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The problem in your image asks you to estimate the partial quotients as you divide \( 6,743 \div 21 \). It also provides a place to check your work by expressing \( 6,743 \) as a product of 21 and some whole number, plus a remainder.

Let's break this problem down step-by-step:

### Step 1: Estimate the Quotients
We will begin by estimating how many times 21 can go into different sections of the number 6,743.

1. First, estimate \( 6,000 \div 21 \):
   \[
   \frac{6,000}{21} \approx 285
   \]

2. Now, subtract \( 285 \times 21 = 5,985 \) from 6,743:
   \[
   6,743 - 5,985 = 758
   \]

3. Next, estimate \( 758 \div 21 \):
   \[
   \frac{758}{21} \approx 36
   \]
   Multiply \( 36 \times 21 = 756 \).

4. Finally, subtract \( 758 - 756 = 2 \).

So, the full division gives us:
\[
6,743 \div 21 \approx 285 + 36 = 321 \text{ remainder } 2
\]

### Step 2: Check the Division
Now, let's check the division by writing the equation:
\[
6,743 = (321 \times 21) + 2
\]
\[
321 \times 21 = 6,741
\]
\[
6,741 + 2 = 6,743
\]
The result matches, confirming that our estimation and division were correct.

---

Would you like more details on this problem or additional clarification? Here are five related questions to practice:

1. Estimate \( 4,512 \div 23 \).
2. How would you estimate \( 9,876 \div 31 \)?
3. Perform long division to solve \( 7,128 \div 19 \).
4. Use partial quotients to estimate \( 5,432 \div 18 \).
5. What is the remainder of \( 8,765 \div 22 \)?

**Tip**: When estimating division, always round the divisor or dividend to numbers that are easier to work with, and adjust your estimate as needed.

Estimate the partial quotients as you divide 6,743 ÷ 21. Make as many estimates as needed. Then check your work.

This problem involves estimating partial quotients to solve 6,743 ÷ 21. It teaches step-by-step division with estimates, demonstrating how to check your work. Suitable for students in Grades 5-6, this task covers long division and estimation techniques.

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