https://file.aiquickdraw.com/mathbot/file/172679646912098bjzjke.jpg

Let's go through the questions based on the image you provided. There are two main parts:

### 1. **Maria's statement about the multiplication problem:**
Maria claims that \( 4 \times \frac{4}{5} \) is the same as \( \frac{3}{5} + \frac{3}{5} + \frac{4}{5} + \frac{4}{5} \).

The options provided are:
- **A:** Yes, because \( 4 \times \frac{4}{5} = \frac{16}{5} \) and the sum \( \frac{3}{5} + \frac{3}{5} + \frac{4}{5} + \frac{4}{5} = \frac{16}{5} \).
- **B:** Yes, because multiplication is repeated addition, and the sum \( \frac{3}{5} + \frac{3}{5} + \frac{4}{5} + \frac{4}{5} \) equals \( 4 \times \frac{4}{5} \).
- **C:** No, because \( 4 \times \frac{4}{5} \) is not the same as adding different fractions \( \frac{3}{5} \) and \( \frac{4}{5} \).
- **D:** No, because \( 4 \times \frac{4}{5} \) is \( \frac{16}{5} \), but the sum of those fractions is also \( \frac{16}{5} \).

#### Correct Explanation:
- **A** is correct because both expressions result in \( \frac{16}{5} \), so Maria is correct mathematically.
- **B** is also correct because multiplication can be seen as repeated addition, and the expression \( 4 \times \frac{4}{5} \) can represent adding the fractions.

Thus, **A and B** are the correct choices.

### 2. **Which model represents the multiplication problem \( \frac{2}{3} \times 3 \)?**
You are asked to select which of the provided models represents this multiplication problem.

- The equation \( \frac{2}{3} \times 3 \) equals \( 2 \), because multiplying \( \frac{2}{3} \times 3 \) cancels out the denominator, leaving \( 2 \).
  
Thus, the correct model should show 2 whole parts.

Looking at the models:
- The third model, which shows two shaded circles, corresponds to the result of \( \frac{2}{3} \times 3 = 2 \).

So, **option C** is correct.

### 3. **Shaded parts of the complete model representing \( 3 \times \frac{2}{10} \):**
The figure given shows 3 groups with 2 shaded parts out of 10 in each group. This represents \( 3 \times \frac{2}{10} \), which equals \( \frac{6}{10} \) or \( 0.6 \).

### 4. **Which expressions are equivalent to \( 3 \times \frac{2}{10} \)?**
The options provided are:
- **A:** \( 3 \times \frac{2}{10} \)
- **B:** \( 6 \times \frac{1}{10} \)
- **C:** \( \frac{2}{10} + \frac{2}{10} + \frac{2}{10} \)
- **D:** \( 2 \times 2 \times 2 \)

The correct answers are:
- **A** is equivalent because it's the original expression.
- **B** is equivalent because multiplying \( 6 \times \frac{1}{10} \) also results in \( \frac{6}{10} \).
- **C** is equivalent because adding \( \frac{2}{10} \) three times equals \( 3 \times \frac{2}{10} \).

So, the correct choices are **A, B, and C**.

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Would you like more details on any of these answers?

Here are 5 follow-up questions:
1. How do you convert a fraction multiplication problem into a sum of fractions?
2. Why is repeated addition a way to understand multiplication?
3. What is the general process for multiplying fractions and whole numbers?
4. Can models always represent multiplication problems accurately?
5. What is the importance of simplifying fraction multiplications?

**Tip:** When multiplying fractions by whole numbers, consider turning the whole number into a fraction (like \( 3 = \frac{3}{1} \)) to make the calculation easier.

Maria says that 4 × 4/5 is the same as 3/5 + 3/5 + 4/5 + 4/5. Is she correct? Why? Choose more than one answer. Which model represents the multiplication problem 2/3 × 3?

Explore whether multiplying 4 × 4/5 is the same as adding fractions 3/5 + 3/5 + 4/5 + 4/5 through repeated addition. Also, learn how to represent 2/3 × 3 using visual models. This problem covers key concepts in fraction multiplication and is suitable for students in Grades 5-7.

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