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Extremely basic simplifying, how does this work? watch

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    Just watching an ExamSolutions video on differentiation and he is able to simplify 6(4/3) by dividing both the 6 and the 3 by 3, to give 2(4)x^1/3. I have never seen this before (I know its really basic, just have never been taught this way).

    Why are you able to take out a factor of 3 from the 6 and the 3? WHy do you only need to divide the denominator by 3 and the 6 by 3, why don't you need to divide the 4 by 3 too? He divides the 6 by 3, and the denominator (3) by 3, he doesn't divide the numerator (4) by 3. Why don't you need to divide the numerator, only the denominator?

    Thanks


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    (Original post by blobbybill)
    Just watching an ExamSolutions video on differentiation and he is able to simplify 6(4/3) by dividing both the 6 and the 3 by 3, to give 2(4)x^1/3. I have never seen this before (I know its really basic, just have never been taught this way).

    Why are you able to take out a factor of 3 from the 6 and the 3? WHy do you only need to divide the denominator by 3 and the 6 by 3, why don't you need to divide the 4 by 3 too? He divides the 6 by 3, and the denominator (3) by 3, he doesn't divide the numerator (4) by 3. Why don't you need to divide the numerator, only the denominator?

    Thanks

    Because 6=2*3

    So it becomes 2*3*(4/3)*x^{1/3} + 2 and factors cancel.
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    (Original post by RDKGames)
    Because 6=2*3

    So it becomes 2*3*(4/3)*x^{1/3} + 2 and factors cancel.
    If it were a case where the numerator was also a factor, do you cancel out factors from the numerator aswell?

    If not, why not?
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    (Original post by blobbybill)
    If it were a case where the numerator was also a factor, do you cancel out factors from the numerator aswell?

    If not, why not?
    Explain what you mean. If the 4 was a number that could be split into its prime factors such that there is a common factor in the numerator and denominator, then yes those particular factors would cancel each other.
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    Don't think of it as dividing the 6 and 3 by 3, he's just multiplying out the bracket to simplify the fraction. 6* (4/3) = 24/3 = 8
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    (Original post by JN17)
    Don't think of it as dividing the 6 and 3 by 3, he's just multiplying out the bracket to simplify the fraction. 6* (4/3) = 24/3 = 8
    Okay. I'll just think of it as that in future, that seems much simpler to me.

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    Because the number outside the bracket is just multiplication:

    6(\frac{4}{3}) = \frac{6 \times 4}{3}

    Or to try and make it completely clear:
    6(\frac{4}{3}) = \frac{6}{1} \times \frac{4}{3}

    You can then simplify the fraction directly by cancelling out the 3 and the 6 to give \frac{2 \times 4}{1}, or if you prefer you can multiply to give \frac{24}{3} = 8

    What you showed is the same thing without the bother of writing out the full fraction
 
 
 
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