A factory uses 7/10 of a barrel of raisins in each batch of granola bars. Yesterday, the factory used 3 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.*

To find out how many batches of granola bars the factory made, we need to divide the total amount of raisins used by the amount of raisins used per batch.

The factory used $ 3 \frac{1}{2} $ barrels of raisins, and each batch requires $ \frac{7}{10} $ of a barrel.

### Step 1: Convert the mixed number to an improper fraction.
$ 3 \frac{1}{2} $ can be converted to an improper fraction as follows:
\[
3 \frac{1}{2} = \frac{7}{2}
\]

### Step 2: Set up the division.
We need to divide $ \frac{7}{2} $ by $ \frac{7}{10} $:
\[
\frac{7}{2} \div \frac{7}{10}
\]

### Step 3: Perform the division by multiplying by the reciprocal.
Dividing fractions is the same as multiplying by the reciprocal of the divisor:
\[
\frac{7}{2} \times \frac{10}{7} = \frac{7 \times 10}{2 \times 7} = \frac{70}{14}
\]

### Step 4: Simplify the fraction.
\[
\frac{70}{14} = 5
\]

Thus, the factory made **5 batches** of granola bars yesterday.

Do you want further details or have any questions?

Here are 5 related questions:
1. If the factory used 4 barrels of raisins, how many batches of granola bars would they make?
2. How many barrels of raisins are needed for 10 batches of granola bars?
3. What would happen if each batch required $ \frac{1}{2} $ a barrel of raisins instead?
4. If a barrel of raisins costs $50, how much did the raisins used yesterday cost?
5. How many raisins would be left after making 4 batches if the factory starts with 5 barrels?

**Tip:** When dividing fractions, remember to multiply by the reciprocal of the divisor!

Learn how to calculate the number of batches of granola bars a factory made using fractions and division. Given that the factory used 3 1/2 barrels of raisins, each batch requires 7/10 of a barrel. Step-by-step solution provided.

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