To break down the mixed number \( 3 \frac{2}{3} \) into the sum of fractions, let's think of it as follows:

### **Step-by-Step Breakdown**:

1. The whole number 3 can be written as the sum of three fractions where each fraction has a denominator of 3:
   \[
   3 = \frac{3}{3} + \frac{3}{3} + \frac{3}{3}
   \]

2. The fraction part \( \frac{2}{3} \) is already in its simplest form.

3. Now, we combine these:

   \[
   3 \frac{2}{3} = \frac{3}{3} + \frac{3}{3} + \frac{3}{3} + \frac{2}{3}
   \]

So, the filled blanks are:

- \( 3 \frac{2}{3} = \frac{3}{3} + \frac{3}{3} + \frac{3}{3} + \frac{2}{3} = \frac{11}{3} \)

### **Filled Blanks**:

\[
3 \frac{2}{3} = \frac{3}{3} + \frac{3}{3} + \frac{3}{3} + \frac{2}{3} = \frac{11}{3}
\]

Would you like to explore more examples like this, or do you have any questions?

### **Related Questions**:
1. How would you express \( 2 \frac{5}{6} \) as a sum of fractions?
2. What is the improper fraction form of \( 4 \frac{1}{5} \)?
3. Can you break down \( 5 \frac{4}{7} \) in the same way?
4. How does adding fractions work when they have different denominators?
5. What is the general approach to converting a sum of fractions back into a mixed number?

**Tip**: Visualizing fractions on a number line can help in understanding how mixed numbers relate to improper fractions!

Learn how to break down the mixed number 3 2/3 into a sum of fractions with a detailed step-by-step solution. This problem covers key concepts in fractions and mixed numbers, suitable for students in Grades 4-6.

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