To solve the problem, we need to determine how many batches of oatmeal cookies the chef can make with 4 cups of raisins, given that each batch requires [tex]\(\frac{1}{3}\)[/tex] cup of raisins.
Here’s how we can do it step by step:
1. Identify the total amount of raisins available:
The chef has 4 cups of raisins.
2. Determine the amount of raisins required per batch:
The recipe calls for [tex]\(\frac{1}{3}\)[/tex] cup of raisins for each batch of cookies.
3. Calculate the number of batches:
To find out how many batches the chef can make, we divide the total amount of raisins by the amount required per batch.
[tex]\[
\text{Number of batches} = \frac{\text{Total raisins available}}{\text{Raisins required per batch}}
\][/tex]
In this case:
[tex]\[
\text{Number of batches} = \frac{4}{\frac{1}{3}}
\][/tex]
4. Simplify the division:
Dividing by a fraction is the same as multiplying by its reciprocal:
[tex]\[
\frac{4}{\frac{1}{3}} = 4 \times 3
\][/tex]
This gives:
[tex]\[
4 \times 3 = 12
\][/tex]
Therefore, the chef can make 12 batches of cookies.
Based on the given options, the correct answer is:
- c. 12
