To find out how much yogurt Sarah needs for 3 servings, we start with the amount of yogurt needed for one serving, which is \( 2 \frac{1}{4} \) cups.
First, we convert \( 2 \frac{1}{4} \) to an improper fraction:
\[ 2 \frac{1}{4} = \frac{9}{4} \]
Now, to find the total amount of yogurt for 3 servings, we multiply by 3:
\[ 3 \times \frac{9}{4} = \frac{27}{4} \]
Next, we convert \( \frac{27}{4} \) back to a mixed number. We divide 27 by 4:
27 divided by 4 is 6 with a remainder of 3. So, we can express \( \frac{27}{4} \) as:
\[ 6 \frac{3}{4} \]
Thus, the total amount of yogurt Sarah needs for 3 servings is \( 6 \frac{3}{4} \) cups.