Results 1 to 3 of 3

Math Help - Trouble understanding basic proportions

  1. #1
    Newbie
    Joined
    Dec 2012
    From
    Get The Hopper Free
    Posts
    1

    Trouble understanding basic proportions

    Ok, so I'm in algebra 1 (7th grade) and I'm having some trouble understanding why solving basic proportions works. I understand that a proportion is two equal ratios. So when one of the numbers is a variable, I'm able to solve for the variable, but I don't understand why it works. So when you start to cross-multiply, my question is why do you multiply the numerator of one ratio by the denominator of the other? I mean, the two ratios are totally separate, except for the fact that they are equal. So, why do you multiply them as if they were the same ratio. Sorry if my question was confusing, I just need someone to explain why solving proportions works the way it does.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member jakncoke's Avatar
    Joined
    May 2010
    Posts
    387
    Thanks
    80

    Re: Trouble understanding basic proportions

    The two ratios are not separate. If you have two fractions  \frac{a}{b} = \frac{a_1}{b_1} then the fractions are multiples of each other. They will both reduce to the same numerator and denominator.

    For example  \frac{5}{15} = \frac{20}{60} .

     \frac{5}{15} = \frac{1}{3} and

     \frac{20}{60} = \frac{4}{12} = \frac{1}{3}


    Usually when you are doing proportions you are given 3 things right? and you have to find one.

    So say you have  \frac{a}{5} = \frac{3}{5} , you want to know what to put in place of a so that  \frac{a}{5} becomes  \frac{3}{5}.

    Observe, the algebra is not just nonense, so multiply both sides by 5, you get  a = \frac{3*5}{5} .

    Now do  \frac{a}{5} = \frac{\frac{3*5}{5}}{5} bring the 5 down, and you get  \frac{3*5}{5*5} knock out the 5 in num and 5 in denom, you get  \frac{3}{5}, just what we wanted out of the equality.


    Also the problem lies with using the = sign, when infact they are equivalent .

    Meaning,  \frac{1}{5} is equivalent to  \frac{2}{10} , you get what i'm saying?  \frac{1}{5} is equal to only  \frac{1}{5}


    Also i admire you for asking such questions, they are of fundamental importance, nothing to be trivialized. Keep thinking this over (Asking questions like what does it mean for 2 things to be equivalent rather than equal ).
    Last edited by jakncoke; December 2nd 2012 at 05:00 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,740
    Thanks
    645

    Re: Trouble understanding basic proportions

    Hello, legotboy!

    Ok, so I'm in algebra 1 (7th grade) and I'm having some trouble understanding why solving basic proportions works.
    I understand that a proportion is two equal ratios.
    So when one of the numbers is a variable, I'm able to solve for the variable.
    But I don't understand why it works.

    So when you start to cross-multiply, my question is:
    why do you multiply the numerator of one ratio by the denominator of the other?
    I mean, the two ratios are totally separate, except for the fact that they are equal.
    So, why do you multiply them as if they were the same ratio?

    Most students accept cross-multiplication as a welcome shortcut.
    . . So I'm impressed that you asked "Why?"
    Your teacher should have explained why it works.

    Suppose we have the proportion: . \frac{a}{b} \:=\:\frac{c}{d}

    Multiply both sides by b: . b\left(\frac{a}{b}\right) \:=\:b\left(\frac{c}{d}\right)

    Multiply both sides by d: . d\cdot{\color{red}\rlap{/}}b\left(\frac{a}{{\color{red}\rlap{/}}b}\right) \:=\:{\color{red}\rlap{/}}d\cdot b\left(\frac{c}{{\color{red}\rlap{/}}d}\right)

    . . And we have: . a\cdot d \:=\:b\cdot c

    which is the same result as we'd get by "cross-multiplying".
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Trouble understanding Subspaces
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 29th 2010, 11:37 PM
  2. Having some trouble understanding ideals...help?
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: April 27th 2010, 05:38 PM
  3. Trouble understanding combinations
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: April 13th 2010, 02:05 PM
  4. Replies: 3
    Last Post: April 11th 2009, 04:06 PM
  5. Having trouble understanding this example
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: March 20th 2009, 11:33 PM

Search Tags


/mathhelpforum @mathhelpforum