You definitely are smart!
An equivalent ratio is a fraction that has the same value as another fraction, just simplified!
You obtain equivalent rations by multiplying with a common multiple across the top and bottom.
Lets start with 1/9 and use a multiple of 2.
Multiply 2 across the top number:
2 • 1 = 2
Now across the bottom:
2 • 9 = 18
Now combine:
2/18
2/18 is an equivalent ration o 1/9!
Now for 5/6, lets use a multiple of 5.
Across the top:
5 • 5 = 25
Across the bottom:
5 • 6 = 30
Now combine:
25/30
25/30 is an equivalent ratio to 5/6.
You can double check this by dividing by the same multiple you used across the top and bottom and seeing if you get the original fraction, and you should!
Hope this helps!