This worksheet provides comprehensive practice for short division, guiding students through dividing four-digit numbers by single-digit divisors across five distinct sections.

The task involves solving a series of short division problems where 4-digit numbers are divided by single-digit divisors. Below, I will solve one problem from each section as an example and explain the process step-by-step.

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Section A: Example Problem

#### Problem: \( 2 \big) 8224 \)

1. Divide the first digit (8) by 2:
- \( 8 \div 2 = 4 \)
- Write 4 above the line.

2. Bring down the next digit (2):
- Now, divide \( 2 \) by 2.
- \( 2 \div 2 = 1 \)
- Write 1 above the line.

3. Bring down the next digit (2):
- Now, divide \( 2 \) by 2.
- \( 2 \div 2 = 1 \)
- Write 1 above the line.

4. Bring down the last digit (4):
- Now, divide \( 4 \) by 2.
- \( 4 \div 2 = 2 \)
- Write 2 above the line.

5. Final Answer:
- The quotient is \( 4112 \).

Solution for \( 2 \big) 8224 \):
\[
\boxed{4112}
\]

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Section B: Example Problem

#### Problem: \( 3 \big) 1223 \)

1. Divide the first digit (1) by 3:
- \( 1 < 3 \), so consider the first two digits (12).
- \( 12 \div 3 = 4 \)
- Write 4 above the line.

2. Bring down the next digit (2):
- Now, divide \( 2 \) by 3.
- \( 2 < 3 \), so consider the next digit to form 23.
- \( 23 \div 3 = 7 \) with a remainder of 2.
- Write 7 above the line.

3. Final Answer:
- The quotient is \( 407 \) with a remainder of 2.

Solution for \( 3 \big) 1223 \):
\[
\boxed{407 \text{ R } 2}
\]

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Section C: Example Problem

#### Problem: \( 4 \big) 4208 \)

1. Divide the first digit (4) by 4:
- \( 4 \div 4 = 1 \)
- Write 1 above the line.

2. Bring down the next digit (2):
- Now, divide \( 2 \) by 4.
- \( 2 < 4 \), so consider the next digit to form 20.
- \( 20 \div 4 = 5 \)
- Write 5 above the line.

3. Bring down the next digit (8):
- Now, divide \( 8 \) by 4.
- \( 8 \div 4 = 2 \)
- Write 2 above the line.

4. Final Answer:
- The quotient is \( 1052 \).

Solution for \( 4 \big) 4208 \):
\[
\boxed{1052}
\]

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Section D: Example Problem

#### Problem: \( 3 \big) 2071 \)

1. Divide the first digit (2) by 3:
- \( 2 < 3 \), so consider the first two digits (20).
- \( 20 \div 3 = 6 \) with a remainder of 2.
- Write 6 above the line.

2. Bring down the next digit (7):
- Add the remainder (2) to 7 to get 27.
- \( 27 \div 3 = 9 \)
- Write 9 above the line.

3. Bring down the last digit (1):
- Now, divide \( 1 \) by 3.
- \( 1 < 3 \), so the remainder is 1.
- Write 0 above the line and note the remainder.

4. Final Answer:
- The quotient is \( 690 \) with a remainder of 1.

Solution for \( 3 \big) 2071 \):
\[
\boxed{690 \text{ R } 1}
\]

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Section E: Example Problem

#### Problem: \( 3 \big) 4869 \)

1. Divide the first digit (4) by 3:
- \( 4 \div 3 = 1 \) with a remainder of 1.
- Write 1 above the line.

2. Bring down the next digit (8):
- Add the remainder (1) to 8 to get 9.
- \( 9 \div 3 = 3 \)
- Write 3 above the line.

3. Bring down the next digit (6):
- Now, divide \( 6 \) by 3.
- \( 6 \div 3 = 2 \)
- Write 2 above the line.

4. Bring down the last digit (9):
- Now, divide \( 9 \) by 3.
- \( 9 \div 3 = 3 \)
- Write 3 above the line.

5. Final Answer:
- The quotient is \( 1623 \).

Solution for \( 3 \big) 4869 \):
\[
\boxed{1623}
\]

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Summary of Solutions

- Section A: \( 2 \big) 8224 = \boxed{4112} \)
- Section B: \( 3 \big) 1223 = \boxed{407 \text{ R } 2} \)
- Section C: \( 4 \big) 4208 = \boxed{1052} \)
- Section D: \( 3 \big) 2071 = \boxed{690 \text{ R } 1} \)
- Section E: \( 3 \big) 4869 = \boxed{1623} \)

These examples illustrate the process of short division for 4-digit numbers. You can apply the same steps to solve the remaining problems in each section.