warren used $\frac{1}{2}$ of a tube of toothpaste in $\frac{1}{3}$ of a year. at that rate, how much…

Explanation:

Step1: Set up the proportion

Let $x$ be the amount of tooth - paste used in 1 year. We know that $\frac{1}{2}$ tube is used in $\frac{1}{3}$ year. So the proportion is $\frac{\frac{1}{2}}{\frac{1}{3}}=\frac{x}{1}$.

Step2: Solve the proportion

Using the rule that $\frac{a}{b}\div\frac{c}{d}=\frac{a}{b}\times\frac{d}{c}$, we have $x = \frac{1}{2}\div\frac{1}{3}=\frac{1}{2}\times3$.

Step3: Calculate the result

$\frac{1}{2}\times3=\frac{3}{2}=1\frac{1}{2}$.

Answer:

$1\frac{1}{2}$