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Math Help - Proportionality

  1. #1
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    Proportionality

    Why is it when you have two equivalent fractions, their cross products are equal? Is there a good illustration/explanation of this that I could explain to a seventh grader?
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  2. #2
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    Re: Proportionality

    This follows from the fact that for all rational numbers x, y and z, if x = y, then xz = yz. So, we start with x=\frac{a}{b} and y=\frac{a'}{b'} and multiply both sides of x = y by z = bb'. It follows that \frac{a}{b}bb'=\frac{a'}{b'}bb'. Since \frac{a}{b}b=a and \frac{a'}{b'}b'=a', we get ab'=a'b.
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