Solved Examples: Three Digit Subtraction in Grade 2

Master three digit subtraction: borrowing, place value understanding, and problem-solving strategies through these 5 detailed examples.

Examples: 1 to 3
1 Basic subtraction
Example 1
Subtract: 578 - 234 = ?
Definition:

Three digit subtraction: Taking away one three-digit number from another, working from right to left (ones, tens, hundreds)

Subtraction method:
  1. Align numbers by place value (ones under ones, etc.)
  2. Subtract from right to left (ones, then tens, then hundreds)
  3. Take away the bottom digit from the top digit in each column
  4. Write the result below each column
Expression
578 - 234
Setup
578
-234
----
Step 1: Subtract the ones place

8 - 4 = 4

Write 4 in the ones place

Step 2: Subtract the tens place

7 - 3 = 4

Write 4 in the tens place

Step 3: Subtract the hundreds place

5 - 2 = 3

Write 3 in the hundreds place

578 - 234 = 344
Final answer:

578 - 234 = 344

Applied rules:

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

• Sequential subtraction: Work from right to left

• No borrowing needed: Top digit is larger than bottom digit in each column

2 Subtraction with borrowing
Example 2
Subtract: 423 - 157 = ?
Definition:

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

Expression
423 - 157
Setup
423
-157
----
Step 1: Subtract the ones place

3 - 7 cannot be done (3 < 7)

We need to borrow 1 from the tens place

Now we have 13 - 7 = 6

Step 2: Subtract the tens place

After borrowing, we have 1 in the tens place (originally 2)

1 - 5 cannot be done (1 < 5)

We need to borrow 1 from the hundreds place

Now we have 11 - 5 = 6

Step 3: Subtract the hundreds place

After borrowing, we have 3 in the hundreds place (originally 4)

3 - 1 = 2

Write 2 in the hundreds place

423 - 157 = 266
Final answer:

423 - 157 = 266

Applied rules:

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

• Place value conversion: 1 hundred = 10 tens, 1 ten = 10 ones

• Sequential subtraction: Continue right to left after borrowing

Before Borrowing

423 (4 hundreds, 2 tens, 3 ones)

→
After Borrowing

3 hundreds, 11 tens, 13 ones

3 Complex borrowing
Example 3
Subtract: 502 - 238 = ?
Definition:

Complex borrowing: When borrowing is needed in multiple consecutive place values

Expression
502 - 238
Setup
502
-238
----
Step 1: Subtract the ones place

2 - 8 cannot be done (2 < 8)

We need to borrow 1 from the tens place

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

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

2 ones becomes 12 ones

Step 4: Now subtract each place

Ones: 12 - 8 = 4

Tens: 9 - 3 = 6

Hundreds: 4 - 2 = 2

502 - 238 = 264
Final answer:

502 - 238 = 264

Applied rules:

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

• Sequential conversion: Convert higher place values step by step

• Place value maintenance: Keep track of all borrowed amounts

Subtraction Concepts and Rules
H T O - H T O = H T O
Three Digit Subtraction
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

Borrowing (Regrouping): 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 borrowing: 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 borrowing 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 borrow, borrowing incorrectly, misaligning columns.
Exam preparation: Practice with various borrowing scenarios, verify answers.
Essential formulas and rules:

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

• Borrowing 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

Examples: 4 to 5
4 Word problem
Example 4
Sarah had 634 stickers. She gave 287 stickers to her friend. How many stickers does Sarah have left?
Definition:

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

Problem
634 - 287
Setup
634
-287
----
Solution
347
Step 1: Identify the operation

"gave stickers to her friend" means subtraction

So we need to subtract 287 from 634

Step 2: Subtract the ones place

4 - 7 cannot be done (4 < 7)

Borrow 1 from tens place: 14 - 7 = 7

Step 3: Subtract the tens place

After borrowing, tens place has 2 (was 3)

2 - 8 cannot be done (2 < 8)

Borrow 1 from hundreds place: 12 - 8 = 4

Step 4: Subtract the hundreds place

After borrowing, hundreds place has 5 (was 6)

5 - 2 = 3

Write 3 in the hundreds place

Sarah has 347 stickers left
Final answer:

Sarah has 347 stickers left.

Applied rules:

• Word translation: Convert words to mathematical operations

• Borrowing: Apply borrowing when top digit < bottom digit

• Contextual answer: Include units in the final answer

5 Advanced borrowing
Example 5
Subtract: 700 - 345 = ?
Definition:

Zero borrowing: Subtraction involving zeros in multiple place values

Expression
700 - 345
Setup
700
-345
----
Result
355
Step 1: Subtract the ones place

0 - 5 cannot be done (0 < 5)

We need to borrow, but tens place also has 0

Must borrow from hundreds place first

Step 2: Borrow from hundreds to tens

7 hundreds becomes 6 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: Subtract each place

Ones: 10 - 5 = 5

Tens: 9 - 4 = 5

Hundreds: 6 - 3 = 3

Step 5: Verify the answer

Check: 355 + 345 = 700 ✓

700 - 345 = 355
Final answer:

700 - 345 = 355

Applied rules:

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

• 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
Subtraction Fundamentals
Complete Definition:

Three Digit Subtraction: The process of taking away one three-digit number from another, requiring careful attention to place value and potentially borrowing from higher place values when necessary.

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. Borrowing 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 borrowing is needed by comparing digits in each column.
Key Insight: Borrowing transforms a subtraction problem by converting higher place values to lower ones.
Foundation Building: Mastering subtraction prepares students for more complex arithmetic operations.
Essential Rules and Properties:

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

• Borrowing 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 Borrowing
Top digit ≥ bottom in all columns
Scenario 2
Single Borrow
Borrow from one column only
Scenario 3
Multiple Borrow
Borrow cascades through columns

Questions & Answers

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

Answer: Great question! We borrow 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 borrow 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 when there are zeros in the number. How can I help them with problems like 502 - 238?

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 borrow
  • Use physical objects: Counters or base-10 blocks help visualize the 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 borrowing 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 borrowing:

  • 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 borrow, 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!