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Let's go through each problem step-by-step.

### Problem 1:
Ethan writes \( \frac{1}{6} \) of a page in \( \frac{1}{12} \) of a minute. We need to find out how long it takes him to write a full page.

1. Let \( x \) be the time it takes to write a full page.
2. Set up a proportion: 
   \[
   \frac{1}{6} : \frac{1}{12} = 1 : x
   \]
3. Cross-multiply:
   \[
   \frac{1}{6} \times x = 1 \times \frac{1}{12}
   \]
4. Solve for \( x \) by isolating it:
   \[
   x = \frac{1}{12} \times 6 = \frac{6}{12} = \frac{1}{2} \text{ minutes}
   \]
   
So, it takes Ethan \( \frac{1}{2} \) minute to write a full page.

### Problem 2:
Mike plays \( \frac{1}{5} \) of a song in \( \frac{1}{15} \) of a minute. We need to find the time it will take him to play the entire song.

1. Let \( y \) be the time to play the full song.
2. Set up a proportion:
   \[
   \frac{1}{5} : \frac{1}{15} = 1 : y
   \]
3. Cross-multiply:
   \[
   \frac{1}{5} \times y = 1 \times \frac{1}{15}
   \]
4. Solve for \( y \):
   \[
   y = \frac{1}{15} \times 5 = \frac{5}{15} = \frac{1}{3} \text{ minutes}
   \]
   
It will take Mike \( \frac{1}{3} \) minute to play the entire song.

### Problem 3:
Kayla uses \( \frac{1}{3} \) of a liter of milk to make \( \frac{1}{9} \) of a jug of tea. We need to find out how much milk is required to fill the jug.

1. Let \( z \) be the total milk needed to fill one full jug.
2. Set up a proportion:
   \[
   \frac{1}{3} : \frac{1}{9} = z : 1
   \]
3. Cross-multiply:
   \[
   \frac{1}{3} \times 1 = z \times \frac{1}{9}
   \]
4. Solve for \( z \):
   \[
   z = \frac{1}{3} \div \frac{1}{9} = \frac{1}{3} \times 9 = 3 \text{ liters}
   \]

Kayla needs 3 liters of milk to fill the jug.

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### Related Questions:
1. How do you set up proportions in real-world problems?
2. What other methods can be used to solve fractions of quantities?
3. How does cross-multiplication work in ratios?
4. How do you convert proportions into equations?
5. Why is understanding units important in fraction problems?

**Tip:** When solving problems with fractions, converting them into simpler proportions often makes the calculation clearer and more manageable.

1. Ethan writes 1/6 of a page in 1/12 of a minute. How much time does it take him to write a full page? 2. Mike plays 1/5 of a song in 1/15 of a minute. How much time will it take for Mike to play the entire song? 3. Kayla used 1/3 of a liter of milk to make 1/9 of a jug of tea. How much milk is required to fill the jug?

Learn how to solve ratio problems involving fractions with these examples: calculate the time for a full page to be written, the duration to play a song, and the milk required to fill a jug. This guide uses ratios, fractions, and proportions to solve real-life problems, suitable for Grade 7 students.

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