Justify why \(\frac{a}{b} \times \frac{b}{c} \times \frac{c}{d} \times \frac{d}{e}\) is equal to \(\frac{a}{e}\) when \(b\), \(c\), \(d\), and \(e\) are not zero.
Answer (2)
b a ∗ c b ∗ d c ∗ e d = e a
lets rewrite the equation so as to better understand why this equation is true..
b a ∗ c b ∗ d c ∗ e d = b c d e ab c d = e a ∗ b b ∗ c c ∗ d d 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.
e a ∗ 1 ∗ 1 ∗ 1 = e a
Since the b's, c's and d's cancel out, a/b b/c c/d*d/e=a/e
The expression b a × c b × d c × e d simplifies to e a by canceling out the common factors in the numerator and denominator, providing both are non-zero. This holds as long as b , c , d , and e are not zero. The simplification respects the rules of algebra regarding fractions.
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