Perform the operation and simplify the answer fully.

To solve the operation ( frac{5}{9} times frac{9}{8} ), you can follow these steps:

1. Multiply the numerators: ( 5 times 9 = 45 )
2. Multiply the denominators: ( 9 times 8 = 72 )
3. Combine these results: ( frac{45}{72} )

Now, simplify ( frac{45}{72} ) by finding the greatest common divisor (GCD) of 45 and 72, which is 9.

4. Divide both the numerator and denominator by 9:

– ( frac{45 div 9}{72 div 9} = frac{5}{8} )

So the simplified answer is ( frac{5}{8} ).

The correct answer is A) ( frac{5}{8} ).