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

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

Exercises: 1 to 3
1 Single regrouping in ones
Exercise 1
Subtract: 423 - 157 = ?
Definition:

Single regrouping: When only one place value column requires borrowing from the next higher place value

Subtraction method with single regrouping:
  1. Align numbers by place value (ones under ones, etc.)
  2. Subtract from right to left (ones, then tens, then hundreds)
  3. When top digit < bottom digit, borrow from next column
  4. Convert borrowed amount to lower place value
  5. Only regroup once in this exercise
Expression
423 - 157
Setup
423
-157
----
Step 1: Subtract the ones place

3 - 7 cannot be done (3 < 7)

Borrow 1 from the tens place (2 becomes 1)

Now we have 13 - 7 = 6

Step 2: Subtract the tens place

After borrowing, tens place has 1 (was 2)

1 - 5 cannot be done (1 < 5)

Borrow 1 from the hundreds place (4 becomes 3)

Now we have 11 - 5 = 6

Step 3: Subtract the hundreds place

After borrowing, hundreds place has 3 (was 4)

3 - 1 = 2

Write 2 in the hundreds place

423 - 157 = 266
Final answer:

423 - 157 = 266

Applied rules:

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

• Single regrouping: Only one borrowing needed per exercise

• Sequential subtraction: Work from right to left

Before Regrouping

423 (4 hundreds, 2 tens, 3 ones)

→
After Regrouping

3 hundreds, 11 tens, 13 ones

2 Single regrouping in tens
Exercise 2
Subtract: 532 - 178 = ?
Definition:

Single regrouping in tens: When only the tens place requires borrowing from the hundreds place

Expression
532 - 178
Setup
532
-178
----
Step 1: Subtract the ones place

2 - 8 cannot be done (2 < 8)

Borrow 1 from the tens place (3 becomes 2)

Now we have 12 - 8 = 4

Step 2: Subtract the tens place

After borrowing, tens place has 2 (was 3)

2 - 7 cannot be done (2 < 7)

Borrow 1 from the hundreds place (5 becomes 4)

Now we have 12 - 7 = 5

Step 3: Subtract the hundreds place

After borrowing, hundreds place has 4 (was 5)

4 - 1 = 3

Write 3 in the hundreds place

532 - 178 = 354
Final answer:

532 - 178 = 354

Applied rules:

• Single regrouping: Only one borrowing needed per exercise

• Cascading effect: Borrowing affects multiple place values

• Sequential subtraction: Continue right to left after borrowing

3 Single regrouping in hundreds
Exercise 3
Subtract: 624 - 287 = ?
Definition:

Single regrouping in hundreds: When only the hundreds place requires borrowing from the thousands place (or imaginary place)

Expression
624 - 287
Setup
624
-287
----
Step 1: Subtract the ones place

4 - 7 cannot be done (4 < 7)

Borrow 1 from the tens place (2 becomes 1)

Now we have 14 - 7 = 7

Step 2: Subtract the tens place

After borrowing, tens place has 1 (was 2)

1 - 8 cannot be done (1 < 8)

Borrow 1 from the hundreds place (6 becomes 5)

Now we have 11 - 8 = 3

Step 3: Subtract the hundreds place

After borrowing, hundreds place has 5 (was 6)

5 - 2 = 3

Write 3 in the hundreds place

Step 4: Verify the answer

Check: 337 + 287 = 624 ✓

624 - 287 = 337
Final answer:

624 - 287 = 337

Applied rules:

• Single regrouping: Only one borrowing needed per exercise

• Cascading conversion: Borrow from highest place value down

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

Single Regrouping Concepts and Rules
H T O - H T O = H T O
Three Digit Subtraction With Single 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

Single regrouping: When only one place value column requires borrowing

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

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

Exercises: 4 to 5
4 Word problem with single regrouping
Exercise 4
Sarah had 713 stickers. She gave 258 stickers to her friends. How many stickers does Sarah have left?
Definition:

Word problem with single regrouping: A mathematical problem presented in a real-world context requiring subtraction with one borrowing

Problem
713 - 258
Setup
713
-258
----
Solution
455
Step 1: Identify the operation

"gave stickers to her friends" means subtraction

So we need to subtract 258 from 713

Step 2: Subtract the ones place

3 - 8 cannot be done (3 < 8)

Borrow 1 from tens place: 13 - 8 = 5

Step 3: Subtract the tens place

After borrowing, tens place has 0 (was 1)

0 - 5 cannot be done (0 < 5)

Borrow 1 from hundreds place: 10 - 5 = 5

Step 4: Subtract the hundreds place

After borrowing, hundreds place has 6 (was 7)

6 - 2 = 4

Write 4 in the hundreds place

Sarah has 455 stickers left
Final answer:

Sarah has 455 stickers left.

Applied rules:

• Word translation: Convert words to mathematical operations

• Single regrouping: Apply borrowing when top digit < bottom digit

• Contextual answer: Include units in the final answer

5 Advanced single regrouping
Exercise 5
Subtract: 831 - 394 = ?
Definition:

Advanced single regrouping: Subtraction requiring careful attention to place values and borrowing

Expression
831 - 394
Setup
831
-394
----
Result
437
Step 1: Subtract the ones place

1 - 4 cannot be done (1 < 4)

Borrow 1 from tens place: 11 - 4 = 7

Step 2: Subtract the tens place

After borrowing, tens place has 2 (was 3)

2 - 9 cannot be done (2 < 9)

Borrow 1 from hundreds place: 12 - 9 = 3

Step 3: Subtract the hundreds place

After borrowing, hundreds place has 7 (was 8)

7 - 3 = 4

Step 4: Verify the answer

Check: 437 + 394 = 831 ✓

831 - 394 = 437
Final answer:

831 - 394 = 437

Applied rules:

• Single regrouping: Only one borrowing needed per exercise

• Cascading effect: Borrowing affects multiple place values

• Verification: Always check answer by adding

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

Three Digit Subtraction With Single Regrouping: The process of taking away one three-digit number from another when only one place value column requires borrowing from the next higher place value.

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. Single regrouping decision: If top digit < bottom digit in one column, 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: Single regrouping simplifies the process by limiting borrowing to one column.
Foundation Building: Mastering single regrouping prepares students for more complex arithmetic operations.
Essential Rules and Properties:

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

• Single Regrouping Rule: When top digit < bottom digit in one column, 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
Ones Regroup
Only ones place needs borrowing
Scenario 2
Tens Regroup
Only tens place needs borrowing
Scenario 3
Hundreds Regroup
Only hundreds place needs borrowing

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 423 - 157, when we look at the ones place (3 - 7), we only have 3 but need to take away 7
  • We can't take 7 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 7 from 13, which equals 6

It's like trading: if you have 1 dollar bill but need to give someone 7 quarters, you go to the bank and trade your dollar for 10 quarters. Now you have enough to give them 7 quarters.

Question: My child is getting confused about when to regroup. How can I help them identify when single regrouping is needed?

Answer: Here's how to help your child identify when single regrouping is needed:

  • Compare digits: In each column, check if the top digit is smaller than the bottom digit
  • Look for patterns: When the top digit is smaller, regrouping is needed
  • Count columns: Only one column should need regrouping in single regrouping problems
  • Practice with visual aids: Use base-10 blocks to help visualize the process
  • Encourage patience: Take it one column at a time

Remind your child that single regrouping means only one column needs borrowing, making the problem simpler.

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!