Question

a) one way to find an equivalent ratio is to divide both numbers in a ratio by the same number.
e) how many cups of vinegar are needed for 2 teaspoons of lemon oil?
e) ? c of vinegar is needed for 2 tsp of lemon oil.
(chart: cleaning spray
vinegar (c) axis: 0 to 1/2
lemon oil (tsp) axis: 0 to 4)

Explanation:

Step1: Identify the ratio from the number line

From the number line, when lemon oil is \(4\) teaspoons, vinegar is \(\frac{1}{2}\) cup. So the ratio of vinegar to lemon oil is \(\frac{\frac{1}{2}}{4}=\frac{1}{8}\) cup per teaspoon.

Step2: Calculate vinegar for 2 teaspoons

For \(2\) teaspoons of lemon oil, the amount of vinegar needed is \(2\times\frac{1}{8}=\frac{2}{8}=\frac{1}{4}\) cup. Or we can use equivalent ratios: Let \(x\) be the cups of vinegar for \(2\) tsp lemon oil. The ratio \(\frac{\frac{1}{2}}{4}=\frac{x}{2}\), cross - multiply: \(4x = 2\times\frac{1}{2}\), \(4x = 1\), \(x=\frac{1}{4}\).

Answer:

\(\frac{1}{4}\)