2. 184x210 round 200x200 = 40,000

3. 77x412 -) 80x400=32,000

Good estimates.

I think there is a mistake in your calculations for both question 2 and question 3. Let me double-check and provide the correct steps for each calculation.

Question 2: 184x210 rounded to the nearest hundred is equal to 200x200

Step 1: Calculate the product 184x210
184 x 210 = 38,640

Step 2: Round the result to the nearest hundred
38,640 rounded to the nearest hundred is 38,600

So, the correct answer for question 2 is 38,600, not 40,000.

Question 3: 77x412 minus by 80x400

Step 1: Calculate the product 77x412
77 x 412 = 31,724

Step 2: Calculate the product 80x400
80 x 400 = 32,000

Step 3: Subtract the second product from the first product
31,724 - 32,000 = -276

So, the correct answer for question 3 is -276, not 32,000.

To calculate these arithmetic operations, you can follow these steps:

1. For the calculation 184x210 - Rounded to 200x200:
- Multiply 184 by 210: 184 x 210 = 38,640.
- Since we want to round the result to the nearest hundred, we need to find the closest hundred to 38,640, which is 38,600.
- Now, we have 38,600, and we want to round to the nearest thousand. The closest thousand to 38,600 is 39,000.
- However, in the given question, we need to round it to 200x200, so we have to adjust our rounding by subtracting 200. 39,000 - 200 = 38,800.
- Therefore, the rounded result of 184x210 to 200x200 is 38,800.

2. For the calculation 77x412 - Rounded to 80x400:
- Multiply 77 by 412: 77 x 412 = 31,804.
- We want to round the result to the nearest hundred. So, we check the value in the tens place (0) to determine whether we should round up or down.
- Since 0 is less than 5, we round down to the nearest hundred and change all digits to the right of the hundreds place to 0.
- Therefore, the rounded result of 77x412 to 80x400 is 31,800.

Please note that the calculations provided here assumed rounding to the nearest hundred and thousand as per the given question. Depending on the specific given instructions or context, rounding may vary.