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To evaluate if Emilia's estimate is reasonable, let's calculate an approximation of \( 261 \times 216 \).

**Step 1: Round the numbers for easier multiplication.**
- \( 261 \) can be rounded to \( 260 \) (or \( 300 \) for a broader approximation).
- \( 216 \) can be rounded to \( 220 \) (or \( 200 \)).

**Step 2: Multiply the rounded values.**
- Using \( 260 \times 220 \):
  \[
  260 \times 220 = 57200
  \]

- Using a broader approximation, \( 300 \times 200 \):
  \[
  300 \times 200 = 60000
  \]

**Comparison to Emilia's estimate:**
Emilia said that the best estimate is around **40,000**. However, the approximations we did give us values around **57,200** and **60,000**, which are significantly higher. Therefore, **I do not agree with Emilia's estimate**. The estimate should be closer to **60,000** rather than **40,000**.

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. How would the estimate change if the numbers were rounded differently, like to the nearest 100 instead?
2. What is the exact value of \( 261 \times 216 \), and how does it compare to the estimate?
3. How can rounding errors affect estimates in multiplication problems?
4. What is a good strategy to choose the best rounding point for estimating products?
5. Can you think of a situation where underestimating a value could lead to a problem?

**Tip:** When estimating, it's usually best to round numbers to values that make mental calculations easier, but still close to the original numbers.

Emilia says the best estimate of 261 × 216 is about 40,000. Do you agree? Why or why not?

Explore the estimation of the product 261 × 216, where Emilia suggests it is about 40,000. Analyze the accuracy of this estimate using rounding techniques, suitable for students in Grades 5-7. Understand the concepts of multiplication and estimation in this detailed breakdown.

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