justify why a/b x b/c x c/d x d/ e is equal to a/e when b,c,d, and e are not zero?

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03-11-2014
Mathematics

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justify why a/b x b/c x c/d x d/ e is equal to a/e when b,c,d, and e are not zero?

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VenusRetrograde VenusRetrograde · Answer 1 · 2015-12-11T02:40:55-05:00

[tex] \frac{a}{b} * \frac{b}{c} * \frac{c}{d} * \frac{d}{e}= \frac{a}{e} [/tex]

lets rewrite the equation so as to better understand why this equation is true..

[tex]\frac{a}{b} * \frac{b}{c} * \frac{c}{d} * \frac{d}{e}= \frac{abcd}{bcde}= \frac{a}{e} * \frac{b}{b} * \frac{c}{c} * \frac{d}{d} [/tex]
If both the numerator and the denominator are the same in a fraction, then that fraction is equivalent to 1. So we can rewrite the equation as such.

[tex]\frac{a}{e} * 1 * 1 *1= \frac{a}{e} [/tex]

Since the b's, c's and d's cancel out, a/b*b/c*c/d*d/e=a/e

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