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?

When you multiply fractions, you multiply across, right? so, for example 5/7 times 4/9 will give you 20/63. So, if you do this to this problem, you will have abcd/bcde. but now you are able to cancel out the b and c and d. think of it like reducing. 5/10 is 1/2. Why? because if you reduce/factor out a 5, you get a 1 in the numerator and a 2 in the denominator. same thing here; you can factor out a b, c, and d(because they show up in both num. and denom. so what you are left with is a/e. Cheers!