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associative? single replacement
Without an equality sign the information given can't be considered as an equation
The probability of ac and bc is 1/5.
There is no distributive property of addition over multiplication. The equation works if a + (b * c) = (a + b)*(a + c) = a2 + ab +ac +bc => a + bc = a2 + ab +ac +bc ie a = a2 + ab + ac = a*(a+b+c) and that, in turn requires that a = 0 or a+b+c = 1 If a, b and c are fractions than the second condition requires the fractions to sum to 1 - not be equal to 1.
(a + b)/(a - b) = (c + d)/(c - d) cross multiply(a + b)(c - d) = (a - b)(c + d)ac - ad + bc - bd = ac + ad - bc - bd-ad + bc = -bc + ad-ad - ad = - bc - bc-2ad = -2bcad = bc that is the product of the means equals the product of the extremesa/b = b/c