To find out how much taller Shelley's sandcastle was than her sister's, we need to subtract the height of her sister's sandcastle from the height of Shelley's sandcastle.
Shelley's sandcastle height = \( \frac{2}{3} \) feet
Her sister's sandcastle height = \( \frac{1}{2} \) feet
First, we need to find a common denominator to perform the subtraction. The denominators 3 and 2 have a least common multiple of 6.
Now, we will convert both fractions to have a denominator of 6:
For \( \frac{2}{3} \): \[ \frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6} \]
For \( \frac{1}{2} \): \[ \frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6} \]
Now we can subtract the two heights: \[ \frac{4}{6} - \frac{3}{6} = \frac{4 - 3}{6} = \frac{1}{6} \]
Thus, Shelley's sandcastle was \( \frac{1}{6} \) feet taller than her sister's sandcastle.
Final answer: \[ \frac{1}{6} \text{ feet} \]