Subtraction with Regrouping Worksheets: 4-Digit Numbers

Complete subtraction with regrouping worksheets for 4-digit numbers: exercises, solutions, and step-by-step guides for mastering borrowing concepts.

Solution: Exercises 1 to 5
1 4-digit subtraction with regrouping
Exercise 1
Calculate:
\(4,235 - 1,789\)
Definition:

4-digit subtraction with regrouping: When subtracting 4-digit numbers, if the digit in any place value of the top number is smaller than the bottom number, we regroup from the next higher place value.

Subtraction method:
  1. Start from the ones place
  2. If the top digit is smaller than the bottom, regroup from the next higher place value
  3. Convert 1 unit from higher place to 10 units in current place
  4. Repeat if needed for higher place values
  5. Complete the subtraction in each place value
Th
H
T
O
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4
2
3
5
-
1
7
8
9
-
Step 1: Ones place: 5 < 9, so we need to regroup from the tens place. Tens place has only 3, so we need to regroup from hundreds first.
↓
4
1
13
5
-
↓
4
1
12
15
-
Step 1: Regroup from hundreds to tens

4235 becomes 4 thousands, 1 hundred, 13 tens, 5 ones (since 1 hundred = 10 tens)

Step 2: Regroup from tens to ones

Now we have 4 thousands, 1 hundred, 12 tens, 15 ones (since 1 ten = 10 ones)

Step 3: Subtract each place value

Ones: 15 - 9 = 6

Tens: 12 - 8 = 4

Hundreds: 1 - 7 = ? (Need to regroup from thousands)

Step 4: Hundreds place: 1 < 7, so we need to regroup from the thousands place.
↓
3
11
12
15
-
Step 5: Complete subtraction

Ones: 15 - 9 = 6

Tens: 12 - 8 = 4

Hundreds: 11 - 7 = 4

Thousands: 3 - 1 = 2

\(4,235 - 1,789 = 2,446\)
Final answer:

\(4,235 - 1,789 = 2,446\)

Applied rules:

• Regrouping: When top digit is smaller, borrow from next higher place value

• Place value: 1 thousand = 10 hundreds, 1 hundred = 10 tens, 1 ten = 10 ones

• Subtraction: Subtract each place value separately

2 4-digit subtraction with regrouping
Exercise 2
Calculate:
\(5,402 - 2,678\)
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H
T
O
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5
4
0
2
-
2
6
7
8
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Step 1: Ones place: 2 < 8, so we need to regroup from the tens place. Tens place has 0, so we need to regroup from hundreds first.
↓
5
3
0
2
-
↓
5
3
9
12
-
Step 1: Regroup from hundreds to tens

5402 becomes 5 thousands, 3 hundreds, 10 tens, 2 ones (since 1 hundred = 10 tens)

Step 2: Regroup from tens to ones

Now we have 5 thousands, 3 hundreds, 9 tens, 12 ones (since 1 ten = 10 ones)

Step 3: Subtract each place value

Ones: 12 - 8 = 4

Tens: 9 - 7 = 2

Hundreds: 3 - 6 = ? (Need to regroup from thousands)

Step 4: Hundreds place: 3 < 6, so we need to regroup from the thousands place.
↓
4
13
9
12
-
Step 5: Complete subtraction

Ones: 12 - 8 = 4

Tens: 9 - 7 = 2

Hundreds: 13 - 6 = 7

Thousands: 4 - 2 = 2

\(5,402 - 2,678 = 2,724\)
Final answer:

\(5,402 - 2,678 = 2,724\)

Applied rules:

• Regrouping: When top digit is smaller, borrow from next higher place value

• Place value: 1 thousand = 10 hundreds, 1 hundred = 10 tens, 1 ten = 10 ones

• Subtraction: Subtract each place value separately

3 4-digit subtraction with regrouping
Exercise 3
Calculate:
\(6,103 - 3,457\)
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H
T
O
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6
1
0
3
-
3
4
5
7
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Step 1: Ones place: 3 < 7, so we need to regroup from the tens place. Tens place has 0, so we need to regroup from hundreds first.
↓
6
0
0
3
-
↓
6
0
9
13
-
Step 1: Regroup from hundreds to tens

6103 becomes 6 thousands, 0 hundreds, 10 tens, 3 ones (since 1 hundred = 10 tens)

Step 2: Regroup from tens to ones

Now we have 6 thousands, 0 hundreds, 9 tens, 13 ones (since 1 ten = 10 ones)

Step 3: Subtract each place value

Ones: 13 - 7 = 6

Tens: 9 - 5 = 4

Hundreds: 0 - 4 = ? (Need to regroup from thousands)

Step 4: Hundreds place: 0 < 4, so we need to regroup from the thousands place.
↓
5
10
9
13
-
Step 5: Complete subtraction

Ones: 13 - 7 = 6

Tens: 9 - 5 = 4

Hundreds: 10 - 4 = 6

Thousands: 5 - 3 = 2

\(6,103 - 3,457 = 2,646\)
Final answer:

\(6,103 - 3,457 = 2,646\)

Applied rules:

• Regrouping: When top digit is smaller, borrow from next higher place value

• Place value: 1 thousand = 10 hundreds, 1 hundred = 10 tens, 1 ten = 10 ones

• Subtraction: Subtract each place value separately

Solution: Exercises 4 to 7
4 4-digit subtraction with regrouping
Exercise 4
Calculate:
\(7,320 - 4,865\)
Th
H
T
O
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7
3
2
0
-
4
8
6
5
-
Step 1: Ones place: 0 < 5, so we need to regroup from the tens place. Tens place has only 2, so we need to regroup from hundreds first.
↓
7
2
12
0
-
↓
7
2
11
10
-
Step 1: Regroup from hundreds to tens

7320 becomes 7 thousands, 2 hundreds, 12 tens, 0 ones (since 1 hundred = 10 tens)

Step 2: Regroup from tens to ones

Now we have 7 thousands, 2 hundreds, 11 tens, 10 ones (since 1 ten = 10 ones)

Step 3: Subtract each place value

Ones: 10 - 5 = 5

Tens: 11 - 6 = 5

Hundreds: 2 - 8 = ? (Need to regroup from thousands)

Step 4: Hundreds place: 2 < 8, so we need to regroup from the thousands place.
↓
6
12
11
10
-
Step 5: Complete subtraction

Ones: 10 - 5 = 5

Tens: 11 - 6 = 5

Hundreds: 12 - 8 = 4

Thousands: 6 - 4 = 2

\(7,320 - 4,865 = 2,455\)
Final answer:

\(7,320 - 4,865 = 2,455\)

Applied rules:

• Regrouping: When top digit is smaller, borrow from next higher place value

• Place value: 1 thousand = 10 hundreds, 1 hundred = 10 tens, 1 ten = 10 ones

• Subtraction: Subtract each place value separately

5 4-digit subtraction with regrouping
Exercise 5
Calculate:
\(8,014 - 5,367\)
Th
H
T
O
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8
0
1
4
-
5
3
6
7
-
Step 1: Ones place: 4 < 7, so we need to regroup from the tens place. Tens place has only 1, so we need to regroup from hundreds first.
↓
8
0
1
4
-
↓
8
0
10
14
-
Step 1: Regroup from hundreds to tens

8014 becomes 7 thousands, 10 hundreds, 1 ten, 4 ones (since 1 thousand = 10 hundreds)

Step 2: Regroup from tens to ones

Now we have 7 thousands, 10 hundreds, 10 tens, 14 ones (since 1 ten = 10 ones)

Step 3: Subtract each place value

Ones: 14 - 7 = 7

Tens: 10 - 6 = 4

Hundreds: 10 - 3 = 7

Thousands: 7 - 5 = 2

\(8,014 - 5,367 = 2,647\)
Final answer:

\(8,014 - 5,367 = 2,647\)

Applied rules:

• Regrouping: When top digit is smaller, borrow from next higher place value

• Place value: 1 thousand = 10 hundreds, 1 hundred = 10 tens, 1 ten = 10 ones

• Subtraction: Subtract each place value separately

6 4-digit subtraction with regrouping
Exercise 6
Calculate:
\(9,201 - 6,743\)
Th
H
T
O
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9
2
0
1
-
6
7
4
3
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Step 1: Ones place: 1 < 3, so we need to regroup from the tens place. Tens place has 0, so we need to regroup from hundreds first.
↓
9
1
0
1
-
↓
9
1
9
11
-
Step 1: Regroup from hundreds to tens

9201 becomes 9 thousands, 1 hundred, 10 tens, 1 one (since 1 hundred = 10 tens)

Step 2: Regroup from tens to ones

Now we have 9 thousands, 1 hundred, 9 tens, 11 ones (since 1 ten = 10 ones)

Step 3: Subtract each place value

Ones: 11 - 3 = 8

Tens: 9 - 4 = 5

Hundreds: 1 - 7 = ? (Need to regroup from thousands)

Step 4: Hundreds place: 1 < 7, so we need to regroup from the thousands place.
↓
8
11
9
11
-
Step 5: Complete subtraction

Ones: 11 - 3 = 8

Tens: 9 - 4 = 5

Hundreds: 11 - 7 = 4

Thousands: 8 - 6 = 2

\(9,201 - 6,743 = 2,458\)
Final answer:

\(9,201 - 6,743 = 2,458\)

Applied rules:

• Regrouping: When top digit is smaller, borrow from next higher place value

• Place value: 1 thousand = 10 hundreds, 1 hundred = 10 tens, 1 ten = 10 ones

• Subtraction: Subtract each place value separately

7 4-digit subtraction with regrouping
Exercise 7
Calculate:
\(6,340 - 2,875\)
Th
H
T
O
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6
3
4
0
-
2
8
7
5
-
Step 1: Ones place: 0 < 5, so we need to regroup from the tens place. Tens place has only 4, so we need to regroup from hundreds first.
↓
6
2
14
0
-
↓
6
2
13
10
-
Step 1: Regroup from hundreds to tens

6340 becomes 6 thousands, 2 hundreds, 14 tens, 0 ones (since 1 hundred = 10 tens)

Step 2: Regroup from tens to ones

Now we have 6 thousands, 2 hundreds, 13 tens, 10 ones (since 1 ten = 10 ones)

Step 3: Subtract each place value

Ones: 10 - 5 = 5

Tens: 13 - 7 = 6

Hundreds: 2 - 8 = ? (Need to regroup from thousands)

Step 4: Hundreds place: 2 < 8, so we need to regroup from the thousands place.
↓
5
12
13
10
-
Step 5: Complete subtraction

Ones: 10 - 5 = 5

Tens: 13 - 7 = 6

Hundreds: 12 - 8 = 4

Thousands: 5 - 2 = 3

\(6,340 - 2,875 = 3,465\)
Final answer:

\(6,340 - 2,875 = 3,465\)

Applied rules:

• Regrouping: When top digit is smaller, borrow from next higher place value

• Place value: 1 thousand = 10 hundreds, 1 hundred = 10 tens, 1 ten = 10 ones

• Subtraction: Subtract each place value separately

Solution: Exercises 8 to 10
8 4-digit subtraction with regrouping
Exercise 8
Calculate:
\(7,502 - 4,836\)
Th
H
T
O
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7
5
0
2
-
4
8
3
6
-
Step 1: Ones place: 2 < 6, so we need to regroup from the tens place. Tens place has 0, so we need to regroup from hundreds first.
↓
7
4
0
2
-
↓
7
4
9
12
-
Step 1: Regroup from hundreds to tens

7502 becomes 7 thousands, 4 hundreds, 10 tens, 2 ones (since 1 hundred = 10 tens)

Step 2: Regroup from tens to ones

Now we have 7 thousands, 4 hundreds, 9 tens, 12 ones (since 1 ten = 10 ones)

Step 3: Subtract each place value

Ones: 12 - 6 = 6

Tens: 9 - 3 = 6

Hundreds: 4 - 8 = ? (Need to regroup from thousands)

Step 4: Hundreds place: 4 < 8, so we need to regroup from the thousands place.
↓
6
14
9
12
-
Step 5: Complete subtraction

Ones: 12 - 6 = 6

Tens: 9 - 3 = 6

Hundreds: 14 - 8 = 6

Thousands: 6 - 4 = 2

\(7,502 - 4,836 = 2,666\)
Final answer:

\(7,502 - 4,836 = 2,666\)

Applied rules:

• Regrouping: When top digit is smaller, borrow from next higher place value

• Place value: 1 thousand = 10 hundreds, 1 hundred = 10 tens, 1 ten = 10 ones

• Subtraction: Subtract each place value separately

9 4-digit subtraction with regrouping
Exercise 9
Calculate:
\(8,130 - 5,674\)
Th
H
T
O
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8
1
3
0
-
5
6
7
4
-
Step 1: Ones place: 0 < 4, so we need to regroup from the tens place. Tens place has only 3, so we need to regroup from hundreds first.
↓
8
0
13
0
-
↓
8
0
12
10
-
Step 1: Regroup from hundreds to tens

8130 becomes 8 thousands, 0 hundreds, 13 tens, 0 ones (since 1 hundred = 10 tens)

Step 2: Regroup from tens to ones

Now we have 8 thousands, 0 hundreds, 12 tens, 10 ones (since 1 ten = 10 ones)

Step 3: Subtract each place value

Ones: 10 - 4 = 6

Tens: 12 - 7 = 5

Hundreds: 0 - 6 = ? (Need to regroup from thousands)

Step 4: Hundreds place: 0 < 6, so we need to regroup from the thousands place.
↓
7
10
12
10
-
Step 5: Complete subtraction

Ones: 10 - 4 = 6

Tens: 12 - 7 = 5

Hundreds: 10 - 6 = 4

Thousands: 7 - 5 = 2

\(8,130 - 5,674 = 2,456\)
Final answer:

\(8,130 - 5,674 = 2,456\)

Applied rules:

• Regrouping: When top digit is smaller, borrow from next higher place value

• Place value: 1 thousand = 10 hundreds, 1 hundred = 10 tens, 1 ten = 10 ones

• Subtraction: Subtract each place value separately

10 4-digit subtraction with regrouping
Exercise 10
Calculate:
\(9,040 - 6,583\)
Th
H
T
O
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9
0
4
0
-
6
5
8
3
-
Step 1: Ones place: 0 < 3, so we need to regroup from the tens place. Tens place has only 4, so we need to regroup from hundreds first.
↓
9
0
4
0
-
↓
9
0
13
10
-
Step 1: Regroup from hundreds to tens

9040 becomes 8 thousands, 10 hundreds, 4 tens, 0 ones (since 1 thousand = 10 hundreds)

Step 2: Regroup from tens to ones

Now we have 8 thousands, 10 hundreds, 13 tens, 10 ones (since 1 ten = 10 ones)

Step 3: Subtract each place value

Ones: 10 - 3 = 7

Tens: 13 - 8 = 5

Hundreds: 10 - 5 = 5

Thousands: 8 - 6 = 2

\(9,040 - 6,583 = 2,457\)
Final answer:

\(9,040 - 6,583 = 2,457\)

Applied rules:

• Regrouping: When top digit is smaller, borrow from next higher place value

• Place value: 1 thousand = 10 hundreds, 1 hundred = 10 tens, 1 ten = 10 ones

• Subtraction: Subtract each place value separately

Subtraction with Regrouping Worksheets: 4-Digit Numbers
Complete Learning Guide

Understanding 4-Digit Subtraction with Regrouping

4-digit subtraction with regrouping builds upon the place value understanding learned in 2-digit and 3-digit subtraction. In 4-digit numbers, students must consider thousands, hundreds, tens, and ones place values, and may need to regroup from multiple place values simultaneously.

Key Concepts for 3rd Graders

• Place Value: Understanding that each digit in a number has a different value based on its position (thousands, hundreds, tens, and ones).

• Regrouping: Converting 1 unit from a higher place value to 10 units in a lower place value.

• Multiple Regrouping: Sometimes needing to regroup from thousands to hundreds, then from hundreds to tens, then from tens to ones.

• Subtraction: Finding the difference between two numbers.

Step-by-Step Process

  1. Align the numbers: Write the larger number on top, ensuring ones align with ones, tens with tens, hundreds with hundreds, and thousands with thousands.
  2. Start from the ones place: Look at the ones digits to determine if regrouping is needed.
  3. Regroup if necessary: If the top digit is smaller than the bottom digit, borrow from the next higher place value.
  4. Handle multiple regroups: If the next higher place value also has a smaller digit, continue regrouping upward.
  5. Subtract each place value: Complete the subtraction in each place value from right to left.
  6. Check your answer: Add the answer to the bottom number to see if you get the top number.

Practice Problems

Here are additional problems for practice:

  • 5,231 - 2,784 = ?
  • 6,402 - 3,857 = ?
  • 7,105 - 4,638 = ?
  • 8,021 - 5,467 = ?
  • 9,304 - 6,758 = ?

Visual Strategies

• Use base-10 blocks to physically demonstrate regrouping

• Draw pictures or use tally marks to represent numbers

• Color-code place values to help distinguish thousands, hundreds, tens, and ones

• Use number lines to show the subtraction process

Common Mistakes to Avoid

• Forgetting to reduce the thousands digit after borrowing from thousands

• Subtracting the smaller number from the larger regardless of position

• Mixing up the order of subtraction (always subtract the bottom from the top)

• Not checking if regrouping is necessary

• Forgetting to regroup from higher place values when needed

\(abcd - efgh = ijkl\)
4-Digit Subtraction
Regrouping Rule
1 thousand = 10 hundreds
Place Value Conversion
Regrouping Rule
1 hundred = 10 tens
Place Value Conversion
Regrouping Rule
1 ten = 10 ones
Place Value Conversion
Key definitions:

Minuend: The number being subtracted from (top number)

Subtrahend: The number being subtracted (bottom number)

Difference: The result of the subtraction

Regrouping: Converting from a higher place value to a lower place value

Complete methodology:
  1. Align numbers: Line up numbers by place value
  2. Start from right: Begin subtraction in the ones place
  3. Check if regrouping needed: If top digit is smaller than bottom digit
  4. Regroup from next place: Convert 1 unit from higher place to 10 units in current place
  5. Repeat if needed: Continue regrouping for higher place values if necessary
  6. Complete subtraction: Subtract each place value
Tip 1: Always check if the top digit is larger than the bottom digit before subtracting.
Tip 2: When regrouping, decrease the higher place value by 1 and increase the lower place value by 10.
Tip 3: Draw arrows to visualize the regrouping process.
Common errors: Forgetting to decrease the higher place value when regrouping, subtracting bottom from top instead of top from bottom.
Key concept: 4-digit subtraction with regrouping may require borrowing from multiple place values simultaneously.
Formulas to know by heart:

• Place value conversion: 1 thousand = 10 hundreds = 100 tens = 1000 ones

• Regrouping rule: When top digit < bottom digit, regroup from next higher place

• Subtraction: Top number - Bottom number = Difference

• Verification: Difference + Subtrahend = Minuend

Questions & Answers

Question: How can I help my students understand when they need to regroup from multiple place values in 4-digit subtraction?

Answer: Teach students to work systematically from right to left. If they need to regroup from the tens place but the tens digit is too small, they must first regroup from the hundreds place to the tens place, then from the tens place to the ones place. Use the phrase "Check, then fix" - check each place value and fix it by regrouping if needed before moving to the next place value. Visual aids like place value charts with arrows showing the regrouping path help students visualize the process.

Question: My child is struggling with 4-digit subtraction regrouping. What can I do at home to help?

Answer: Start with manipulatives like base-10 blocks to physically demonstrate the regrouping process. Practice with simpler 2-digit and 3-digit problems first, then gradually increase to 4-digit problems. Use graph paper to help align digits properly. Create simple word problems that connect to your child's life. Practice for 10-15 minutes daily rather than longer, infrequent sessions. Be patient and celebrate small improvements to build confidence.

Question: What are some effective visual strategies for teaching 4-digit regrouping?

Answer: Use color-coded place value charts where thousands, hundreds, tens, and ones are in different colors. Draw arrows to show the direction of borrowing. Create anchor charts with step-by-step visual instructions. Use base-10 block drawings to show the actual exchanging of units. For struggling students, use physical manipulatives alongside visual representations. Create story problems that connect to students' lives to make the concept more meaningful.