Question

a factory uses 2 1/2 barrels of raisins in each batch of granola bars. yesterday, the factory used 7 1/2 barrels of raisins. how many batches of granola bars did the factory make yesterday? write your answer as a fraction or as a whole or mixed number. batches

Explanation:

Step1: Convert mixed - numbers to improper fractions

$2\frac{1}{2}=\frac{2\times2 + 1}{2}=\frac{5}{2}$; $7\frac{1}{2}=\frac{7\times2+1}{2}=\frac{15}{2}$

Step2: Divide total raisins by raisins per batch

The number of batches $n=\frac{\text{Total raisins}}{\text{Raisins per batch}}=\frac{\frac{15}{2}}{\frac{5}{2}}$
When dividing by a fraction, we multiply by its reciprocal, so $n=\frac{15}{2}\times\frac{2}{5}$

Step3: Simplify the fraction

$\frac{15}{2}\times\frac{2}{5}=\frac{15\times2}{2\times5}=\frac{30}{10} = 3$

Answer:

3