At a party Kelly ate four and a half cakes alexia ate two and one third cakes 

To compare how much Kelly and Alexia ate, let's convert their cake consumption into improper fractions:

1. **Kelly's cakes:**
   - Kelly ate four and a half cakes.
   - Four and a half can be written as \(4 \frac{1}{2}\).
   - Convert this to an improper fraction:
     \[
     4 \frac{1}{2} = \frac{(4 \times 2) + 1}{2} = \frac{8 + 1}{2} = \frac{9}{2}
     \]

2. **Alexia's cakes:**
   - Alexia ate two and one-third cakes.
   - Two and one-third can be written as \(2 \frac{1}{3}\).
   - Convert this to an improper fraction:
     \[
     2 \frac{1}{3} = \frac{(2 \times 3) + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3}
     \]

Now, let's compare how much they ate:

- Kelly ate \( \frac{9}{2} \) cakes.
- Alexia ate \( \frac{7}{3} \) cakes.

To compare, we can convert these to fractions with a common denominator, or convert them to decimal form.

3. **Find a common denominator:**
   - The denominators are 2 and 3. The least common denominator is 6.

   - Convert \( \frac{9}{2} \) to a fraction with a denominator of 6:
     \[
     \frac{9}{2} = \frac{9 \times 3}{2 \times 3} = \frac{27}{6}
     \]

   - Convert \( \frac{7}{3} \) to a fraction with a denominator of 6:
     \[
     \frac{7}{3} = \frac{7 \times 2}{3 \times 2} = \frac{14}{6}
     \]

4. **Compare the fractions:**
   - Kelly ate \( \frac{27}{6} \) cakes.
   - Alexia ate \( \frac{14}{6} \) cakes.

Since \( \frac{27}{6} \) is greater than \( \frac{14}{6} \), Kelly ate more cakes than Alexia.

Would you like any more details or have any questions?

Here are 5 related questions:
1. How do you convert mixed numbers to improper fractions?
2. How do you compare two fractions with different denominators?
3. What is the process of finding the least common denominator?
4. How can you add or subtract mixed numbers?
5. How do you convert an improper fraction back to a mixed number?

**Tip:** When comparing fractions, it’s often easier to convert them to have a common denominator or to decimal form.

Learn how to compare the amount of cake consumed by Kelly and Alexia using fractions and mixed numbers. Kelly ate 4 and a half cakes while Alexia ate 2 and one third cakes. Understand the conversion of mixed numbers to improper fractions, finding common denominators, and comparing fractions with different denominators. Suitable for students in Grades 5-6.

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