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Math Help - Solving Proportions.

  1. #1
    Newbie
    Joined
    Mar 2009
    Posts
    4

    Smile Solving Proportions.

    I need help with some problems and i would really appreciate it if somebody could help me with them.

    1.) 2x-3 6x
    ____= ____
    5 8




    2.) 2p-6 p+4
    ____ = ____
    7 11





    3.) 9y-6 6y+2
    ____=_____
    4 8



    4.) 7d-5 6d+3
    ____=_____
    8 7




    5.) 5b-2 4b+5
    ____=_____
    6 11




    6.) 11 3
    _____=_____
    6p-2 4p+5
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  2. #2
    Member
    Joined
    Sep 2007
    Posts
    81
    \frac{2x-3}{5} - \frac{6x}{8}

    The first step is to think, what is the first number that both 5 and 8 go into. We want to get them both to that number so we can have a common denominator to work with. In this case it's 40.

    We need to multiply the side with 5 by 8 to get 40, and the side with 8 by 5 to get 40.

    A shortcut to do this is simply to do what they call cross-multiplication. We multiply the bottom of the first fraction by the top of the second, and the top of the first fraction by the bottom of the second.

     8 * (2x-3) = 5 * 6x

     16x - 24 = 30x

     14x = -24

     x = \frac{-24}{14}

    Now you try the rest of them.
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  3. #3
    MHF Contributor
    Joined
    Mar 2007
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    1,240

    Talking

    Quote Originally Posted by angelica2619 View Post
    1.) 2x-3 6x
    ____= ____
    5 8
    To learn how to format math using plain text, please try here. In the meantime, I will assume that the above means the following:

    . . . . .1) Solve: (2x - 3)/5 = (6x)/8

    A good first step might be to multiply through by 40 to clear the denominators, leaving you with:

    . . . . .8(2x - 3) = 5(6x)

    . . . . .16x - 24 = 30x

    Then solve the linear equation.

    Quote Originally Posted by angelica2619 View Post
    2.) 2p-6 p+4
    ____ = ____
    7 11
    Assuming you mean (2p - 6)/7 = (p + 4)/11, this exercise works just like (1) above: Find the common denominator, multiply through by it, and then solve the resulting linear equation; namely, 22p - 66 = 7p + 28.

    Quote Originally Posted by angelica2619 View Post
    3.) 9y-6 6y+2
    ____=_____
    4 8
    Assuming the above means (9y - 6)/4 = (6y + 2)/8, this works just like (1): Multiply through by the common denominator, and then solve 8(9y - 6) = 4(6y + 2).

    Quote Originally Posted by angelica2619 View Post
    4.) 7d-5 6d+3
    ____=_____
    8 7
    Assuming the above means (7d - 5)/8 = (6d + 3)/7, this works just like the others: Multiply through by the common denominator of 8*7, and solve the resulting linear equation.

    Quote Originally Posted by angelica2619 View Post
    5.) 5b-2 4b+5
    ____=_____
    6 11
    Assuming the above means (5b - 2)/6 = (4b + 5)/11, this works just like the others.

    Quote Originally Posted by angelica2619 View Post
    6.) 11 3
    _____=_____
    6p-2 4p+5
    I will assume that the above means 11/(6p - 2) = 3/(4p + 5).

    This one looks somewhat different, but it works the same way: Multiply through by the common denominator of (6p - 2)(4p + 5), and then solve the resulting linear equation; namely, 11(4p + 5) = 3(6p - 2).

    Note that, since the variables were in the denominator, and since you cannot divide by zero, you will need to check your solutions against the original equation, to verify that the value does not cause a "division by zero" problem.

    If you get stuck, please reply showing how far you have gotten. Thank you!
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