Question

The juice dispenser in the cafeteria holds 22 1/2 pints of juice. The glasses in the cafeteria only hold 1/4 of a pint of juice. How many full glasses can be served at breakfast?

Answer 1

To find out how many full glasses can be served at breakfast, we need to divide the total amount of juice in the dispenser by the capacity of each glass.

The juice dispenser holds \( 22 \frac{1}{2} \) pints of juice. We can convert this mixed number into an improper fraction for easier calculation:

\[
22 \frac{1}{2} = 22 + \frac{1}{2} = \frac{44}{2} + \frac{1}{2} = \frac{45}{2} \text{ pints}
\]

Each glass holds \( \frac{1}{4} \) of a pint. To find out how many glasses can be filled, we divide the total amount of juice by the amount each glass holds:

\[
\text{Number of glasses} = \frac{\text{Total juice}}{\text{Juice per glass}} = \frac{\frac{45}{2}}{\frac{1}{4}}
\]

To divide by a fraction, we multiply by its reciprocal:

\[
\frac{45}{2} \div \frac{1}{4} = \frac{45}{2} \times \frac{4}{1} = \frac{45 \times 4}{2 \times 1} = \frac{180}{2} = 90
\]

Thus, the number of full glasses that can be served at breakfast is

\[
\boxed{90}
\]