x = 0.436363636... (recurring). Prove algebraically that x can be written as 24/55.

We need to multiply x by powers of 10 in order to get the recurring part on its own after the decimal point, and then be able to eliminate it. 10x = 4.363636... and 1000x = 436.363636...So subtracting we get 1000x - 10x = 436.363636... - 4.363636...so 990x = 432.Then dividing both sides by 990, we get x = 432/990.We now just need to simplify this fraction: x = 432/990 = 216/495 = 72/165 = 24/55.So we have x = 24/55.