Final answer:
To find the shaded fraction of shape C, we convert 3/5 and 7/9 to have a common denominator of 45, add them to get 62/45, subtract the whole, and simplify to 1/3. However, this result is not listed in the provided answer choices, indicating a potential error in the question or choices.
Step-by-step explanation:
The student is asking to find out what fraction of shape C is shaded given that 3/5 of shape A is shaded and 7/9 of shape B is shaded, with all three shapes being identical. To solve this problem, we need to work with the common denominator for the fractions 3/5 and 7/9 to find out what fraction of shape C would be shaded if we combined the shaded parts of shapes A and B.
Looking at the denominators 5 and 9, the least common denominator (LCD) is 45. Converting fractions to have the same denominator, we get 3/5 = 27/45 and 7/9 = 35/45. Now we can simply add these two fractions to find the combined shaded fraction. However, since the shapes are identical and cannot have more than the whole shaded, the fraction of shape C that is shaded must be the remainder after whole shapes are subtracted. Adding 27/45 and 35/45 gives 62/45 which is 1 and 17/45. Therefore, after subtracting the whole, we are left with 17/45, which simplifies to 5/15 or 1/3. Unfortunately, this fraction is not listed in the answer options, which suggests a possible mistake in either the question or the answer choices provided.