Question

4(1) one way to find an equivalent ratio is to divide both numbers in a ratio by the same number.
4(2) how many cups of vinegar are needed for 2 teaspoons of lemon oil?
4(3) \\(\frac{1}{4}\\) c of vinegar is needed for 2 tsp of lemon oil.
4(4) what is the rate in cups of vinegar per teaspoon of lemon oil?
4(5) ? c of vinegar per tsp of lemon oil
(right side chart: cleaning spray
vinegar (c) 0, \\(\frac{1}{4}\\), \\(\frac{1}{2}\\)
lemon oil (tsp) 0, \\(\frac{1}{2}\\), \\(\frac{1}{4}\\))

Explanation:

Step1: Identify the given values

We know that for 2 teaspoons (tsp) of lemon oil, we need $\frac{1}{4}$ cups (c) of vinegar.

Step2: Calculate the rate per teaspoon

To find the rate in cups of vinegar per teaspoon of lemon oil, we divide the amount of vinegar by the amount of lemon oil. So we have the formula: Rate = $\frac{\text{Vinegar (c)}}{\text{Lemon Oil (tsp)}}$. Substituting the given values, we get Rate = $\frac{\frac{1}{4}}{2}$.

Step3: Simplify the division

Dividing by a number is the same as multiplying by its reciprocal. So $\frac{\frac{1}{4}}{2}=\frac{1}{4}\times\frac{1}{2}=\frac{1}{8}$.

Answer:

$\frac{1}{8}$