Solved Exercises: Three Digit Subtraction With Regrouping Practice in Grade 2

Master three digit subtraction with regrouping: place value understanding, regrouping, and problem-solving strategies through these 5 detailed practice exercises.

Practice Exercises: 1 to 3
1 Basic regrouping practice
Practice Problem 1
Subtract: 523 - 178 = ?
Definition:

Regrouping (Borrowing): When the top digit is smaller than the bottom digit in a column, we borrow from the next higher place value

Subtraction method with regrouping:
  1. Align numbers by place value (ones under ones, etc.)
  2. Subtract from right to left (ones, then tens, then hundreds)
  3. If top digit < bottom digit, borrow from next column
  4. Convert borrowed amount to lower place value (1 hundred = 10 tens, etc.)
  5. Subtract normally after regrouping
Expression
523 - 178
Setup
523
-178
----
Step 1: Subtract the ones place

3 - 8 cannot be done (3 < 8)

Borrow 1 from the tens place (2 becomes 1)

Now we have 13 - 8 = 5

Step 2: Subtract the tens place

After borrowing, tens place has 1 (was 2)

1 - 7 cannot be done (1 < 7)

Borrow 1 from the hundreds place (5 becomes 4)

Now we have 11 - 7 = 4

Step 3: Subtract the hundreds place

After borrowing, hundreds place has 4 (was 5)

4 - 1 = 3

Write 3 in the hundreds place

523 - 178 = 345
Final answer:

523 - 178 = 345

Applied rules:

• Place value: Each column represents ones, tens, hundreds

• Regrouping: When top digit < bottom digit, borrow from next column

• Sequential subtraction: Work from right to left

Before Regrouping

523 (5 hundreds, 2 tens, 3 ones)

→
After Regrouping

4 hundreds, 11 tens, 13 ones

2 Double regrouping practice
Practice Problem 2
Subtract: 402 - 157 = ?
Definition:

Double regrouping: When borrowing is needed in both ones and tens places, requiring borrowing from hundreds place to tens, then from tens to ones

Expression
402 - 157
Setup
402
-157
----
Step 1: Subtract the ones place

2 - 7 cannot be done (2 < 7)

We need to borrow from the tens place

But the tens place has 0, so we must borrow from hundreds first

Step 2: Borrow from hundreds to tens

4 hundreds becomes 3 hundreds

0 tens becomes 10 tens

Step 3: Borrow from tens to ones

10 tens becomes 9 tens

2 ones becomes 12 ones

Step 4: Now subtract each place

Ones: 12 - 7 = 5

Tens: 9 - 5 = 4

Hundreds: 3 - 1 = 2

402 - 157 = 245
Final answer:

402 - 157 = 245

Applied rules:

• Double borrowing: When borrowing from zero, go to the next non-zero column

• Cascading effect: Borrowing affects multiple place values

• Sequential subtraction: Continue right to left after borrowing

3 Triple regrouping practice
Practice Problem 3
Subtract: 600 - 287 = ?
Definition:

Triple regrouping: When borrowing is needed across all three place values simultaneously

Expression
600 - 287
Setup
600
-287
----
Step 1: Subtract the ones place

0 - 7 cannot be done (0 < 7)

We need to borrow from the tens place

But tens place also has 0, so we must go to hundreds

Step 2: Borrow from hundreds to tens

6 hundreds becomes 5 hundreds

0 tens becomes 10 tens

Step 3: Borrow from tens to ones

10 tens becomes 9 tens

0 ones becomes 10 ones

Step 4: Now subtract each place

Ones: 10 - 7 = 3

Tens: 9 - 8 = 1

Hundreds: 5 - 2 = 3

Step 5: Verify the answer

Check: 313 + 287 = 600 ✓

600 - 287 = 313
Final answer:

600 - 287 = 313

Applied rules:

• Triple borrowing: When all columns require regrouping

• Cascading conversion: Borrow from highest place value down

• Verification: Always check by adding the result to the subtracted number

Regrouping Concepts and Rules
H T O - H T O = H T O
Three Digit Subtraction With Regrouping
Rule 1
Ones - Ones
Subtract rightmost digits
Rule 2
If top < bottom
Borrow from next column
Rule 3
1 ten = 10 ones
Convert place values
Key definitions:

Subtraction: The operation of taking one number away from another

Regrouping (Borrowing): Taking 1 from a higher place value to add 10 to a lower place value

Place value: Value of a digit based on its position in the number

Three-digit number: A number with hundreds, tens, and ones places

Complete methodology:
  1. Align numbers: Match ones with ones, tens with tens, hundreds with hundreds
  2. Subtract from right to left: Start with ones place, then tens, then hundreds
  3. Check for regrouping: If top digit < bottom digit, borrow from next column
  4. Convert place values: 1 hundred = 10 tens, 1 ten = 10 ones
  5. Repeat for each column: Continue the process for all place value columns
  6. Write the final answer: Combine all digits from each column
Tip 1: Always start subtracting from the rightmost column (ones place).
Tip 2: Cross out and rewrite digits when regrouping to stay organized.
Tip 3: Check your answer by adding the result to the subtracted number.
Tip 4: Use estimation to verify your answer makes sense.
Common errors: Forgetting to regroup, regrouping incorrectly, misaligning columns.
Exam preparation: Practice with various regrouping scenarios, verify answers.
Essential formulas and rules:

• Place value positions: H (Hundreds) T (Tens) O (Ones)

• Regrouping rule: When top digit < bottom digit, borrow 1 from next column

• Conversion rules: 1 hundred = 10 tens, 1 ten = 10 ones

• Subtraction sequence: Right to left (O → T → H)

• Verification method: Minuend - Subtrahend = Difference

Practice Exercises: 4 to 5
4 Word problem practice
Practice Problem 4
Tom had 703 stickers. He gave 268 stickers to his friends. How many stickers does Tom have left?
Definition:

Word problem: A mathematical problem presented in a real-world context requiring translation to arithmetic

Problem
703 - 268
Setup
703
-268
----
Solution
435
Step 1: Identify the operation

"gave stickers to his friends" means subtraction

So we need to subtract 268 from 703

Step 2: Subtract the ones place

3 - 8 cannot be done (3 < 8)

We need to borrow, but tens place has 0

Borrow from hundreds place: 7 becomes 6, 0 becomes 10

Now 10 tens becomes 9 tens, 3 ones becomes 13 ones

Step 3: Subtract the tens place

After regrouping, tens place has 9 (was 0)

9 - 6 = 3

Step 4: Subtract the hundreds place

After borrowing, hundreds place has 6 (was 7)

6 - 2 = 4

Write 4 in the hundreds place

Tom has 435 stickers left
Final answer:

Tom has 435 stickers left.

Applied rules:

• Word translation: Convert words to mathematical operations

• Regrouping: Apply borrowing when top digit < bottom digit

• Contextual answer: Include units in the final answer

5 Advanced regrouping practice
Practice Problem 5
Subtract: 805 - 397 = ?
Definition:

Advanced regrouping: Subtraction involving zeros in multiple place values requiring careful regrouping

Expression
805 - 397
Setup
805
-397
----
Result
408
Step 1: Subtract the ones place

5 - 7 cannot be done (5 < 7)

We need to borrow from the tens place

But the tens place has 0, so we must borrow from hundreds first

Step 2: Borrow from hundreds to tens

8 hundreds becomes 7 hundreds

0 tens becomes 10 tens

Step 3: Borrow from tens to ones

10 tens becomes 9 tens

5 ones becomes 15 ones

Step 4: Subtract each place

Ones: 15 - 7 = 8

Tens: 9 - 9 = 0

Hundreds: 7 - 3 = 4

Step 5: Verify the answer

Check: 408 + 397 = 805 ✓

805 - 397 = 408
Final answer:

805 - 397 = 408

Applied rules:

• Zero handling: When regrouping from zero, go to next non-zero column

• Cascading effect: Regrouping affects multiple place values

• Verification: Always check answer by adding

Comprehensive Summary and Key Concepts
H T O - H T O = H T O
Regrouping Fundamentals
Complete Definition:

Three Digit Subtraction With Regrouping: The process of taking away one three-digit number from another, requiring borrowing from higher place values when the top digit is smaller than the bottom digit in any column.

Detailed Methodology:
  1. Alignment: Position numbers vertically with matching place values
  2. Right-to-left processing: Begin with ones place, proceed to tens, then hundreds
  3. Comparison: In each column, compare top digit to bottom digit
  4. Regrouping decision: If top digit < bottom digit, borrow from next higher place value
  5. Place value conversion: 1 in higher place = 10 in lower place
  6. Subtraction execution: Complete subtraction in each column
  7. Result compilation: Combine results from all columns
Memorization Tip: Remember "Right to Left" - start with ones, then tens, then hundreds.
Verification Strategy: Add your answer to the subtracted number to get the original number.
Visualization Aid: Use base-10 blocks to represent each digit before subtracting.
Common Pattern: Look for when regrouping is needed by comparing digits in each column.
Key Insight: Regrouping transforms a subtraction problem by converting higher place values to lower ones.
Foundation Building: Mastering regrouping prepares students for more complex arithmetic operations.
Essential Rules and Properties:

• Place Value Integrity: Each digit maintains its positional value throughout the operation

• Regrouping Rule: When top digit < bottom digit, borrow 1 from next higher place value

• Conversion Principle: 1 hundred = 10 tens, 1 ten = 10 ones

• Sequential Order: Maintain right-to-left processing pattern

• Verification Method: Minuend - Subtrahend = Difference

Common Scenarios
Problem Types
Scenario 1
No Regrouping
Top digit ≥ bottom in all columns
Scenario 2
Single Regroup
Regroup from one column only
Scenario 3
Multiple Regroup
Regroup cascades through columns

Questions & Answers

Question: I don't understand why we need to regroup when subtracting. Why can't I just subtract the bigger number from the smaller one?

Answer: Great question! We regroup because we can't take away more than we have. Think of it like this:

  • In 523 - 178, when we look at the ones place (3 - 8), we only have 3 but need to take away 8
  • We can't take 8 away from 3, so we regroup by borrowing 1 ten from the tens place
  • That 1 ten becomes 10 ones, so now we have 13 ones
  • Now we can take 8 from 13, which equals 5

It's like trading: if you have 1 dollar bill but need to give someone 8 quarters, you go to the bank and trade your dollar for 10 quarters. Now you have enough to give them 8 quarters.

Question: My child is getting confused when there are zeros in the number. How can I help them with problems like 600 - 287?

Answer: Zero subtraction problems can be tricky! Here's how to help your child:

  • Break it down: Explain that when we see 0, we need to go to the next column to regroup
  • Use physical objects: Counters or base-10 blocks help visualize the regrouping process
  • Work step by step: First regroup from hundreds to tens, then from tens to ones
  • Practice with simpler problems: Start with problems like 100 - 25 before moving to more complex ones
  • Encourage patience: Take it one column at a time

Remind your child that regrouping is like making change - sometimes we need to break a larger unit into smaller units.

Question: Sometimes I forget which direction to go when subtracting. Should I go left to right or right to left?

Answer: Always go from right to left when subtracting! This is important for regrouping:

  • Start with the ones place (rightmost column)
  • Then go to the tens place (middle column)
  • Finally go to the hundreds place (leftmost column)

This order is important because when you need to regroup, you take from the next column to the left. If you went left to right, you wouldn't know if you needed to adjust a column later.

Remember: Right to Left - Ones, Tens, Hundreds!