Question

A cookie factory uses 3/8 of a barrel of oatmeal in each batch of cookies. The factory used 3/4 of a barrel 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.

Answer 1

To determine how many batches of cookies the factory made yesterday, we need to divide the amount of oatmeal used by the amount of oatmeal needed for each batch.

The factory used \( \frac{3}{4} \) of a barrel of oatmeal, and each batch requires \( \frac{3}{8} \) of a barrel of oatmeal.

We perform the division:

\[
\text{Number of batches} = \frac{\text{Amount of oatmeal used}}{\text{Amount of oatmeal per batch}} = \frac{\frac{3}{4}}{\frac{3}{8}}
\]

Dividing fractions involves multiplying by the reciprocal of the divisor:

\[
\frac{3}{4} \div \frac{3}{8} = \frac{3}{4} \times \frac{8}{3}
\]

We can simplify this:

- The \( 3 \) in the numerator (of the first fraction) and the \( 3 \) in the denominator (of the second fraction) cancel each other out.

Now let's calculate the multiplication:

\[
\frac{3 \times 8}{4 \times 1} = \frac{24}{4} = 6
\]

Therefore, the factory made a total of \( 6 \) batches of cookies.

Thus, the answer is:

\[
\boxed{6}
\]