Solved Exercises: Three Digit Subtraction With Regrouping and Zeros in Grade 2

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

Exercises: 1 to 3
1 Basic zero regrouping
Exercise 1
Subtract: 402 - 157 = ?
Definition:

Zero regrouping: When regrouping is needed but one or more place values contain zeros, requiring borrowing from higher place values

Subtraction method with zeros:
  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. If column has zero, go to next non-zero column to borrow
  5. Convert borrowed amount to lower place value
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:

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

• Zero handling: When column has zero, borrow from next non-zero column

• Sequential subtraction: Work from right to left after regrouping

Before Regrouping

402 (4 hundreds, 0 tens, 2 ones)

→
After Regrouping

3 hundreds, 9 tens, 12 ones

2 Double zero regrouping
Exercise 2
Subtract: 500 - 238 = ?
Definition:

Double zero regrouping: When both tens and ones places contain zeros, requiring borrowing from the hundreds place

Expression
500 - 238
Setup
500
-238
----
Step 1: Subtract the ones place

0 - 8 cannot be done (0 < 8)

We need to borrow from the tens place

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

Step 2: Borrow from hundreds to tens

5 hundreds becomes 4 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 - 8 = 2

Tens: 9 - 3 = 6

Hundreds: 4 - 2 = 2

500 - 238 = 262
Final answer:

500 - 238 = 262

Applied rules:

• Double zero handling: When tens and ones are both zero, borrow from hundreds

• Cascading effect: Borrowing affects multiple place values

• Sequential subtraction: Continue right to left after borrowing

3 Triple regrouping with zeros
Exercise 3
Subtract: 600 - 287 = ?
Definition:

Triple regrouping with zeros: When all three place values require regrouping due to zeros and borrowing needs

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 zero handling: When all lower places require borrowing

• Cascading conversion: Borrow from highest place value down

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

Zero Regrouping Concepts and Rules
H T O - H T O = H T O
Three Digit Subtraction With Zeros
Rule 1
Ones - Ones
Subtract rightmost digits
Rule 2
If top < bottom
Borrow from next column
Rule 3
If zero
Go to next non-zero
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

Zero regrouping: When borrowing is needed but the place value contains zero

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. Handle zeros: If column has 0, go to next non-zero column to borrow
  5. Convert place values: 1 hundred = 10 tens, 1 ten = 10 ones
  6. Repeat for each column: Continue the process for all place value columns
  7. Write the final answer: Combine all digits from each column
Tip 1: Always start subtracting from the rightmost column (ones place).
Tip 2: When you see a zero that needs to borrow, go to the next non-zero column.
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 handle zeros, regrouping incorrectly, misaligning columns.
Exam preparation: Practice with various zero regrouping scenarios, verify answers.
Essential formulas and rules:

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

• Zero handling: When column has 0, borrow from next non-zero 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 zeros
Exercise 4
Tom had 700 stickers. He gave 284 stickers to his friends. How many stickers does Tom have left?
Definition:

Word problem with zeros: A mathematical problem presented in a real-world context requiring subtraction with zero regrouping

Problem
700 - 284
Setup
700
-284
----
Solution
416
Step 1: Identify the operation

"gave stickers to his friends" means subtraction

So we need to subtract 284 from 700

Step 2: Subtract the ones place

0 - 4 cannot be done (0 < 4)

We need to borrow from the tens place

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

Step 3: Borrow from hundreds to tens

7 hundreds becomes 6 hundreds

0 tens becomes 10 tens

Step 4: Borrow from tens to ones

10 tens becomes 9 tens

0 ones becomes 10 ones

Step 5: Now subtract each place

Ones: 10 - 4 = 6

Tens: 9 - 8 = 1

Hundreds: 6 - 2 = 4

Tom has 416 stickers left
Final answer:

Tom has 416 stickers left.

Applied rules:

• Word translation: Convert words to mathematical operations

• Zero handling: Apply borrowing when column has zero

• Contextual answer: Include units in the final answer

5 Advanced zero regrouping
Exercise 5
Subtract: 805 - 397 = ?
Definition:

Advanced zero 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
Zero Regrouping Fundamentals
Complete Definition:

Three Digit Subtraction With Regrouping and Zeros: The process of taking away one three-digit number from another when one or more place values contain zeros, requiring careful attention to borrowing from higher place values.

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. Zero handling: If column has 0 and needs to borrow, go to next non-zero column
  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: Zero regrouping requires going to the next non-zero place value when borrowing.
Foundation Building: Mastering zero regrouping prepares students for more complex arithmetic operations.
Essential Rules and Properties:

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

• Zero Handling Rule: When place value has 0 and needs to borrow, go to next non-zero column

• 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
One Zero
One place value has 0
Scenario 2
Two Zeros
Two place values have 0
Scenario 3
Three Zeros
All place values have 0

Questions & Answers

Question: I don't understand why I have to go to the next column when there's a zero. Why can't I just borrow from the zero?

Answer: Great question! You can't borrow from zero because zero means there's nothing to borrow. Think of it like this:

  • In 402 - 157, when we look at the tens place (0), there are no tens to borrow from
  • We need to go to the hundreds place (4) because that's where we have actual tens to convert
  • When we borrow from 4 hundreds, we get 10 tens, so the tens place becomes 10
  • Now we can borrow 1 ten (which is 10 ones) to add to the ones place

It's like having $0 in your pocket but $40 in your wallet - you can't borrow money from an empty pocket!

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

Answer: Multiple zero 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 find something to borrow
  • Use physical objects: Counters or base-10 blocks help visualize the regrouping process
  • Work step by step: First borrow 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 with zeros 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!