Page 2 of 2 FirstFirst 12
Results 16 to 20 of 20
Like Tree12Thanks

Math Help - Addition with fractions

  1. #16
    Member
    Joined
    Oct 2011
    Posts
    170
    Thanks
    3

    Re: Addition with fractions

    [QUOTE=Plato;794073]Why do you complicate this so?

    What a ridiculous thing to say... I made it complicated because I didn't know what I was doing, also your post doesn't help at all, you have not told me what you did the arrive at that answer. HallsOfIvy, topsquark and emakarov - Thank you for explaining.
    Last edited by uperkurk; August 1st 2013 at 01:51 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #17
    Member
    Joined
    Jun 2012
    From
    Georgia
    Posts
    176
    Thanks
    22

    Re: Addition with fractions

    uperkurk...

    \frac{2}{5} is a fraction.

    \frac{3}{x(x+2)} is a fraction.

    \frac{2x^2 + 5x + 3}{x^2 - 10x + 25} is a fraction.

    Don't let the complicated terms scare you. Essentially, they're just fractions. That means they have to follow all the rules of fractions. So whatever you'd normally do with \frac{2}{3} + \frac{4}{5}, you apply the same set of rules with \frac{3x}{x-2} + \frac{4}{x+3}.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  3. #18
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Addition with fractions

    Quote Originally Posted by uperkurk View Post
    Quote Originally Posted by Plato View Post
    Why do you complicate this so?...
    What a ridiculous thing to say... I made it complicated because I didn't know what I was doing, also your post doesn't help at all, you have not told me what you did the arrive at that answer. HallsOfIvy, topsquark and emakarov - Thank you for explaining.
    I'm certain Plato meant no offense...he was simply demonstrating what is sometimes referred to as "cross multiplying."

    If you are given an equation of the form:

    \frac{a}{b}=\frac{c}{d}

    Then, by this process, you may take as one side of the equation the product of the numerator on one side and the denominator on the other, and then then other side of the equation is the product of the other numerator-denominator pair. So, the equation above can then be written as:

    ad=bc
    Last edited by MarkFL; August 1st 2013 at 08:25 PM.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  4. #19
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,281
    Thanks
    673

    Re: Addition with fractions

    Fractional quantities are a by-product of wanting number systems "complete under division (except for 0)". As a result, multiplying with fractions is EASY, but adding them is HARD. The general rule is, of course:

    a/b + c/d = (ad +bc)/(bd)

    Sometimes, that is as good as it gets...it's not always possible to "factor out common factors" (although textbook problems often feature this, misleading students into an overly optimistic view of how things will turn out).

    The equation:

    a/b = c/d is often taken by definition to MEAN:

    ad = bc...it's how we can tell that 1/2 is the same fraction as 2/4 (...because 1*4 = 2*2, see?). In other words "fractional expressions" aren't UNIQUE, we can always multiply top and bottom by the same thing (because a/a = 1, if a isn't 0), to get a "different-looking fraction". "Cancelling" is this process "in reverse" we are DIVIDING by a/a (and when you DIVIDE by b/c, you multiply by c/b (the reciprocal), and the reciprocal of a/a is, strangely enough, a/a again).

    I've always felt that too much emphasis is placed upon putting things in "simplest form". It doesn't make an answer any more or less CORRECT, it just takes up less space on a piece of paper (and it might simplify calculations if you have to USE that answer later on). Fractions are often messy, and ugly-looking beasts. It may not seem so to you, dear uperkurk, but the problems you are tasked with solving have been tailored to shield you from the full blunt force of what fractional expressions can be.
    Thanks from MarkFL and topsquark
    Follow Math Help Forum on Facebook and Google+

  5. #20
    Junior Member
    Joined
    Mar 2013
    From
    Iowa, USA
    Posts
    37
    Thanks
    9

    Re: Addition with fractions

    What you have to remember, uperkurk, is that the denominator has to be the same in all terms of the equation. It's no different from when you learned to add fractions in Arithmetic.

    Example: \displaystyle\frac{1}{4} + 1 +\displaystyle\frac{2}{3}

    \displaystyle\frac{1}{4} = \displaystyle\frac{1(3)}{4(3)} = \displaystyle\frac{3}{12}

    \displaystyle\frac{2}{3} = \displaystyle\frac{2(4)}{3(4)} = \displaystyle\frac{8}{12}

    1= \displaystyle\frac{1(3)(4)}{1(3)(4)} = \displaystyle\frac{12}{12}


    \displaystyle\frac{1}{4} + 1 + \displaystyle\frac{2}{3} = \displaystyle\frac{3}{12} +\displaystyle\frac{12}{12} + \displaystyle\frac{8}{12} = \displaystyle\frac{23}{12}

    You are doing the same thing when adding in algebraic equations. I believe this was explained in earlier posts, but I thought that one more example would help.
    Last edited by jpritch422; August 6th 2013 at 08:31 AM.
    Follow Math Help Forum on Facebook and Google+

Page 2 of 2 FirstFirst 12

Similar Math Help Forum Discussions

  1. Addition/ subtraction of fractions
    Posted in the Algebra Forum
    Replies: 1
    Last Post: June 9th 2013, 02:29 PM
  2. Addition and subtraction with fractions
    Posted in the Algebra Forum
    Replies: 9
    Last Post: November 8th 2009, 12:27 PM
  3. Replies: 4
    Last Post: November 8th 2009, 05:54 AM
  4. [SOLVED] Addition of Algeraic Fractions
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 27th 2009, 02:13 PM
  5. addition/subtraction of algebraic fractions
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: July 1st 2008, 07:03 AM

Search Tags


/mathhelpforum @mathhelpforum