Questions: Logan bought 5 / 9 gallons of apple juice. If he drank 2 / 5 of this amount with his friends, how many gallons of apple juice did they drink? 17 / 18 11 / 9 2 / 45 2 / 9

Logan bought 5 / 9 gallons of apple juice. If he drank 2 / 5 of this amount with his friends, how many gallons of apple juice did they drink? 17 / 18 11 / 9 2 / 45 2 / 9
Transcript text: Logan bought $5 / 9$ gallons of apple juice. If he drank $2 / 5$ of this amount with his friends, how many gallons of apple juice did they drink? $17 / 18$ $11 / 9$ $2 / 45$ $2 / 9$
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Solution

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Solution Steps

Step 1: Identify the total amount of apple juice

Logan bought \(5 \frac{1}{3}\) gallons of apple juice. Convert this mixed number to an improper fraction: \[ 5 \frac{1}{3} = \frac{16}{3} \]

Step 2: Determine the fraction of apple juice consumed

Logan drank \(\frac{2}{5}\) of the total amount. To find out how much this is, multiply the total amount by \(\frac{2}{5}\): \[ \frac{16}{3} \times \frac{2}{5} \]

Step 3: Perform the multiplication

Multiply the numerators and the denominators: \[ \frac{16 \times 2}{3 \times 5} = \frac{32}{15} \]

Step 4: Simplify the fraction (if necessary)

The fraction \(\frac{32}{15}\) is already in its simplest form.

Final Answer

\[ \frac{32}{15} \] gallons of apple juice were consumed.

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