Shaded Fraction 779D54

1. **State the problem:** We have three identical shapes A, B, and C. - $\frac{3}{5}$ of shape A is shaded. - $\frac{7}{9}$ of shape B is shaded. We need to find the fraction of shape C that is shaded. 2. **Understand the shapes and shading:** Since the shapes are identical, the total area of each shape is the same. 3. **Analyze the shading in shapes A and B:** - Shape A has a top-left white region and a lower blue region. The shaded part is $\frac{3}{5}$. - Shape B has a small white top-left region and the rest mostly shaded, with $\frac{7}{9}$ shaded. 4. **Relate the shaded parts to shape C:** Shape C has a small blue top-left region, a larger blue lower region, and a white middle region. 5. **Use the given fractions to find the shaded fraction of shape C:** Since the shapes are identical and the dotted lines divide the shapes into parts, the shaded fraction of shape C can be found by combining the shaded parts from A and B appropriately. 6. **Calculate the shaded fraction of shape C:** The shaded fraction of shape C is the sum of the shaded parts corresponding to the blue regions in A and B minus the overlapping white region. 7. **Express the shaded fraction of shape C as a fraction:** The shaded fraction of shape C is $\frac{3}{5} + \frac{7}{9} - 1$ (subtracting the overlapping white region counted twice). Calculate: $$\frac{3}{5} + \frac{7}{9} - 1 = \frac{27}{45} + \frac{35}{45} - \frac{45}{45} = \frac{27 + 35 - 45}{45} = \frac{17}{45}$$ 8. **Simplify the fraction:** $\frac{17}{45}$ is already in simplest form since 17 is prime and does not divide 45. **Final answer:** The fraction of shape C that is shaded is $\boxed{\frac{17}{45}}$.