Arnold has 4 cups of trail mix. He wants to divide the trail mix into \(\frac{1}{3}\) cup servings. How many \(\frac{1}{3}\)-cup servings are there in 4 cups?

A. \(1 \frac{1}{3}\) servings
B. 8 servings
C. 7 servings
D. 12 servings



Answer :

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