Cancelling

Tuesday 20 April 2004 at 4:27 pm | In Articles | 1 Comment

Students love to cancel wherever they can, so much so that the book Comic Sections (now out of print) had the following joke:

    The student law of universal cancellation: If the same symbol x occurs in any two different places on the one page it may be cancelled

So you get horrors like \dfrac{\sin x}{n}=\dfrac{\text{si}\hspace{-1mm}\not{n}\hspace{1mm} x}{\not n}=$ six$ :o

And yet strange things can happen. It is true that \frac{2666}{6665}=\frac{266}{665}=\frac{2}{5}.
What is remarkable is that you can have as many sixes as you like and cancel them as many times as you like so, for example, \frac{26666666}{66666665}=\frac{266}{665}. Can you prove this is true? Can you find 3 other similar fractions?

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  1. my math teacher in high school went over the same idea of canceling versus reducing often.
    He used the example 16/64 and 64/16. Without the 6s, it makes a true statement.

    Comment by chris — Saturday 18 September 2004 3:35 am #

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