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Ben drinks tea at an incredible rate. he drinks $\frac{7}{2}$ liters of tea every $\frac{2}{3}$ of an hour. how many liters of tea does he drink in one hour

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Multiply decimals and whole numbers: word problems

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Q. Ben drinks tea at an incredible rate. he drinks

\frac{7}{2}

liters of tea every

\frac{2}{3}

of an hour. how many liters of tea does he drink in one hour

Identify rate and time period: Identify the rate at which Ben drinks tea and the time period for that rate. $\newline$ Ben drinks $3\frac{1}{2}$ liters of tea every $\frac{2}{3}$ of an hour.
Convert to improper fraction: Convert the mixed number $3 \frac{1}{2}$ to an improper fraction to make the calculation easier. $3 \frac{1}{2} = \left(3 \times 2 + 1\right) / 2 = \frac{7}{2}$ liters of tea.
Calculate amount in one hour: Calculate the amount of tea Ben drinks in one hour by setting up a proportion. $\newline$ Since Ben drinks $\frac{7}{2}$ liters in $\frac{2}{3}$ of an hour, we can find out how much he drinks in $1$ hour by dividing the amount of tea by the fraction of the hour. $\newline$ $\left(\frac{7}{2}\right)$ liters / $\left(\frac{2}{3}\right)$ hour = $\left(\frac{7}{2}\right) \times \left(\frac{3}{2}\right)$ liters per hour.
Perform multiplication for rate: Perform the multiplication to find the rate per hour. $\newline$ $(\frac{7}{2}) \times (\frac{3}{2}) = \frac{21}{4}$ liters per hour.
Convert to mixed number: Convert the improper fraction to a mixed number if necessary. $\frac{21}{4} = 5 \frac{1}{4}$ liters per hour.

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