, I'm thinking in terms of other questions, Is that right? Thanks again.
    All of the work in your original post except -a^0 was correct
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,841
    Thanks
    320
    Awards
    1
    Quote Originally Posted by shenton View Post
    That was quick. Thanks!

    I didn't know what -a^0 is. So I put in something like -22^0 in the calculator and it gives me a 1, so I thought -a^0 is 1. Your proof of -a^0 is equal -1 certainly helps.

    (3a/-b) (b^2/6b) (b/-a)

    = (3/6) (a/-a) (b^3/-b^2)

    I'm not good in math, my head is still spinning about negative fractions. Since the mistake is in -a^0, I think the (3/6) in the second step is correct. It should not be (-3/6). It sounds silly to ask this, I'm thinking in terms of other questions, Is that right? Thanks again.


    Quote Originally Posted by classicstrings View Post
    That should not be the case.....-22^0 = -1 too

    Maybe the calculator thinks (-22)^0 = 1
    but -22^0 = -1
    Quote Originally Posted by Glaysher View Post
    The web based calculator should get 1 as it is really calculating (-22)^0

    Your calculator should require brackets to get 1 and get -1 without them
    This is why you never trust calculators if you can do the problem yourself! (Just one of my many "Rules to Live By" that my Math students hate me for.)

    -Dan
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor Quick's Avatar
    Joined
    May 2006
    From
    New England
    Posts
    1,024
    Quote Originally Posted by topsquark View Post
    This is why you never trust calculators if you can do the problem yourself! (Just one of my many "Rules to Live By" that my Math students hate me for.)

    -Dan
    I agree with your math students
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Member
    Joined
    Sep 2006
    Posts
    99
    Quote Originally Posted by classicstrings View Post
    I'm not sure...

    See picture... top on is TI-84 Plus, bottom CASIO fx-82MS
    Wow! This is interesting. Maybe the person who can solve this will win the Nobel prize.

    Thanks, anyway for coming in.
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Member
    Joined
    Sep 2006
    Posts
    99
    Quote Originally Posted by Quick View Post
    All of the work in your original post except -a^0 was correct
    Thanks, Quick for for verifying and correcting my work.
    Follow Math Help Forum on Facebook and Google+

  13. #13
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by shenton View Post
    Wow! This is interesting.
    The reason for this discrepenacy is based on the way the calculator takes an operation. His calculator computes,
    -(22)^0=-(1)=-1
    The online calculator computes,
    (-22)^0=1

    Maybe the person who can solve this will win the Nobel prize.
    First, it is a matter of definition of how to define the zero exponent, it cannot be proved to be correct, thus there is no breakthrough.

    Second, there is no such thing as a Nobel prize for mathematics. Because Nobel believed that math does not affect society (which is true). Alternatively, there is a legend that a mathematicion had adultery with his wife, which is probably false. Because for one thing, Nobel never did have a wife.
    Follow Math Help Forum on Facebook and Google+

  14. #14
    MHF Contributor Quick's Avatar
    Joined
    May 2006
    From
    New England
    Posts
    1,024
    Quote Originally Posted by shenton View Post
    Wow! This is interesting. Maybe the person who can solve this will win the Nobel prize.

    Thanks, anyway for coming in.
    I would just like to say that:

    (-22)^0=1

    and

    -22^0=-1

    this has been long established and isn't debatable. Notice that online calculator has paranthesis around what you type.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. fractions with negative exponents
    Posted in the Algebra Forum
    Replies: 23
    Last Post: March 1st 2011, 02:27 PM
  2. How do i deal with fractions when using Modulo?
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: February 11th 2011, 01:25 PM
  3. Dividing by negative fractions
    Posted in the Algebra Forum
    Replies: 6
    Last Post: July 2nd 2010, 07:58 PM
  4. Negative fractions
    Posted in the Algebra Forum
    Replies: 1
    Last Post: July 31st 2007, 06:48 PM
  5. negative fractions to negative exponents
    Posted in the Algebra Forum
    Replies: 2
    Last Post: September 24th 2006, 06:02 PM

Search Tags


/mathhelpforum @mathhelpforum