To determine the unit rate of lemonade to cranberry juice, we need to compare the amounts of lemonade and cranberry juice in the recipe.
Here are the amounts given in the recipe:
- Lemonade: [tex]\(\frac{1}{2}\)[/tex] liter
- Cranberry Juice: [tex]\(\frac{1}{10}\)[/tex] liter
The unit rate is found by dividing the amount of lemonade by the amount of cranberry juice:
[tex]\[
\text{Unit rate} = \frac{\text{amount of lemonade}}{\text{amount of cranberry juice}} = \frac{\frac{1}{2}}{\frac{1}{10}}
\][/tex]
To simplify this division of fractions, we can multiply by the reciprocal of the denominator:
[tex]\[
\frac{\frac{1}{2}}{\frac{1}{10}} = \frac{1}{2} \times \frac{10}{1} = \frac{1 \times 10}{2 \times 1} = \frac{10}{2} = 5
\][/tex]
Thus, the unit rate of lemonade to cranberry juice is [tex]\(5\)[/tex].
Therefore, the correct answer is:
D. 5
