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Lian's dog eats $\frac{3}{8}$ of a bag of dog food each week. Lian currently has $\frac{5}{8}$ of a bag remaining. How many weeks will it take Lian's dog to finish this remaining food?

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Identify quotients of rational numbers: word problems

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Q. Lian's dog eats

\frac{3}{8}

of a bag of dog food each week. Lian currently has

\frac{5}{8}

of a bag remaining. How many weeks will it take Lian's dog to finish this remaining food?

Identify Food Amounts: Step $1$ : Identify the amount of food the dog eats each week and the amount remaining. $\newline$ - Amount eaten each week = $\frac{3}{8}$ bag $\newline$ - Remaining amount = $\frac{5}{8}$ bag
Calculate Weeks Needed: Step $2$ : Calculate the number of weeks needed to finish the remaining food. $\newline$ - Number of weeks $= \frac{\text{Remaining amount}}{\text{Amount eaten each week}}$ $\newline$ - Number of weeks $= \frac{5}{8} \div \frac{3}{8}$ $\newline$ - Number of weeks $= \frac{5}{8} \times \frac{8}{3} = \frac{40}{24} = \frac{5}{3}$ weeks

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