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------------------------------------------------ How many cups of vinegar are needed for 2 teaspoons of lemon oil if the ratio is [tex]\frac{1}{8}[/tex] cup of vinegar for 2 teaspoons of lemon oil?

To determine how many cups of vinegar are needed for 2 teaspoons of lemon oil, follow these steps:

1. Understand the Ratio: The problem states that [tex]\(\frac{1}{8}\)[/tex] cup of vinegar is needed for every 2 teaspoons of lemon oil.

2. Set Up the Proportion: Since the ratio [tex]\(\frac{1}{8}\)[/tex] cup of vinegar for 2 teaspoons of lemon oil is given, we can use it to find out the actual cups of vinegar needed for exactly 2 teaspoons of lemon oil.

3. Proportion Calculation:
- The given ratio is [tex]\(\frac{1}{8}\)[/tex] cup of vinegar per 2 teaspoons of lemon oil.
- We need to determine the amount of vinegar for 2 teaspoons of lemon oil.

4. Multiply to Find the Answer:
- [tex]\[
\text{Vinegar needed} = \left(\frac{1}{8} \text{ cups}\right) \times 2 \text{ teaspoons}
\][/tex]
- Carry out the multiplication:
[tex]\[
\frac{1}{8} \times 2 = \frac{2}{8} = \frac{1}{4}
\][/tex]

5. Conclusion: The calculation shows that [tex]\(\frac{1}{4}\)[/tex] cup of vinegar is needed for 2 teaspoons of lemon oil.

So, the final answer is that [tex]\(0.25\)[/tex] cups (or [tex]\(\frac{1}{4}\)[/tex] cups) of vinegar are needed for 2 teaspoons of lemon oil.