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Basic rules of algebra (Manipulating equations and such)

  1. Jul 17, 2013 #1
    Hi, im a grade 12 student, finishing my advanced functions at the moment, in a few short weeks i shall be taking calculus, in my last trig unit my teacher remarked that although i did well, i should brush up on my 'basic rules for algebra' from what i understand this is stuff that i dont really remember, stuff that is taught very early, but for some reason i didnt learn it or didnt pay attention back then and now im sort of regretting it, stuff like what do you do when you bring something over the equal sign to the other side of the equation, when you can cancel stuff out, how to cancel stuff out when dealing with fractions, when to cross multiply, etc etc etc...

    can someone please recommend me a great book that will teach me how to do this stuff...i feel so bad...this stuff is probably taught to grade 5 kids and i dont really know how to do this...

    Just a book that will teach me thoroughly how to manipulate equations and stuff..

    thanks in advance gentlemen :)

    #edit, i would post this in the learning material/book section but for some reason it wouldnt let me post there.
  2. jcsd
  3. Jul 17, 2013 #2


    Staff: Mentor

    is this because you routinely do things wrong in solving for x? or was the comment meant to prepare you for abstract algebra ideas?

    One key point if you're doing things correctly is to remember never divide by any variable that could be zero or at least make note of it that its undefined.

    a / b = c / d then you can multiply both sides by b to get a = c*b / d and again both sides by d to get a*d = c*b which is the cross product you mentioned.
    Last edited: Jul 17, 2013
  4. Jul 17, 2013 #3
    Hi supernova1203
    If you talk about rules like what to do when 'sending something at the other side of the equation' then you should just forget about those 'rules'
    They don't exist
    You only need to know that an equation is a magic formula involving the most powerful symbol of the universe :), the symbol '='
    It allows you to know that something is just the same thing ('on the other side') but written differently.
    since the two sides of the equation are 'the same thing', then whatever you do on the left also holds on the right, and vice versa.
    so for instance, to solve 3x+1=4, you don't need a rule that says "I send the +1 from the left to the right and therefore it becomes a -1" (it is true, but it is not a rule that you should learn as a 'first fact')
    so 3x+1 is difficult to deal with, so it would be nice if it was just 3x
    easy, I remove 1
    but 'the other side' being the same thing, I have to do the same operation
    so 3x+1=4 -> 3x=4-1=3 is not because you 'sent the one on the other side' but because you did this:
    now, it would be so much better if instead of 3x it was just x
    well, I just have to divide by 3, both sides (and hence 'send the 3 at the other side')
    3x/3=3/3 and thus x=1
    of course, you aren't going to solve most equations doing it so 'slowly', you will eventually 'send things on the other side of the equation', but it would be better if that becomes a second nature because of doing it so much than it being a set of rules 'just because' :)

  5. Jul 17, 2013 #4
    A good way to brush up on your basics would be to look through the Algebra and pre-Algebra playlists on the Khan Academy. I believe that they also have exercises after each lecture to reinforce the topics.

    Also, many Calculus books have a chapter before the core material reserved for prerequisites. Go here and identify the areas that you want to get some more practice on and work the exercises.
  6. Jul 17, 2013 #5


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  7. Jul 17, 2013 #6


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    Find any old high school Beginning Algebra textbook and study the whole course by yourself. You will learn it much better than when you studied it before. Reviewing the whole course on your own should take 3 or 4 months. Using beginning basic Algebra should become as natural to you as reading and writing in your normal language.
  8. Jul 17, 2013 #7


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