Perform the operation and simplify the answer fully. 1/4 divided by 8/9

To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction. In this case, we have:

1/4 ÷ 8/9 = 1/4 * 9/8

Now, we can multiply the numerators and denominators together:
1 * 9 = 9
4 * 8 = 32

So, 1/4 ÷ 8/9 simplifies to 9/32.