# After Lily's graduation party she had half of her cake left. She shared it with her sister Kala and her brother Logan. How much cake do they each get?

If Lily has some cake, the $\frac{1}{2}$ cake is divided three ways, into thirds, so each share is $\frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$.
If Lily is already full and only Kala and Logan have cake, it's divided two ways, into halves, so $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$.