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Answer :
Let's start by analyzing the given information and calculating the needed values:
1. Understanding the Ratio Provided:
You have a cleaning spray that contains [tex]\( \frac{1}{2} \)[/tex] cup of vinegar for every 4 teaspoons of lemon oil. This is our initial ratio.
2. Finding the Unit Rate:
To find the rate in cups of vinegar per teaspoon of lemon oil, you divide the amount of vinegar by the amount of lemon oil. Thus, you have:
[tex]\[
\text{Rate of vinegar per teaspoon of lemon oil} = \frac{1/2}{4}
\][/tex]
Simplifying this fraction:
[tex]\[
\frac{1/2}{4} = \frac{1}{2} \times \frac{1}{4} = \frac{1}{8}
\][/tex]
This means that the rate is [tex]\( \frac{1}{8} \)[/tex] cup of vinegar per teaspoon of lemon oil.
3. Calculating the Vinegar Needed for 2 Teaspoons of Lemon Oil:
Now that we know the rate, we want to find out how many cups of vinegar are needed for 2 teaspoons of lemon oil.
You simply multiply the rate by the number of teaspoons:
[tex]\[
\text{Vinegar for 2 teaspoons} = \frac{1}{8} \times 2 = \frac{2}{8} = \frac{1}{4}
\][/tex]
Therefore, [tex]\( \frac{1}{4} \)[/tex] cup of vinegar is needed for 2 teaspoons of lemon oil.
Conclusion:
The rate in cups of vinegar per teaspoon of lemon oil is [tex]\( \frac{1}{8} \)[/tex] cup per teaspoon. For 2 teaspoons of lemon oil, you will need [tex]\( \frac{1}{4} \)[/tex] cup of vinegar.
1. Understanding the Ratio Provided:
You have a cleaning spray that contains [tex]\( \frac{1}{2} \)[/tex] cup of vinegar for every 4 teaspoons of lemon oil. This is our initial ratio.
2. Finding the Unit Rate:
To find the rate in cups of vinegar per teaspoon of lemon oil, you divide the amount of vinegar by the amount of lemon oil. Thus, you have:
[tex]\[
\text{Rate of vinegar per teaspoon of lemon oil} = \frac{1/2}{4}
\][/tex]
Simplifying this fraction:
[tex]\[
\frac{1/2}{4} = \frac{1}{2} \times \frac{1}{4} = \frac{1}{8}
\][/tex]
This means that the rate is [tex]\( \frac{1}{8} \)[/tex] cup of vinegar per teaspoon of lemon oil.
3. Calculating the Vinegar Needed for 2 Teaspoons of Lemon Oil:
Now that we know the rate, we want to find out how many cups of vinegar are needed for 2 teaspoons of lemon oil.
You simply multiply the rate by the number of teaspoons:
[tex]\[
\text{Vinegar for 2 teaspoons} = \frac{1}{8} \times 2 = \frac{2}{8} = \frac{1}{4}
\][/tex]
Therefore, [tex]\( \frac{1}{4} \)[/tex] cup of vinegar is needed for 2 teaspoons of lemon oil.
Conclusion:
The rate in cups of vinegar per teaspoon of lemon oil is [tex]\( \frac{1}{8} \)[/tex] cup per teaspoon. For 2 teaspoons of lemon oil, you will need [tex]\( \frac{1}{4} \)[/tex] cup of vinegar.
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