Question

The Roman Empire began in 27 B.C. and ended in 476 A.D. The Persian Empire lasted approximately 5/11 as long as the Roman Empire. Based on this approximation, if the Persian Empire began in 550 BC, in what year did it end?

Answer 1

well, from 27 BC to 476 AD we're looking at 27 + 476 = 503 years for the Roman Empire, now 5/11 of that is how long the Persian one lasted, so since we're on the BC section let's subtract 5/11 of those 503 from 550, since on the BCE section the years approach zero after that is all AD.

`550~~ - ~~\left( 503\cdot \cfrac{5}{11} \right)\implies 550-\cfrac{2515}{11}\implies \cfrac{3535}{11}\implies 321(4)/(11) ~~ \approx ~~ \text{\LARGE 322}~BC`