Question

the chef at andys restaurant used \\(\frac{2}{3}\\) of a bag of onions in \\(\frac{1}{6}\\) of an hour. compute the unit rate of bags of onions per hour. a \\(2\\) bags per hour b \\(3\\) bags per hour c \\(4\\) bags per hour d \\(6\\) bags per hour

Explanation:

Step1: Recall unit rate formula

Unit rate (bags per hour) is total bags used divided by total hours taken. So formula: $\text{Unit Rate} = \frac{\text{Bags of Onions}}{\text{Hours}}$

Step2: Substitute values

Bags of onions = $\frac{2}{3}$, Hours = $\frac{1}{6}$. So $\text{Unit Rate} = \frac{\frac{2}{3}}{\frac{1}{6}}$

Step3: Divide fractions (multiply by reciprocal)

Dividing by a fraction is multiplying by its reciprocal. So $\frac{\frac{2}{3}}{\frac{1}{6}} = \frac{2}{3} \times \frac{6}{1}$

Step4: Simplify the multiplication

$\frac{2 \times 6}{3 \times 1} = \frac{12}{3} = 4$

Answer:

C. 4 bags per hour