Question

a factory uses 7/10 of a barrel of raisins in each batch of granola bars. yesterday, the factory used 1 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 number to improper fraction

The total raisins used is \( 1\frac{1}{2} \) barrels. Convert this to an improper fraction: \( 1\frac{1}{2}=\frac{1\times2 + 1}{2}=\frac{3}{2} \) barrels.

Step2: Divide total raisins by raisins per batch

Each batch uses \( \frac{7}{10} \) barrels. To find the number of batches, divide total raisins by raisins per batch: \( \frac{3}{2}\div\frac{7}{10} \). When dividing fractions, multiply by the reciprocal: \( \frac{3}{2}\times\frac{10}{7}=\frac{3\times10}{2\times7}=\frac{30}{14} \). Simplify this fraction: \( \frac{30\div2}{14\div2}=\frac{15}{7}=2\frac{1}{7} \).

Answer:

\( 2\frac{1}{7} \) batches