Question

1. (standard 7.pr.2) a recipe for a large batch of salad dressing calls for \\(\frac{1}{2}\\) cup of olive oil for every \\(\frac{2}{3}\\) cup of vinegar. how much olive oil is needed for exactly 1 cup of vinegar? (find the unit rate).

Explanation:

Step1: Define the ratio

We know that for $\frac{2}{3}$ cup of vinegar, we need $\frac{1}{2}$ cup of olive oil. Let $x$ be the amount of olive oil needed for 1 cup of vinegar. So the ratio of olive oil to vinegar should be constant, which gives us the proportion $\frac{\frac{1}{2}}{\frac{2}{3}}=\frac{x}{1}$.

Step2: Solve for $x$

To solve for $x$, we can use the rule of cross - multiplication or simplify the left - hand side. When dividing fractions, we multiply by the reciprocal. So $\frac{\frac{1}{2}}{\frac{2}{3}}=\frac{1}{2}\times\frac{3}{2}=\frac{3}{4}$. And since $\frac{x}{1}=x$, we have $x = \frac{3}{4}$.

Answer:

$\frac{3}{4}$ cup