Subtraction with Regrouping Worksheets with Answers for Grade 3

Master subtraction with regrouping: borrowing across place values, step-by-step solutions, and visual examples for grade 3 students.

Subtraction with Regrouping Exercises 1-5
1 Basic Regrouping
Exercise 1
Solve: 52 - 18 = ?
Definition:

Subtraction with regrouping: When subtracting, if the digit in the minuend is smaller than the digit in the subtrahend in any place value, we borrow from the next higher place value.

Regrouping method:
  1. Start from the rightmost digit (ones place)
  2. If the top number is smaller than the bottom number, borrow 1 from the next place value
  3. Add 10 to the current place value and subtract 1 from the next place value
  4. Continue subtracting in each place value from right to left
Tens
5
Ones
2
→
Borrow
-
Tens
1
Ones
8
1
Look at ones place: 2 < 8, so borrow from tens place
2
Borrow 1 ten from 5 tens, leaving 4 tens. Add 10 to ones: 2 + 10 = 12 ones
3
Subtract ones: 12 - 8 = 4
4
Subtract tens: 4 - 1 = 3
52 - 18 = 34
Check: 34 + 18 = 52 ✓
Final answer:

52 - 18 = 34

Applied rules:

• Borrowing: When minuend digit is smaller than subtrahend digit

• Place value: Maintain correct place value relationships

• Regrouping: Add 10 to current place value when borrowing

2 Two-Digit Regrouping
Exercise 2
Solve: 73 - 29 = ?
Definition:

Regrouping across multiple places: Sometimes we need to borrow from multiple place values in a single problem.

Tens
7
Ones
3
-
Tens
2
Ones
9
1
Look at ones place: 3 < 9, so borrow from tens place
2
Borrow 1 ten from 7 tens, leaving 6 tens. Add 10 to ones: 3 + 10 = 13 ones
3
Subtract ones: 13 - 9 = 4
4
Subtract tens: 6 - 2 = 4
73 - 29 = 44
Check: 44 + 29 = 73 ✓
Final answer:

73 - 29 = 44

Applied rules:

• Borrowing: When minuend digit is smaller than subtrahend digit

• Place value: Maintain correct place value relationships

• Regrouping: Add 10 to current place value when borrowing

3 Three-Digit Regrouping
Exercise 3
Solve: 342 - 157 = ?
Definition:

Three-digit regrouping: The same regrouping principle applies to larger numbers with multiple place values.

Hunds
3
Tens
4
Ones
2
-
Hunds
1
Tens
5
Ones
7
1
Look at ones place: 2 < 7, so borrow from tens place
2
Tens place is also smaller: 4 < 5, so borrow from hundreds place first
3
Borrow 1 hundred from 3 hundreds, leaving 2 hundreds. Add 10 to tens: 4 + 10 = 14 tens
4
Now borrow from tens: 14 tens → 13 tens, 2 ones → 12 ones
5
Subtract each place value: 12-7=5, 13-5=8, 2-1=1
342 - 157 = 185
Check: 185 + 157 = 342 ✓
Final answer:

342 - 157 = 185

Applied rules:

• Sequential borrowing: Borrow from left to right when needed

• Place value: Maintain correct place value relationships

• Regrouping: Add 10 to current place value when borrowing

Subtraction with Regrouping Exercises 6-10
4 Mixed Regrouping
Exercise 4
Solve: 603 - 247 = ?
Definition:

Zero regrouping: Special cases arise when there are zeros in the minuend that require borrowing.

Hunds
6
Tens
0
Ones
3
-
Hunds
2
Tens
4
Ones
7
1
Look at ones place: 3 < 7, so borrow from tens place
2
Tens place is 0, so borrow from hundreds place first
3
Borrow 1 hundred from 6 hundreds, leaving 5 hundreds. Add 10 to tens: 0 + 10 = 10 tens
4
Now borrow from tens: 10 tens → 9 tens, 3 ones → 13 ones
5
Subtract each place value: 13-7=6, 9-4=5, 5-2=3
603 - 247 = 356
Check: 356 + 247 = 603 ✓
Final answer:

603 - 247 = 356

Applied rules:

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

• Sequential borrowing: Borrow from left to right when needed

• Regrouping: Add 10 to current place value when borrowing

5 Advanced Regrouping
Exercise 5
Solve: 812 - 358 = ?
Definition:

Advanced regrouping: Multiple borrowing scenarios in a single problem.

Hunds
8
Tens
1
Ones
2
-
Hunds
3
Tens
5
Ones
8
1
Look at ones place: 2 < 8, so borrow from tens place
2
Tens place is 1, but 1 < 5, so borrow from hundreds place first
3
Borrow 1 hundred from 8 hundreds, leaving 7 hundreds. Add 10 to tens: 1 + 10 = 11 tens
4
Now borrow from tens: 11 tens → 10 tens, 2 ones → 12 ones
5
Subtract each place value: 12-8=4, 10-5=5, 7-3=4
812 - 358 = 454
Check: 454 + 358 = 812 ✓
Final answer:

812 - 358 = 454

Applied rules:

• Sequential borrowing: Borrow from left to right when needed

• Place value: Maintain correct place value relationships

• Regrouping: Add 10 to current place value when borrowing

6 Practice Problem
Exercise 6
Solve: 427 - 189 = ?
1
Ones place: 7 < 9, so borrow from tens (but tens is 2)
2
Tens place: 2 < 8, so borrow from hundreds (4 becomes 3, 2 becomes 12)
3
Now borrow from tens: 12 tens → 11 tens, 7 ones → 17 ones
4
Subtract each place: 17-9=8, 11-8=3, 3-1=2
427 - 189 = 238
Check: 238 + 189 = 427 ✓
Final answer:

427 - 189 = 238

7 Practice Problem
Exercise 7
Solve: 504 - 267 = ?
1
Ones place: 4 < 7, so borrow from tens (but tens is 0)
2
Tens is 0, so borrow from hundreds (5 becomes 4, 0 becomes 10)
3
Now borrow from tens: 10 tens → 9 tens, 4 ones → 14 ones
4
Subtract each place: 14-7=7, 9-6=3, 4-2=2
504 - 267 = 237
Check: 237 + 267 = 504 ✓
Final answer:

504 - 267 = 237

Subtraction with Regrouping Concepts
Minuend - Subtrahend = Difference
Basic Subtraction Formula
🔄
Regrouping/Borrowing
When a digit in the minuend is smaller than the corresponding digit in the subtrahend, we borrow 1 from the next higher place value and add 10 to the current place value.
🔢
Place Value
Each digit has a specific value based on its position (ones, tens, hundreds, etc.). Understanding place value is crucial for regrouping.

Regrouping Process

1️⃣
Start from the rightmost digit
2️⃣
Compare digits in each place
3️⃣
Borrow when needed
4️⃣
Subtract each place value
5
Tens
→
4
After Borrowing
+
10
To Ones
2
Ones
→
12
After Borrowing
Detailed Summary

Definitions: Subtraction with regrouping (also called borrowing) is a method used when subtracting numbers where the digit in the minuend (top number) is smaller than the corresponding digit in the subtrahend (bottom number) in any place value position. In grade 3, this extends to larger numbers and requires careful attention to place value.

Core Rules: When performing subtraction with regrouping:

  • Always start subtraction from the ones place (rightmost digit)
  • If top digit is smaller than bottom digit, borrow from the next place value
  • When borrowing, subtract 1 from the higher place value and add 10 to the lower place value
  • Continue the process for each place value from right to left
  • Check your answer by adding the difference and subtrahend to verify
  • For problems with zeros in the minuend, plan ahead for multiple borrowings

Methods: The standard algorithm involves aligning numbers by place value, starting from the rightmost digit, and borrowing when necessary. When a digit in the minuend is smaller than the corresponding digit in the subtrahend, we borrow 1 from the next higher place value and add 10 to the current place value.

Examples:

  • Basic: 52 - 18 = 34 (borrow from tens to ones)
  • With zeros: 503 - 127 = 376 (borrow from hundreds to tens, then from tens to ones)
  • Multi-digit: 342 - 157 = 185 (multiple borrowings needed)

Tips: Cross out and rewrite digits when borrowing to avoid confusion. Always check your answer by adding the difference to the subtrahend - the result should equal the minuend. For problems with zeros in the minuend, practice with problems that have zeros in different positions.

Key Notes: In grade 3, students work with numbers up to 1000, so they need to understand regrouping across hundreds, tens, and ones. Practice with problems that have zeros in the minuend is particularly important for developing fluency.

Key Rules for Regrouping:

• Always start subtraction from the ones place

• If top digit is smaller than bottom digit, borrow from the next place value

• When borrowing, subtract 1 from the higher place value and add 10 to the lower place value

• Continue the process for each place value

• Check your answer by adding the difference to the subtrahend

• For zeros, plan ahead for multiple borrowings

Problem Solving Strategies & More Practice
705 - 238 = ?
Challenge Problem
Key definitions:

Minuend: The number being subtracted from

Subtrahend: The number being subtracted

Difference: The result of subtraction

Regrouping: Reorganizing numbers by borrowing from higher place values

Complete methodology:
  1. Align numbers: Write numbers vertically with place values aligned
  2. Start from ones: Begin subtraction from the rightmost digit
  3. Check each place: Compare if top digit is greater than bottom digit
  4. Borrow when needed: Take 1 from next higher place value
  5. Subtract systematically: Move from right to left
  6. Check answer: Add difference and subtrahend to verify
Tip 1: Draw arrows to show where you're borrowing from and to.
Tip 2: Cross out and rewrite digits when borrowing to avoid confusion.
Tip 3: Always check your answer by adding the difference to the subtrahend.
Tip 4: Practice with problems that require multiple borrowings.
Common errors: Forgetting to reduce the higher place value when borrowing, subtracting bottom number from top number instead of vice versa, misaligning place values.
Success strategies: Practice regularly, use visual aids, verify answers by addition, work with place value charts, use estimation to check reasonableness.
Challenge Problem
705 - 238 = ?
Solution Steps:

1. Ones: 5 < 8, so borrow from tens (but tens is 0)

2. Borrow from hundreds: 7→6, tens: 0→10

3. Now borrow from tens: 10→9, ones: 5→15

4. Subtract: 15-8=7, 9-3=6, 6-2=4

5. Answer: 467

Questions & Answers

Question: Why do I need to borrow when doing subtraction? It seems confusing when I have to take from another number.

Answer: Great question! Borrowing (also called regrouping) is necessary when the top number in a column is smaller than the bottom number. Think of it like exchanging money: if you have $5 but need to pay $8, you might exchange one $10 bill for ten $1 bills. In subtraction:

  • When you borrow 1 from the tens place, you're taking 1 ten and turning it into 10 ones
  • This gives you enough in the current place value to subtract
  • For example, in 52 - 18: since 2 < 8, we borrow 1 ten (making it 4 tens) and add 10 to the ones (making it 12 ones)

This maintains the total value while allowing subtraction in each place value.

Question: My child gets confused when there's a zero in the middle of the number. How can I help them understand regrouping when the tens place is 0?

Answer: Zero regrouping is indeed challenging! Here's a helpful approach:

  • Use concrete examples: If you have $603 and spend $247, how do you make change?
  • Break it down: For 603 - 247, you can't borrow from 0 tens, so go to the hundreds first
  • Visualize: Show 603 as 6 hundreds, 0 tens, 3 ones. To subtract 7 ones, you need to break apart a hundred first
  • Practice: Start with simpler problems like 102 - 35 before moving to harder ones

Remind your child that borrowing is just rearranging the same total amount into different groupings.

Question: How do I know if my subtraction with regrouping is correct? Sometimes I'm not sure about my answers.

Answer: The best way to check subtraction is to use the inverse operation - addition!

If you calculated 52 - 18 = 34, check by adding: 34 + 18 should equal 52

Other verification methods:

  • Estimate first: 52 is about 50, 18 is about 20, so the answer should be about 30
  • Count up: From 18 to 52, count up by tens and ones to see if it matches your answer
  • Use base-10 blocks or draw pictures to model the subtraction

Always verify your work, especially when learning new concepts!