To figure out what the number is, just do the inverse operations in the opposite order:
Start by adding 7/18 to 1 5/6, which gives you 2 2/9.
Next, multiply 2 2/9 by 1 1/5, which gives you 2 2/3.
Finally, divide 2 2/3 by 2 1/2, which gives you 1.06666...
Therefore, the number you thought of is 1.06666...
Hope this helps! :)