Multi-Digit Subtraction Worksheet

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

Solution: Exercises 1 to 3
1 Basic Subtraction
Exercise 1
745 - 283 = ?
Definition:

Multi-Digit Subtraction: The process of finding the difference between two or more numbers with multiple digits, using place value and regrouping when necessary

Subtraction Method:
  1. Align numbers by place value (ones under ones, tens under tens, etc.)
  2. Start subtracting from the rightmost digit (ones place)
  3. If top number is smaller than bottom number, regroup from next higher place value
  4. Continue to the left until all digits are subtracted
Set Up Problem:
745
-283
Ones Place:
5 > 3, so 5 - 3 = 2
Tens Place:
4 < 8, so we need to borrow from hundreds
Regrouping:
7→6 hundreds, 4→14 tens
Tens Place After Regrouping:
14 - 8 = 6
Hundreds Place:
6 - 2 = 4
Calculate:
Answer: 462
Step 1: Set up the problem

Write 745 above 283, aligning by place value

Step 2: Check ones place

5 > 3, so we can subtract directly: 5 - 3 = 2

Step 3: Check tens place

4 < 8, so we need to regroup from hundreds place

Step 4: Regroup from hundreds

Take 1 hundred from 7 hundreds (becomes 6 hundreds), add 10 to tens place (4 + 10 = 14 tens)

Step 5: Subtract in tens place

14 - 8 = 6

Step 6: Subtract in hundreds place

6 - 2 = 4

745 - 283 = 462
Final answer:

745 - 283 = 462

Applied rules:

• Place Value Alignment: 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 Subtraction with Zeros
Exercise 2
602 - 378 = ?
Definition:

Subtraction with Zeros: When zeros appear in the minuend, special regrouping is required since zeros cannot provide value to borrow from

Set Up Problem:
602
-378
Ones Place:
2 < 8, need to borrow
Tens Place:
0 < 7, need to borrow but zero can't give!
Hundreds Place:
6 > 3, can borrow from here
Chain Regrouping:
6→5 hundreds, 0→10 tens, then 10→9 tens, 2→12 ones
Calculate Each Place:
Ones: 12 - 8 = 4
Tens: 9 - 7 = 2
Hundreds: 5 - 3 = 2
Calculate:
Answer: 224
Step 1: Set up the problem

Write 602 above 378, aligning by place value

Step 2: Check ones place

2 < 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

Step 4: Borrow from hundreds

Take 1 hundred from 6 hundreds (becomes 5 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 (2 + 10 = 12 ones)

Step 6: Subtract each place value

Ones: 12 - 8 = 4, Tens: 9 - 7 = 2, Hundreds: 5 - 3 = 2

602 - 378 = 224
Final answer:

602 - 378 = 224

Applied rules:

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

• Chain Borrowing: May need to borrow from multiple places in sequence

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

3 Four-Digit Subtraction
Exercise 3
4,825 - 1,967 = ?
Definition:

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

Set Up Problem:
4,825
-1,967
Ones Place:
5 > 7, need to borrow
Tens Place:
2 < 6, need to borrow after regrouping
Hundreds Place:
7 < 9, need to borrow after regrouping
Thousands Place:
4 > 1, can borrow from here
Chain Regrouping:
4→3 thousands, 8→7 hundreds, 2→12 tens, 5→15 ones
Calculate Each Place:
Ones: 15 - 7 = 8
Tens: 11 - 6 = 5
Hundreds: 7 - 9 = ? (need to borrow again)
Thousands: 3→2, Hundreds: 17 - 9 = 8
Final Calculation:
Ones: 8, Tens: 5, Hundreds: 8, Thousands: 2
Answer: 2,858
Step 1: Set up the problem

Write 4,825 above 1,967, aligning by place value

Step 2: Check ones place

5 < 7, so we need to regroup from tens place

Step 3: Check tens place after borrowing

1 ten from 2 tens leaves 1 ten, but 1 < 6, so we need to regroup from hundreds

Step 4: Borrow from hundreds

Take 1 hundred from 8 hundreds (becomes 7 hundreds), add 10 to tens place (1 + 10 = 11 tens)

Step 5: Check hundreds place after borrowing

7 hundreds but 7 < 9, so we need to regroup from thousands

Step 6: Borrow from thousands

Take 1 thousand from 4 thousands (becomes 3 thousands), add 10 to hundreds place (7 + 10 = 17 hundreds)

Step 7: Subtract each place value

Ones: 15 - 7 = 8, Tens: 11 - 6 = 5, Hundreds: 17 - 9 = 8, Thousands: 3 - 1 = 2

4,825 - 1,967 = 2,858
Final answer:

4,825 - 1,967 = 2,858

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

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

Worksheet: A structured practice sheet with multiple problems for skill development

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: Th|H|T|O for thousands, 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, misaligning numbers.
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

Practice Problems

567 - 234
803 - 476
3,421 - 1,857
600 - 289
7,250 - 3,891
4,105 - 2,768
Solution: Exercises 4 to 5
4 Mixed Regrouping Challenge
Exercise 4
5,003 - 2,847 = ?
Definition:

Mixed Regrouping Challenge: Involves multiple zeros and complex borrowing sequences

Set Up Problem:
5,003
-2,847
Ones Place:
3 < 7, need to borrow
Tens Place:
0 < 4, need to borrow but zero can't give!
Hundreds Place:
0 < 8, need to borrow but zero can't give!
Thousands Place:
5 > 2, can borrow from here
Chain Regrouping:
5→4 thousands, 0→10 hundreds, 10→9 hundreds, 0→10 tens, 10→9 tens, 3→13 ones
Calculate Each Place:
Ones: 13 - 7 = 6
Tens: 9 - 4 = 5
Hundreds: 9 - 8 = 1
Thousands: 4 - 2 = 2
Calculate:
Answer: 2,156
Step 1: Set up the problem

Write 5,003 above 2,847, 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 < 4, 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 5 thousands (becomes 4 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 (3 + 10 = 13 ones)

Step 8: Subtract each place value

Ones: 13 - 7 = 6, Tens: 9 - 4 = 5, Hundreds: 9 - 8 = 1, Thousands: 4 - 2 = 2

5,003 - 2,847 = 2,156
Final answer:

5,003 - 2,847 = 2,156

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

5 Advanced Subtraction
Exercise 5
8,304 - 5,729 = ?
Definition:

Advanced Subtraction: Complex multi-digit subtraction requiring multiple regrouping steps

Set Up Problem:
8,304
-5,729
Ones Place:
4 < 9, need to borrow
Tens Place:
0 < 2, need to borrow but zero can't give!
Hundreds Place:
3 > 7, can borrow from here
Chain Regrouping:
8→7 thousands, 3→2 hundreds, 0→10 tens, 10→9 tens, 4→14 ones
Calculate Each Place:
Ones: 14 - 9 = 5
Tens: 9 - 2 = 7
Hundreds: 2 - 7 = ? (need to borrow again)
Thousands: 7→6, Hundreds: 12 - 7 = 5
Final Calculation:
Ones: 5, Tens: 7, Hundreds: 5, Thousands: 2
Answer: 2,575
Step 1: Set up the problem

Write 8,304 above 5,729, aligning by place value

Step 2: Check ones place

4 < 9, so we need to regroup from tens place

Step 3: Check tens place

0 < 2, but we can't borrow from zero! Go to hundreds place

Step 4: Borrow from hundreds

Take 1 hundred from 3 hundreds (becomes 2 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 (4 + 10 = 14 ones)

Step 6: Check hundreds place

2 < 7, so we need to borrow from thousands

Step 7: Borrow from thousands

Take 1 thousand from 8 thousands (becomes 7 thousands), add 10 to hundreds place (2 + 10 = 12 hundreds)

Step 8: Subtract each place value

Ones: 14 - 9 = 5, Tens: 9 - 2 = 7, Hundreds: 12 - 7 = 5, Thousands: 7 - 5 = 2

8,304 - 5,729 = 2,575
Final answer:

8,304 - 5,729 = 2,575

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

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

Worksheet: A structured practice sheet designed to develop and reinforce mathematical skills through repeated practice

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

Additional Practice Problems

6,247 - 3,891
9,005 - 4,678
7,320 - 2,845
4,806 - 1,937
5,000 - 2,456
8,153 - 3,967

Complete Summary: Multi-Digit Subtraction Worksheet

Key Concepts and Definitions

Multi-Digit Subtraction: The mathematical operation of finding the difference between two or more numbers that have two or more digits, using place value and regrouping when necessary.

Minuend: The number from which another number is subtracted (the top number in vertical subtraction).

Subtrahend: The number that is subtracted (the bottom number in vertical subtraction).

Difference: The result of the subtraction operation.

Regrouping: The process of exchanging value between place values to enable subtraction when the top number is smaller than the bottom number.

Worksheet: A structured practice sheet designed to develop and reinforce mathematical skills through repeated practice of similar problems.

Core Rules and Principles

Rule 1 - Place Value Alignment: Always align numbers by their place values (ones under ones, tens under tens, etc.).

Rule 2 - Right-to-Left Processing: Always start subtracting from the rightmost digit (ones place) and move left.

Rule 3 - Regrouping Condition: When the top digit is smaller than the bottom digit in any place value, regroup from the next higher place value.

Rule 4 - Value Exchange: When borrowing, the higher place value decreases by 1, and the lower place value increases by 10.

Rule 5 - Zero Handling: When encountering zero that needs to provide value, go to the next non-zero place value to borrow.

Rule 6 - Sequential Processing: Handle each place value in order from right to left, addressing regrouping as needed.

Step-by-Step Methods and Procedures

  1. Setup: Write the numbers vertically, aligning by place value with the larger number on top.
  2. Start from Right: Begin with the ones place and move left to tens, hundreds, thousands, etc.
  3. Compare Digits: At each place value, compare the top and bottom digits.
  4. Direct Subtraction: If top ≥ bottom, subtract directly.
  5. Regrouping: If top < bottom, borrow 1 from the next higher place value.
  6. Adjust Values: Reduce the higher place value by 1, increase the lower by 10.
  7. Continue Process: Move to the next place value and repeat.
  8. Verify Answer: Add the difference to the subtrahend to ensure it equals the original minuend.

Examples: From Simple to Advanced

Simple Example: 745 - 283

• Ones: 5 > 3, so 5 - 3 = 2

• Tens: 4 < 8, so borrow: 7→6 hundreds, 4→14 tens, then 14 - 8 = 6

• Hundreds: 6 - 2 = 4

• Result: 462

Intermediate Example: 602 - 378

• Ones: 2 < 8, need to borrow

• Tens: 0 < 7, but zero can't give, go to thousands

• Chain: 6→5 hundreds, 0→10 tens, 10→9 tens, 2→12 ones

• Result: 224

Advanced Example: 5,003 - 2,847

• Multiple zeros require chain borrowing

• 5→4 thousands, 0→10 hundreds, 10→9 hundreds, 0→10 tens, 10→9 tens, 3→13 ones

• Result: 2,156

Tips, Tricks, and Common Pitfalls

Tips:

  • Draw place value columns (Th|H|T|O) to keep numbers aligned
  • Cross out old numbers and write new numbers above when borrowing
  • Always verify by adding difference to subtrahend
  • Remember: 1 borrowed = 10 added to the next place value
  • When encountering zeros, mentally say "go to the next non-zero place"

Common Mistakes:

  • Trying to borrow from zero without going to the next place value
  • Forgetting to reduce the higher place value after borrowing
  • Subtracting bottom from top when the top number is smaller
  • Misaligning numbers when writing vertically
  • Not carrying the borrowing effect through the chain

Key Notes for Memorization

Memory Aid: "Zeros Can't Give, Go to Next!" - When you see a zero that needs to provide value, remember it can't give, so go to the next non-zero place value.

Value Conservation: The total value of the minuend remains the same after regrouping; only the representation changes.

Chain Effect: Each borrow creates a chain reaction affecting subsequent place values.

Verification: Always add your difference to the subtrahend to ensure you get back to the original minuend.

Systematic Approach: Handle each place value in order from right to left, addressing regrouping as needed.

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 745 - 283: When you borrow 1 ten from the 4 tens, you're taking a value of 10. That 10 gets added to the 5 ones, making it 15 ones. The total value stays the same (745), but it's now represented as 3 tens and 15 ones instead of 4 tens and 5 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 602 - 378, 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 602 - 378:

  1. You want to subtract 8 from 2 in ones place: 2 < 8, 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 6 (6 becomes 5)
  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 (2 + 10 = 12)
  6. Now you can subtract: 12 - 8 = 4, 9 - 7 = 2, 5 - 3 = 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.