Place Value Subtraction with Regrouping Worksheets for Grade 3

Comprehensive worksheets with detailed solutions and practice materials for mastering place value subtraction with regrouping.

Worksheets and Practice Problems
1 Basic Regrouping Worksheet
Basic Regrouping Problems
Solve these subtraction problems with regrouping:
Practice Problems
Problem 1: 52 - 17
Solution:

Ones: 2 < 7, so regroup: 52 = 40 + 12, then 12 - 7 = 5, 4 - 1 = 3, answer: 35

Problem 2: 64 - 28
Solution:

Ones: 4 < 8, so regroup: 64 = 50 + 14, then 14 - 8 = 6, 5 - 2 = 3, answer: 36

Problem 3: 73 - 49
Solution:

Ones: 3 < 9, so regroup: 73 = 60 + 13, then 13 - 9 = 4, 6 - 4 = 2, answer: 24

Problem 4: 81 - 56
Solution:

Ones: 1 < 6, so regroup: 81 = 70 + 11, then 11 - 6 = 5, 7 - 5 = 2, answer: 25

Problem 5: 95 - 68
Solution:

Ones: 5 < 8, so regroup: 95 = 80 + 15, then 15 - 8 = 7, 8 - 6 = 2, answer: 27

2 Three-Digit Regrouping Worksheet
Three-Digit Regrouping Problems
Solve these three-digit subtraction problems with regrouping:
Advanced Practice Problems
Problem 1: 304 - 127
Solution:

Ones: 4 < 7, regroup from tens (0), regroup from hundreds: 304 = 200 + 90 + 14, then 14 - 7 = 7, 9 - 2 = 7, 2 - 1 = 1, answer: 177

Problem 2: 400 - 158
Solution:

Ones: 0 < 8, regroup from tens (0), regroup from hundreds: 400 = 300 + 100 = 300 + 90 + 10, then 10 - 8 = 2, 9 - 5 = 4, 3 - 1 = 2, answer: 242

Problem 3: 503 - 246
Solution:

Ones: 3 < 6, regroup from tens (0), regroup from hundreds: 503 = 400 + 100 + 3 = 400 + 90 + 13, then 13 - 6 = 7, 9 - 4 = 5, 4 - 2 = 2, answer: 257

Problem 4: 600 - 387
Solution:

Ones: 0 < 7, regroup from tens (0), regroup from hundreds: 600 = 500 + 100 = 500 + 90 + 10, then 10 - 7 = 3, 9 - 8 = 1, 5 - 3 = 2, answer: 213

Problem 5: 705 - 429
Solution:

Ones: 5 < 9, regroup from tens (0), regroup from hundreds: 705 = 600 + 100 + 5 = 600 + 90 + 15, then 15 - 9 = 6, 9 - 2 = 7, 6 - 4 = 2, answer: 276

Complete Summary: Place Value Subtraction with Regrouping
Key Concepts and Definitions

Place Value: The value of a digit based on its position in a number (ones, tens, hundreds, etc.)

Regrouping: Converting 1 unit from a higher place value to 10 units of the next lower place value

Borrowing: Another term for regrouping in subtraction operations

Base-Ten System: Our number system where each place value is 10 times the previous one

Worksheet: A collection of practice problems designed to reinforce specific mathematical concepts

Core Rules and Principles

Regrouping Rule: When the bottom digit is larger than the top digit in a place value, you must regroup from the next higher place value

Value Conversion: 1 hundred = 10 tens, 1 ten = 10 ones

Subtraction Sequence: Always start from the rightmost digit (ones place) and move left

Zero Handling: When you encounter a zero and need to regroup, continue to the next non-zero place value

Practice Principle: Repetition with varied difficulty levels leads to mastery

Step-by-Step Method
  1. Align Numbers: Write the numbers vertically with place values aligned
  2. Start from Right: Begin subtraction in the ones place
  3. Check Need: Compare digits in each place value (bottom vs top)
  4. Regroup if Needed: If bottom digit is larger, borrow from next higher place
  5. Subtract Digit: Perform subtraction in that place value
  6. Move Left: Continue to next place value (tens, then hundreds)
  7. Combine Results: Write the final answer combining all place values
  8. Verify: Add the difference back to the subtracted number to check accuracy
Examples - From Simple to Complex

Simple Example: \(42 - 15\)

Ones: \(2 < 5\), so regroup: \(42 = 30 + 12\), then \(12 - 5 = 7\), \(3 - 1 = 2\), answer: \(27\)

Intermediate Example: \(203 - 147\)

Ones: \(3 < 7\), regroup from tens (but tens is 0), so regroup from hundreds: \(203 = 100 + 100 + 3 = 100 + 90 + 13\), then \(13 - 7 = 6\), \(9 - 4 = 5\), \(1 - 1 = 0\), answer: \(56\)

Complex Example: \(500 - 289\)

Ones: \(0 < 9\), regroup from tens (0), regroup from hundreds: \(500 = 400 + 100 = 400 + 90 + 10\), then \(10 - 9 = 1\), \(9 - 8 = 1\), \(4 - 2 = 2\), answer: \(211\)

Tips, Tricks, and Common Pitfalls

Tips:

  • Always start subtracting from the ones place
  • Draw lines to separate place values visually
  • Check your answer by adding the difference back to the subtracted number
  • Practice with base-ten blocks to visualize the process
  • When you see a zero, always check if regrouping is needed from higher places

Common Mistakes:

  • Forgetting to regroup when needed
  • Subtracting smaller number from larger regardless of position
  • Misaligning digits when writing numbers vertically
  • Forgetting to reduce the higher place value after borrowing
  • Not continuing regrouping when there are zeros in higher places
Key Notes for Memorization

Memory Aids:

  • "More on the floor, go next door" - when bottom number is bigger, borrow from next place
  • "1 hundred = 10 tens = 100 ones" - know these conversions
  • Always start from the right (ones place)
  • After borrowing, the higher place value decreases by 1
  • Check your work: Difference + Subtracted = Original number
Word Problem Worksheets
3 Real-World Applications
Word Problem Worksheet
Solve these real-world subtraction problems with regrouping:
Word Problems
Problem 1: Sarah collected 250 seashells. She gave 87 to her friend. How many does she have left?
Solution:

250 - 87: Ones: 0 < 7, regroup from tens (5 becomes 4), 10 - 7 = 3, tens: 4 < 8, regroup from hundreds (2 becomes 1), 14 - 8 = 6, hundreds: 1 - 0 = 1, answer: 163 seashells

Problem 2: Tom had 305 stickers. He used 168 for a project. How many stickers does he have remaining?
Solution:

305 - 168: Ones: 5 < 8, regroup from tens (0), regroup from hundreds: 305 = 200 + 100 + 5 = 200 + 90 + 15, then 15 - 8 = 7, 9 - 6 = 3, 2 - 1 = 1, answer: 137 stickers

Problem 3: A school library had 400 books. Students borrowed 237 books. How many books are left in the library?
Solution:

400 - 237: Ones: 0 < 7, regroup from tens (0), regroup from hundreds: 400 = 300 + 100 = 300 + 90 + 10, then 10 - 7 = 3, 9 - 3 = 6, 3 - 2 = 1, answer: 163 books

Problem 4: Maria saved $502 for a toy. She spent $346. How much money does she have left?
Solution:

502 - 346: Ones: 2 < 6, regroup from tens (0), regroup from hundreds: 502 = 400 + 100 + 2 = 400 + 90 + 12, then 12 - 6 = 6, 9 - 4 = 5, 4 - 3 = 1, answer: $156

Problem 5: A farmer harvested 600 apples. He sold 429 apples at the market. How many apples does he still have?
Solution:

600 - 429: Ones: 0 < 9, regroup from tens (0), regroup from hundreds: 600 = 500 + 100 = 500 + 90 + 10, then 10 - 9 = 1, 9 - 2 = 7, 5 - 4 = 1, answer: 171 apples

4 Mixed Practice Worksheet
Mixed Practice Problems
Solve these mixed subtraction problems (some need regrouping, some don't):
Mixed Problems
Problem 1: 78 - 23
Solution:

No regrouping needed: 8 - 3 = 5, 7 - 2 = 5, answer: 55

Problem 2: 94 - 58
Solution:

Ones: 4 < 8, regroup: 94 = 80 + 14, then 14 - 8 = 6, 8 - 5 = 3, answer: 36

Problem 3: 200 - 145
Solution:

Ones: 0 < 5, regroup from tens (0), regroup from hundreds: 200 = 100 + 100 = 100 + 90 + 10, then 10 - 5 = 5, 9 - 4 = 5, 1 - 1 = 0, answer: 55

Problem 4: 63 - 21
Solution:

No regrouping needed: 3 - 1 = 2, 6 - 2 = 4, answer: 42

Problem 5: 407 - 198
Solution:

Ones: 7 < 8, regroup from tens (0), regroup from hundreds: 407 = 300 + 100 + 7 = 300 + 90 + 17, then 17 - 8 = 9, 9 - 9 = 0, 3 - 1 = 2, answer: 209

Questions & Answers

Question: I don't understand why I have to regroup when the bottom number is bigger than the top number in subtraction. Why can't I just subtract the smaller from the larger?

Answer: Great question! In subtraction, we always subtract the bottom number FROM the top number. When the bottom digit is larger than the top digit in a place value, we can't take away more than we have. That's why we need to regroup.

Think of it like this: If you have 2 apples and someone asks for 7 apples, you can't give them 7 because you only have 2. You'd need to get more apples first.

In math: When you see 2 ones and need to subtract 7 ones, you need to borrow 1 ten (which equals 10 ones) from the tens place. Now you have 12 ones, and you can subtract 7 ones to get 5 ones.

Example: In 52 - 17, we can't do 2 - 7 in the ones place, so we borrow 1 ten from the 5 tens, making it 4 tens and 12 ones. Then we can do 12 - 7 = 5 in the ones place.

Question: My child gets confused when there's a zero in the middle of a number like 402. How can I help them understand regrouping across zeros?

Answer: Numbers with zeros can be tricky! When there's a zero in a place value, your child needs to keep going to the next non-zero place value to borrow from. Think of it like a chain reaction.

For 402 - 157, here's the process:

  • Ones place: 2 - 7 (can't do this, need to borrow)
  • Tens place: There's a 0, so can't borrow from here
  • Hundreds place: Borrow 1 hundred (4 becomes 3), giving 10 tens
  • Now tens place: 10 tens, borrow 1 ten (10 becomes 9), giving 10 ones
  • Now ones place: 12 - 7 = 5

Use visual aids like base-ten blocks or draw the process out. Explain that the zero is like a "bridge" - you can't stop there, you have to go further to get what you need.

Question: I learned the standard algorithm, but this place value approach seems more complex. Why do we teach it this way now?

Answer: The place value approach builds conceptual understanding rather than just procedural fluency. Students who understand why regrouping works are better prepared for advanced math.

Benefits of the place value approach:

  • Students understand the base-ten system and why algorithms work
  • They can apply the concept to different number bases
  • They develop number sense and mental math skills
  • They can explain their thinking and catch errors more easily
  • It prepares them for algebra and higher-level mathematics

The standard algorithm is still taught, but building understanding first makes the procedure more meaningful. Students who understand place value can better adapt when faced with unusual problems or when learning decimals later.