Question

a cookie factory uses $2\\ 1/2$ barrels of oatmeal in each batch of cookies. the factory used $7\\ 1/2$ barrels of oatmeal yesterday. how many batches of cookies did the factory make? write your answer as a fraction or as a whole or mixed number. \boxed{} batches submit

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(2\frac{1}{2}\) to an improper fraction. \(2\frac{1}{2}=\frac{2\times2 + 1}{2}=\frac{5}{2}\).
Then, convert \(7\frac{1}{2}\) to an improper fraction. \(7\frac{1}{2}=\frac{7\times2+1}{2}=\frac{15}{2}\).

Step2: Divide the total oatmeal by oatmeal per batch

To find the number of batches, we divide the total oatmeal used (\(\frac{15}{2}\) barrels) by the oatmeal used per batch (\(\frac{5}{2}\) barrels per batch). The formula for the number of batches \(n\) is \(n=\frac{\text{Total Oatmeal}}{\text{Oatmeal per Batch}}\).
So, \(n = \frac{\frac{15}{2}}{\frac{5}{2}}\). When dividing fractions, we multiply by the reciprocal, so \(n=\frac{15}{2}\times\frac{2}{5}\). The 2s cancel out, and we have \(\frac{15}{5}=3\).

Answer:

3