Question

The fraction F below is an extended fraction. What simple fraction in lowest terms is equal to F?

Answer 1

I was really scared when I first looked at this ... I thought it was gonna
keep going to infinity, and I don't know how to handle those.

But this fraction only has 2 or 3 levels to it, so I think we can do it without
too much trouble.

The secret is: You definitely have to start at the bottom and work
your way up.

-- See the bottom level ?  It's  2 + 1/3 . 
-- Change that number all to an improper fraction, and it's  7/3 .

The reason I want to do that is because it's the denominator of the
next fraction up, and that fraction is (1 over it). 

-- The denominator of the next fraction up is 7/3, so 1 over it is just 3/7.

-- Now, before we go up to the top level, it looks like we're supposed to
add the big black ' 1 ' to where we are now ... to the 3/7 .

' 1 ' = 7/7 .  Add that to the 3/7, and we have  10/7 .

All we have left now, out of the whole pile, is  (1 over 10/7).

And that's just 7/10.