Question

At the beach, Shelley and her sister both built sandcastles and then measured their heights. Shelley's sandcastle was 2/3 of a foot tall and her sister's was 1/2 of a foot tall. How much taller was Shelley's sandcastle than her sister's?

Write your answer as a fraction or as a whole or mixed number.

feet

Answer 1

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:
\[
\frac{1}{6} \text{ feet}
\]