Multi-Digit Subtraction with Regrouping Worksheets

Master multi-digit subtraction with regrouping through 5 detailed exercises with step-by-step solutions, rules, and visual examples.

Solution: Exercises 1 to 3
1 Basic Regrouping
Exercise 1
Subtract: 52 - 27
Definition:

Regrouping (Borrowing): Taking value from a higher place value to make subtraction possible in a lower place value

Subtraction Method:
  1. Align numbers by place value (ones under ones, tens under tens)
  2. Start subtracting from the rightmost digit (ones place)
  3. If top number is smaller than bottom number, regroup/borrow from next higher place value
  4. Continue to the left until all digits are subtracted
Original Problem:
52
-27
Ones Place Check:
2 < 7 (Need to borrow)
Regrouping:
Borrow 1 ten from 5 tens
52 becomes 4 tens and 12 ones
New Problem:
4 tens, 12 ones
-2 tens, 7 ones
Calculate:
Ones: 12 - 7 = 5
Tens: 4 - 2 = 2
Answer: 25
Step 1: Set up the problem

Write 52 above 27, aligning by place value

Step 2: Check ones place

2 < 7, so we need to regroup from tens place

Step 3: Regroup/Borrow

Take 1 ten from 5 tens (leaving 4 tens) and add 10 to ones place (2 + 10 = 12 ones)

Step 4: Subtract in ones place

12 - 7 = 5

Step 5: Subtract in tens place

4 - 2 = 2

52 - 27 = 25
Final answer:

52 - 27 = 25

Applied rules:

• Place Value: Align digits by their place value

• Regrouping Rule: When top number is smaller, borrow 1 from next higher place value

• Borrowing Effect: Borrowed amount adds 10 to the current place value

2 Three-Digit Regrouping
Exercise 2
Subtract: 342 - 178
Definition:

Three-Digit Subtraction: Requires careful attention to place value and potential multiple regroupings

Original Problem:
342
-178
Ones Place Check:
2 < 8 (Need to borrow)
Tens Place Check:
3 < 7 (After borrowing, need to borrow again)
Multiple Regrouping:
Borrow 1 hundred from 3 hundreds
Then borrow 1 ten from new tens place
New Values:
2 hundreds, 13 tens, 12 ones
Calculate:
Ones: 12 - 8 = 4
Tens: 13 - 7 = 6
Hundreds: 2 - 1 = 1
Answer: 164
Step 1: Set up the problem

Write 342 above 178, aligning by place value

Step 2: Check ones place

2 < 8, so we need to regroup from tens place

Step 3: Check tens place after borrowing

4 tens - 1 borrowed = 3 tens, but 3 < 7, so we need to regroup from hundreds

Step 4: Multiple regrouping

Borrow 1 hundred (3 hundreds become 2 hundreds), add 10 to tens place (2 + 10 = 12 tens)

Step 5: Now regroup ones

Borrow 1 ten from 13 tens (13 tens become 12 tens), add 10 to ones place (2 + 10 = 12 ones)

Step 6: Subtract each place value

Ones: 12 - 8 = 4, Tens: 12 - 7 = 5, Hundreds: 2 - 1 = 1

342 - 178 = 164
Final answer:

342 - 178 = 164

Applied rules:

• Sequential Regrouping: May need to regroup multiple times in one problem

• Chain Effect: Borrowing affects subsequent place values

• Place Value Conservation: Total value remains the same after regrouping

3 Zero Regrouping
Exercise 3
Subtract: 503 - 267
Definition:

Zero Regrouping: When there are zeros in the minuend, regrouping requires special attention

Original Problem:
503
-267
Ones Place Check:
3 > 7 (No need to borrow)
Tens Place Check:
0 < 6 (Need to borrow, but zero can't give!)
Special Regrouping:
Borrow from hundreds first
5 hundreds becomes 4 hundreds, 0 tens becomes 10 tens
Now Borrow Again:
Borrow from tens to ones
10 tens becomes 9 tens, 3 ones becomes 13 ones
Calculate:
Ones: 13 - 7 = 6
Tens: 9 - 6 = 3
Hundreds: 4 - 2 = 2
Answer: 236
Step 1: Set up the problem

Write 503 above 267, aligning by place value

Step 2: Check ones place

3 < 7, so we need to regroup from tens place

Step 3: Check tens place

0 < 6, but we can't borrow from zero! We must borrow from hundreds first

Step 4: Borrow from hundreds

Take 1 hundred from 5 hundreds (becomes 4 hundreds), add 10 to tens place (0 + 10 = 10 tens)

Step 5: Now borrow from tens to ones

Take 1 ten from 10 tens (becomes 9 tens), add 10 to ones place (3 + 10 = 13 ones)

Step 6: Subtract each place value

Ones: 13 - 7 = 6, Tens: 9 - 6 = 3, Hundreds: 4 - 2 = 2

503 - 267 = 236
Final answer:

503 - 267 = 236

Applied rules:

• Zero Handling: When encountering zero, borrow from next non-zero place value

• Cascading Borrow: May require multiple borrow steps in sequence

• Place Value Preservation: Value remains constant despite regrouping

Rules and Methods for Multi-Digit Subtraction
Minuend - Subtrahend = Difference
Basic Subtraction Formula
Rule 1
Align by Place Value
Always align digits by their place value
Rule 2
Regroup When Needed
Borrow when top digit is smaller than bottom
Rule 3
Subtract from Right
Start subtracting from the rightmost digit
Key Terms:

Minuend: The number being subtracted from

Subtrahend: The number being subtracted

Difference: The result of subtraction

Regrouping: Exchanging value between place values

Complete Subtraction Method:
  1. Align numbers: Place digits in correct columns by place value
  2. Start from right: Begin with ones place, then move left
  3. Check each place: If top number ≥ bottom number, subtract directly
  4. Regroup if needed: If top number < bottom number, borrow from next higher place
  5. Repeat: Continue for each place value moving left
  6. Verify: Add difference to subtrahend to check result
Tip 1: Draw lines to separate place values: H|T|O for hundreds, tens, ones.
Tip 2: When borrowing, cross out old number and write new number above it.
Tip 3: Remember: borrowing adds 10 to the current place value.
Tip 4: Always check your work by adding the difference to the subtrahend.
Common errors: Forgetting to adjust higher place value after borrowing, subtracting bottom from top when top is smaller without borrowing.
Success strategies: Always start from the right, check each place value systematically, use visual aids like place value charts.
Essential Rules:

• Alignment Rule: Numbers must be aligned by place value

• Right-to-Left Rule: Always start subtracting from the rightmost digit

• Borrowing Rule: When top number is smaller, borrow 1 from next higher place value

• Value Exchange: Borrowed 1 equals 10 in the next lower place value

• Zero Handling: When borrowing from zero, go to next non-zero place value

Solution: Exercises 4 to 5
4 Four-Digit Regrouping
Exercise 4
Subtract: 2,405 - 1,678
Definition:

Four-Digit Subtraction: Extends the same principles to thousands place with potentially complex regrouping scenarios

Original Problem:
2,405
-1,678
Ones Place Check:
5 < 8 (Need to borrow)
Tens Place Check:
0 < 7 (Need to borrow, but zero can't give!)
Hundreds Place Check:
4 > 6 (Wait, after borrowing...)
Complex Regrouping:
Borrow from hundreds first (4→3), then tens (0→10), then ones (5→15)
Final Calculation:
Ones: 15 - 8 = 7
Tens: 9 - 7 = 2 (after borrowing 1 from 10)
Hundreds: 3 - 6 = ? (Need another borrow!)
Thousands: 2→1, Hundreds: 13 - 6 = 7
Answer: 727
Step 1: Set up the problem

Write 2,405 above 1,678, aligning by place value

Step 2: Check ones place

5 < 8, so we need to regroup from tens place

Step 3: Check tens place

0 < 7, but we can't borrow from zero! We must go to hundreds place first

Step 4: Borrow from hundreds

Take 1 hundred from 4 hundreds (becomes 3 hundreds), add 10 to tens place (0 + 10 = 10 tens)

Step 5: Now borrow from tens to ones

Take 1 ten from 10 tens (becomes 9 tens), add 10 to ones place (5 + 10 = 15 ones)

Step 6: Check hundreds place

3 < 6, so we need to borrow from thousands place

Step 7: Borrow from thousands

Take 1 thousand from 2 thousands (becomes 1 thousand), add 10 to hundreds place (3 + 10 = 13 hundreds)

Step 8: Subtract each place value

Ones: 15 - 8 = 7, Tens: 9 - 7 = 2, Hundreds: 13 - 6 = 7, Thousands: 1 - 1 = 0

2,405 - 1,678 = 727
Final answer:

2,405 - 1,678 = 727

Applied rules:

• Multi-Level Regrouping: May need to regroup across multiple place values

• Sequential Adjustment: Each borrow affects the next place value

• Systematic Approach: Process each place value methodically

5 Mixed Regrouping Challenge
Exercise 5
Subtract: 6,004 - 2,837
Definition:

Mixed Regrouping Challenge: Involves multiple zeros and complex borrowing sequences

Original Problem:
6,004
-2,837
Ones Place Check:
4 < 7 (Need to borrow)
Tens Place Check:
0 < 3 (Need to borrow, but zero can't give!)
Hundreds Place Check:
0 < 8 (Need to borrow, but zero can't give!)
Chain Regrouping:
Borrow from thousands → hundreds → tens → ones
Final Setup:
5 thousands, 9 hundreds, 9 tens, 14 ones
Calculate:
Ones: 14 - 7 = 7
Tens: 9 - 3 = 6
Hundreds: 9 - 8 = 1
Thousands: 5 - 2 = 3
Answer: 3,167
Step 1: Set up the problem

Write 6,004 above 2,837, aligning by place value

Step 2: Check ones place

4 < 7, so we need to regroup from tens place

Step 3: Check tens place

0 < 3, but we can't borrow from zero! Go to hundreds place

Step 4: Check hundreds place

0 < 8, but we can't borrow from zero! Go to thousands place

Step 5: Borrow from thousands

Take 1 thousand from 6 thousands (becomes 5 thousands), add 10 to hundreds place (0 + 10 = 10 hundreds)

Step 6: Now borrow from hundreds to tens

Take 1 hundred from 10 hundreds (becomes 9 hundreds), add 10 to tens place (0 + 10 = 10 tens)

Step 7: Now borrow from tens to ones

Take 1 ten from 10 tens (becomes 9 tens), add 10 to ones place (4 + 10 = 14 ones)

Step 8: Subtract each place value

Ones: 14 - 7 = 7, Tens: 9 - 3 = 6, Hundreds: 9 - 8 = 1, Thousands: 5 - 2 = 3

6,004 - 2,837 = 3,167
Final answer:

6,004 - 2,837 = 3,167

Applied rules:

• Chain Regrouping: When multiple consecutive zeros exist, borrow sequentially

• Value Conservation: Total value remains the same despite multiple regroupings

• Systematic Processing: Handle each place value in order from right to left

Comprehensive Guide: Laws, Methods, Rules, Definitions
Minuend - Subtrahend = Difference
Subtraction Formula
Key definitions:

Minuend: The number from which another number is subtracted

Subtrahend: The number that is subtracted

Difference: The result of subtraction

Regrouping: Trading value between place values to enable subtraction

Borrowing: Another term for regrouping in subtraction

Complete methodology:
  1. Align numbers: Place digits in correct columns by place value (ones, tens, hundreds, etc.)
  2. Start from right: Begin with the ones place and move left
  3. Compare digits: At each place value, compare top and bottom digits
  4. Subtract if possible: If top ≥ bottom, subtract directly
  5. Regroup if needed: If top < bottom, borrow 1 from next higher place value
  6. Adjust values: Reduce higher place value by 1, increase current place value by 10
  7. Continue: Repeat for each place value moving left
  8. Verify: Add difference to subtrahend to check result
Tip 1: Always start subtracting from the ones place and move left.
Tip 2: When borrowing, the higher place value decreases by 1, the lower increases by 10.
Tip 3: When you encounter zeros, keep going to the next non-zero place value to borrow.
Tip 4: Always check your answer by adding the difference to the subtrahend.
Tip 5: Use place value charts to visualize the process.
Common errors: Forgetting to reduce the higher place value after borrowing, subtracting the wrong way (bottom from top), misaligning numbers.
Success strategies: Use visual aids, check each step, practice with simpler problems first, always verify your answer.
Essential rules to know:

• Place Value Alignment: Always align numbers by place value

• Right-to-Left Processing: Start subtracting from the rightmost digit

• Borrowing Rule: When top number is smaller, borrow 1 from next higher place value

• Value Exchange: 1 unit borrowed = 10 units in the next lower place value

• Zero Handling: When borrowing from zero, continue to next non-zero place value

• Sequential Regrouping: May need multiple borrows in one problem

• Verification: Difference + Subtrahend = Minuend

Questions & Answers

Question: I don't understand why when I borrow from the tens place, the tens number goes down by 1 but the ones number goes up by 10. Why does it go up by 10 and not just 1?

Answer: Great question! This is about place value. Think of it this way:

  • In our number system, each place value is worth 10 times more than the place to its right
  • One ten is equal to ten ones (1 ten = 10 ones)
  • So when you take 1 ten from the tens place, you're taking a value of 10
  • To keep the total value the same, you add that value of 10 to the ones place

For example, in 52 - 27: When you borrow 1 ten from the 5 tens, you're taking a value of 10. That 10 gets added to the 2 ones, making it 12 ones. The total value stays the same (52), but it's now represented as 4 tens and 12 ones instead of 5 tens and 2 ones.

It's like exchanging a $10 bill for ten $1 bills - you still have the same amount of money, just in different denominations!

Question: When I have a problem like 503 - 267, I see the zero in the middle and I get confused. How do I handle the zero?

Answer: Zeros can be tricky, but here's the strategy:

  • When you need to borrow from a zero, you can't! The zero has nothing to give
  • Instead, you must go to the next non-zero place value to the left
  • Borrow from that place value, which turns the zero into 10
  • Then you can borrow from the newly created 10

For 503 - 267:

  1. You want to subtract 7 from 3 in ones place: 3 < 7, so you need to borrow
  2. Look at tens place: it's 0, so you can't borrow from there
  3. Go to hundreds place: borrow 1 from 5 (5 becomes 4)
  4. This gives 10 to the tens place (0 becomes 10)
  5. Now from the tens place, borrow 1 (10 becomes 9) to add to ones place (3 becomes 13)
  6. Now you can subtract: 13 - 7 = 6, 9 - 6 = 3, 4 - 2 = 2

Think of it as a chain reaction - you might need to "wake up" several place values!

Question: How can I help my students who are struggling with regrouping? They seem to forget to reduce the higher place value after borrowing.

Answer: Here are effective strategies for teaching regrouping:

  • Use concrete manipulatives: Base-10 blocks help students visualize the exchange of value
  • Emphasize the process: Have students say out loud what they're doing at each step
  • Visual cues: Cross out old numbers and write new numbers above them
  • Check each step: After borrowing, have students verify the higher place value decreased by 1
  • Practice in isolation: Focus on just the regrouping step before attempting full problems

Also try the "take away and add" method: physically show that taking 1 from the tens place means reducing that number by 1, while adding 10 to the ones place means increasing that number by 10.

Encourage students to always verify their final answer by adding the difference to the subtrahend to see if they get back to the original number.