martina used $\frac{3}{4}$ of a bottle of con...

martina used $\frac{3}{4}$ of a bottle of conditioner in $\frac{7}{12}$ of a year. how much conditioner would she use in a full year? simplify your answer and write it as a proper fraction, mixed number, or whole number. bottles of conditioner

Answer

# Explanation: ## Step1: Set up the proportion Let $x$ be the amount of conditioner used in a year. We know that $\frac{3}{4}$ of a bottle is used in $\frac{7}{12}$ of a year. So the proportion is $\frac{\frac{3}{4}}{\frac{7}{12}}=\frac{x}{1}$. ## Step2: Solve for $x$ Cross - multiply to get $x=\frac{3}{4}\div\frac{7}{12}$. When dividing by a fraction, we multiply by its reciprocal, so $x = \frac{3}{4}\times\frac{12}{7}$. ## Step3: Calculate the product $\frac{3}{4}\times\frac{12}{7}=\frac{3\times12}{4\times7}=\frac{36}{28}$. Simplify the fraction by dividing both the numerator and denominator by 4, we get $\frac{9}{7}=1\frac{2}{7}$. # Answer: $1\frac{2}{7}$