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Thread: Pre algebra question: 2/3 + 3/y divided by 3/y - 2/y

  1. #1
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    Pre algebra question: 2/3 + 3/y divided by 3/y - 2/y

    Hi. I have two problems that are confusing me and I don't even know where to begin. I have tried everything that I know possible to try to figure them out but keep coming up with nothing. I really need some help. Thank you so much for helping me.

    Simplify

    2/3 + 3/y
    _________ (divided by)
    3/y-2/y



    Simplify

    12/x+h+15 - 12/x+15
    ___________________ (divided by)
    h


    Thank you so much!!!
    h

  2. #2
    Elite Member mmm4444bot's Avatar
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    If you've tried everything possible, why don't we see any of your work shown?

    On the first exercise, combine the two terms in the numerator into a single fraction. Do the same with the two terms in the denominator. You will then have a single fraction divided by another.

    Next, use the rule that tells us to change such a division of ratios into a multiplication of ratios: multiply the top fraction by the reciprocal of the bottom fraction.

    If you do not understand these instructions, then let me know, and I will type an example for you.

    On the second exercise, something looks funky, to me. In the numerator, 12/x - 12/x is zero. (Did you see that cancellation of like terms?) 15 + 15 is also a combination of like terms.

    After combining like terms, we have the following.

    (h + 30)/h

    I'm thinking that there's probably more to the second exercise than combining like terms in the numerator.

    Can you retype the second expression using grouping symbols, so that I can be sure that I've got it correctly?

    MY EDITS: inserted offer to provide example; fixed ambiguous statement; correct grammar mistake (urrgggh)
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

  3. #3
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    Re: Pre algebra question

    Quote Originally Posted by malac
    Hi. I have two problems that are confusing me and I don't even know where to begin. I have tried everything that I know possible to try to figure them out but keep coming up with nothing. I really need some help. Thank you so much for helping me.

    Simplify

    2/3 + 3/y
    _________ (divided by)
    3/y-2/y



    Simplify

    12/(x+h+15) - 12/(x+15)
    ___________________ (divided by) <--- Did your problem include these grouping symbols?
    h


    Thank you so much!!!
    h
    I have tried everything...

    Please show us what you have tried, indicating exactly where you are stuck - so that we know where to begin to help you.
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  4. #4
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    Re: Pre algebra question

    Hi. This is what I have tried for the first problem

    2/x +3/y (xy) 2x^2 y + 3xy^2
    ___________ = _______________
    3/x - 2/y (xy) 3x^2y - 2xy^2

    There were other things I have tried but I have erased them and this was the last thing I wrote for this problem.


    12/ x +h +15 - 12/x + 15
    _______________________
    h

    For this one I canceled the h's out which and multiplied top by 15 which got me 180. After that I'm not sure where to go.

    Thank you!!!

  5. #5
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    Re: Pre algebra question

    the second problem did not include grouping

  6. #6
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    Re: Pre algebra question

    Quote Originally Posted by malac
    Hi. This is what I have tried for the first problem

    2/x +3/y (xy) 2x^2 y + 3xy^2
    ___________ = _______________
    3/x - 2/y (xy) 3x^2y - 2xy^2

    Can you please explain - what you are trying to do above?

    If you are trying multiply the numerator and the denominator by (xy) - a correct approach - then you should get

    Numerator

    (2/x + 3/y) * xy = 2*x*y/x + 3*x*y/y = 2*y + 3*x

    denominator

    (3/x - 2/y) * (xy) = 3*x*y/x - 2*x*y/y = 3*y - 2*x

    Now continue....



    There were other things I have tried but I have erased them and this was the last thing I wrote for this problem.


    12/ x +h +15 - 12/x + 15
    _______________________
    h

    Did your problem look like:

    [tex]\frac{\frac{12}{x+h+15} \, - \, \frac{12}{x+15}}{h}[/tex]

    Then there are implied grouping symbols arising from order of operations.

    For this one I canceled the h's out which and multiplied top by 15 which got me 180. After that I'm not sure where to go.<<< Incorrect

    If you did that - you need assistance from a face-to-face tutor - who can explain to you why you should not even think about doing that.

    Thank you!!!
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  7. #7
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    Re: Pre algebra question

    2/x +3/y (xy) 2x^2 y + 3xy^2
    ___________ = _______________
    3/x - 2/y (xy) 3x^2y - 2xy^2

    I think I see what you are attempting. I think you are multiplying both numerator and denominator by the lcd. EXCELLENT! But your mechanics are wrong. Follow this and figure out what was done, i.e. canceling, etc.
    [tex]\frac{\frac{2}{x}+\frac{3}{y}}{\frac{3}{x}-\frac{2}{y}}\cdot \frac{\frac{xy}{1}}{\frac{xy}{1}}=\frac{2y+3x}{3y-2x}=[/tex].

  8. #8
    Elite Member mmm4444bot's Avatar
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    Quote Originally Posted by malac

    the second problem did not include grouping [symbols]


    We realize this. Grouping symbols are not necessary when writing by hand or using mathematical-typesetting software to obtain fraction bars. You received this expression either written by hand or properly typeset. We cannot see what you received.

    You are trying to reproduce these compound fractions by typing them on a keyboard. Therefore, YOU are responsible for inserting the grouping symbols, so that other people can "see" what you're looking at.

    I'll try to explain the ambiguity to you.

    If I type the expression 1/4x, what does that mean to you?

    Do you "see" it as the fraction 1/4 times the variable x?

    Do you "see" it as the number 1 divided by the expression 4x?

    In other words, where is the x in 1/4x? Is it in the numerator or in the denominator?

    Who knows? The way that I typed it is not clear. It could mean either of the following:

    (1/4)x

    1/(4x)

    These two expressions clearly mean two different things because I inserted grouping symbols.

    You need to do the same, whenever there is ambiguity in your typed expressions.

    I still do not know what the second exercise is. Subhotosh typed ONE possible interpretation using fraction bars via TEX formatting. Does that interpretation match what you're looking at?

    Using the keyboard, instead of TEX, Subhotosh's guess is typed like so:

    [12/(x + h + 15) - 12/(x + 15)]/h

    The parentheses show clearly what expression each of the twelves is divided by, and the square brackets show clearly what expression h is dividing into.

    Do you understand the difference between the following two expressions?

    12/(x + h + 15)

    12/x+h+15

    The first one is clear; the second one is not clear at all.

    You can read a lot more about how to type mathematical expressions by hovering your mouse pointer over the drop-down menu "Forum Help" at the top of this page, followed by clicking on "Karl's Notes - Typing Math".

    ----------------------------------------------------------------

    I see that you've changed the first exercise, but my initial instructions still apply. Loren's post describes another valid method -- probably the preferred method, if you understand the rationale for using the LCD.

    I'll show you how the method that I described gives the same result. This will give you some practice at reading and interpreting typed expressions containing grouping symbols.

    (2/x + 3/y)/(3/x - 2/y)

    Combine the two terms in the numerator into a single ratio

    [(2y + 3x)/(xy)]/(3/x - 2/y)

    Combine the two terms in the denominator of the compound fraction into a single ratio, also

    [(2y + 3x)/(xy)]/[(3y - 2x)/(xy)]

    Multiply the ratio on top by the RECIPROCAL of the ratio on the bottom

    (2y + 3x)/(xy) * (xy)/(3y - 2x)

    The factors of (xy) cancel

    (2y + 3x)/(3y - 2x)

    Thanks for showing your work. If you would like more help, then please try to ask specific questions.

    Finally, there is a Preview button next to the Submit button. Using it allows you to see exactly what your post will look like. In other words, it's a great opportunity to proofread what you've typed.

    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

  9. #9
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    Re: Pre algebra question

    Quote Originally Posted by malac
    12/ x +h +15 - 12/x + 15
    _______________________
    h

    For this one I canceled the h's out ...
    After such a statement, if is unfortunately obvious that malac is missing the basics,
    and Sir Khan's remark:
    "If you did that - you need assistance from a face-to-face tutor - who can explain to you why you
    should not even think about doing that."
    is appropriate, as nothing else can be done here...
    I'm just an imagination of your figment !

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