Question

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. \\(\square\\) bottles of conditioner

Explanation:

Step1: Define the unit rate formula

To find the amount used in a full year, we use the formula for unit rate: \(\text{Unit Rate} = \frac{\text{Amount Used}}{\text{Time}}\). Here, the amount used is \(\frac{3}{4}\) of a bottle, and the time is \(\frac{7}{12}\) of a year. So we need to calculate \(\frac{\frac{3}{4}}{\frac{7}{12}}\) to find the amount per year.

Step2: Divide the fractions

Dividing by a fraction is the same as multiplying by its reciprocal. So \(\frac{\frac{3}{4}}{\frac{7}{12}}=\frac{3}{4}\times\frac{12}{7}\).

Step3: Multiply the numerators and denominators

Multiply the numerators: \(3\times12 = 36\). Multiply the denominators: \(4\times7 = 28\). So we get \(\frac{36}{28}\).

Step4: Simplify the fraction

Simplify \(\frac{36}{28}\) by dividing both the numerator and denominator by their greatest common divisor, which is 4. \(\frac{36\div4}{28\div4}=\frac{9}{7}\), which can also be written as \(1\frac{2}{7}\).

Answer:

\(\frac{9}{7}\) (or \(1\frac{2}{7}\))