https://file.aiquickdraw.com/mathbot/file/1726971311449eixfizek.jpg

Let's solve the problem shown in the image.

Jack and Jill shared \(\frac{1}{2}\) of a cake. Jack ate twice as much as Jill. We need to find what fraction of the whole cake Jack ate.

### Step 1: Assign variables
Let \( x \) represent the fraction of the \(\frac{1}{2}\) cake that Jill ate. Since Jack ate twice as much as Jill, Jack ate \( 2x \) of the \(\frac{1}{2}\) cake.

### Step 2: Set up the equation
Together, they ate the entire \(\frac{1}{2}\) of the cake:
\[
x + 2x = \frac{1}{2}
\]
Simplifying the equation:
\[
3x = \frac{1}{2}
\]
Solving for \(x\):
\[
x = \frac{1}{6}
\]

So Jill ate \(\frac{1}{6}\) of the total cake, and Jack ate \(2x = 2 \times \frac{1}{6} = \frac{1}{3}\) of the total cake.

### Step 3: Conclusion
Jack ate \(\frac{1}{3}\) of the whole cake.

If you have any further questions or need additional details, feel free to ask!

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Here are 5 follow-up questions:
1. What fraction of the whole cake did Jill eat?
2. How much of the whole cake was left after Jack and Jill ate their portions?
3. If the cake was divided into 12 slices, how many slices did Jack eat?
4. What if Jack ate three times as much as Jill instead? What fraction would Jack eat?
5. How would the answer change if Jack and Jill shared \(\frac{3}{4}\) of the cake instead?

**Tip:** When solving word problems, carefully define your variables and set up equations based on the relationships described in the problem.

Jack and Jill shared 1/2 of a cake. Jack got to eat twice as much cake as Jill. What fraction of the whole cake did Jack eat?

Solve the problem where Jack and Jill share 1/2 of a cake, with Jack eating twice as much as Jill. Learn how to find the fraction of the whole cake that Jack ate using basic algebraic concepts. This is suitable for students in Grades 5-7.

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