To determine how many \(\frac{1}{3}\)-cup servings are in 4 cups of trail mix, we need to divide the total amount of trail mix by the size of each serving.
1. Arnold has 4 cups of trail mix.
2. Each serving is \(\frac{1}{3}\) of a cup.
To find the number of \(\frac{1}{3}\)-cup servings, we divide the total number of cups (4 cups) by the size of each serving (\(\frac{1}{3}\) cup):
[tex]\[
\text{Number of servings} = \frac{\text{Total cups}}{\text{Serving size}} = \frac{4}{\frac{1}{3}}
\][/tex]
When dividing by a fraction, we multiply by its reciprocal. The reciprocal of \(\frac{1}{3}\) is 3. Therefore:
[tex]\[
\frac{4}{\frac{1}{3}} = 4 \times 3 = 12
\][/tex]
So, there are 12 \(\frac{1}{3}\)-cup servings in 4 cups of trail mix.
Thus, the correct answer is:
(D) 12 servings
