The challenge with these problems is making sure you keep track of the steps. Each step is fairly simple.
ORIGINAL PROBLEM: 8/9 ÷ 2/5 = FLIP and CHANGE OPERATION: 8/9 * 5/2 = REDUCE (if possible): 4/9 * 5/1 = MULTIPLY: 20/9 CONVERT ANSWER TO MIXED: 2 2/9
ORIGINAL PROBLEM: 2/9 ÷ 2/11 = FLIP and CHANGE OPERATION: 2/9 * 11/2 = REDUCE (if possible): 1/9 * 11/1 = MULTIPLY: 11/9 CONVERT ANSWER TO MIXED: 1 2/9
Now you get to try a few.