Question

kates new juicer is able to squeeze \\(\frac{3}{4}\\) of a cup of orange juice from \\(\frac{1}{12}\\) of a bag of oranges. compute the unit rate of cups per bag. a 3 cups per bag b 6 cups per bag c 9 cups per bag d 12 cups per bag

Explanation:

Step1: Recall unit rate formula

Unit rate (cups per bag) is calculated by dividing the number of cups by the number of bags. So, we use the formula: \(\text{Unit Rate} = \frac{\text{Cups of Juice}}{\text{Bags of Oranges}}\)

Step2: Substitute the values

We know that the cups of juice is \(\frac{3}{4}\) and the bags of oranges is \(\frac{1}{12}\). So, substituting these values into the formula, we get: \(\text{Unit Rate} = \frac{\frac{3}{4}}{\frac{1}{12}}\)

Step3: Divide the fractions

Dividing by a fraction is the same as multiplying by its reciprocal. So, \(\frac{\frac{3}{4}}{\frac{1}{12}}=\frac{3}{4}\times\frac{12}{1}\)

Step4: Simplify the multiplication

First, multiply the numerators: \(3\times12 = 36\). Then, multiply the denominators: \(4\times1=4\). So, we have \(\frac{36}{4}\)

Step5: Simplify the fraction

\(\frac{36}{4}=9\)

Answer:

C. 9 cups per bag