[Solved] Can you divide through an addition/subtraction?

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  1. StylaBoy's Avatar
    1 02-06-2012  11:56
    • Exalted Member
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    [Solved] Can you divide through an addition/subtraction?


    In this question, Examsolution is dividing the whole fraction by CosACosB. But there are + and - signs and you can't divide?
    Last edited by StylaBoy; 02-06-2012 at 12:34.
  2. TenOfThem's Avatar
    2 02-06-2012  12:16
    • TSR Royalty
    Re: Can you divide through an addition/subtraction?
    Can you tell me what time as I do not really want to sit through nearly 5 mins of trig just to find the bit you don't understand
  3. Brit_Miller's Avatar
    3 02-06-2012  12:16
    • Benevolent Member
    • Location: Bristol
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    Re: Can you divide through an addition/subtraction?
    It doesn't matter if there's addition/subtraction in the fraction. As long as you do the same to the top and the bottom of the fraction, it's okay.
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  4. StylaBoy's Avatar
    4 02-06-2012  12:22
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    Re: Can you divide through an addition/subtraction?
    (Original post by TenOfThem)
    Can you tell me what time as I do not really want to sit through nearly 5 mins of trig just to find the bit you don't understand
    at around 2:40

    (Original post by Brit_Miller)
    It doesn't matter if there's addition/subtraction in the fraction. As long as you do the same to the top and the bottom of the fraction, it's okay.

    So if I divide denominator or numerator ONLY, that's invalid but if I apply operation to top and bottom thats ok?
  5. TenOfThem's Avatar
    5 02-06-2012  12:31
    • TSR Royalty
    Re: Can you divide through an addition/subtraction?
    (Original post by StylaBoy)
    at around 2:40




    So if I divide denominator or numerator ONLY, that's invalid but if I apply operation to top and bottom thats ok?
    Yes, it is no different to cancelling

    \frac{6}{10} = \frac{3}{5}

    \frac{2+4}{4+6} = \frac{1+2}{2+3}
  6. Brit_Miller's Avatar
    6 02-06-2012  12:36
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    Re: Can you divide through an addition/subtraction?
    (Original post by StylaBoy)
    So if I divide denominator or numerator ONLY, that's invalid but if I apply operation to top and bottom thats ok?
    Think about it practically. If you divide just the top or the bottom by something, you change the fraction.

    e.g. Say you had the fraction 1/2, if divide just the top by 2, you'd end up with 0.5/2 = 1/4, which is clearly different. Doing the same to top and bottom can't change the fraction as anything divided by itself is 1.
  7. notnek's Avatar
    7 02-06-2012  12:38
    • TSR Demigod
    • Location: Bangkok, Thailand
    Re: Can you divide through an addition/subtraction?
    (Original post by StylaBoy)
    at around 2:40




    So if I divide denominator or numerator ONLY, that's invalid but if I apply operation to top and bottom thats ok?
    If you multiply/divide both top and bottom of a fraction by the same thing (call it a) then all you're doing is multiplying/dividing the fraction by a/a=1. So what you're doing doesn't change the fraction.

    If you only multiply/divide the numerator/denominator by a number a then you are changing the fraction by multiplying/dividing the whole fraction by a.

    Here's what's happening in the working in the video:

    \displaystyle \frac{\sin A \cos B + \sin B \cos A} {\sin A \cos B - \sin B \cos A} \times \frac{\left(\frac{1}{\cos A \cos B}\right)}{\left(\frac{1}{\cos A \cos B}\right)} = ...

    \displaystyle \frac{\left(\frac{1}{\cos A \cos B}\right)}{\left(\frac{1}{\cos A \cos B}\right)} is equal to 1 so you're not changing the fraction by multiplying it by this.
    Last edited by notnek; 02-06-2012 at 12:39.
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  8. miml's Avatar
    8 02-06-2012  12:54
    • Overlord in Training
    • Location: Warwickshire
    • Posts: 3,103
    Re: [Solved] Can you divide through an addition/subtraction?
    As long as the denominator isn't 0, you are free to do pretty much anything you want.
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