In order to conclude whether she is correct or not, we can express both operations as fractions, then if we get the same result we can say that she is correct.
For the mixed number 2 4/9, we can rewrite it as a fraction like this:
1. Multiply the whole part of the number by the denominator of the fraction:
2×9 = 18
2. Add the previous result to the numerator of the fraction:
18 + 4 = 22
3. Use the previous result as the numerator of the fraction and leave the denominator unchanged:
22/9
Then 2 4/9 equals 22/9.
She says that 22/9 equals 9÷22.
We can express 9÷22 as a fraction by taking the first number (9) as the numerator of the fraction and the second one (22) as the denominator, then we get:
9÷22 = 9/22
As you can see, from the first operation we got 22/9, from the second one we get 9/22, since 22/9 is not equal to 9/22, we can conclude that Ivanna is not correct.