Answer to Question #30572 in Algebra for Aryan

Question

1÷[1+1÷{1+1÷(1+1÷3)}]

Answer 1

ok, let's begin from the bottom (or the right side of our expression):


1÷[1+1÷{1+1÷(1+1÷3)}]
=

1÷[1+1÷{1+1÷(1+1/3)}]
=

1÷[1+1÷{1+1÷(4/3)}]
=
Now we proceed "to the left" opening the braces:
=1÷[1+1÷{1+3/4}]
=1÷[1+1÷{7/4}]
=1÷[1+4/7]
=1÷[11/7]
=7/11 or in decimals it's approximately 0.64