Three-digit subtraction with regrouping: Subtracting numbers where borrowing is needed from a higher place value when the top digit is smaller than the bottom digit.
Note: Regrouping is also known as "borrowing" and is essential for subtracting when the top digit in any column is smaller than the bottom digit.
- Start from the ones column (rightmost digits)
- If the top digit is smaller than the bottom digit, borrow from the next higher place value
- Subtract the ones column
- Move to the tens column and repeat the process
- Move to the hundreds column and repeat the process
6 > 3, so no regrouping needed: 6 - 3 = 3
5 > 2, so no regrouping needed: 5 - 2 = 3
4 > 1, so no regrouping needed: 4 - 1 = 3
333
• Place value: Each digit represents its value based on position
• Borrowing: When top digit < bottom digit, borrow from next column
• Order: Always start from rightmost column (ones)
• Practice Tip: Always check your answer by adding: 333 + 123 = 456
- 567 - 234 = 333 - Practice with different numbers
- 789 - 456 = 333 - Same result with different order
- 478 - 245 = 233 - Practice with regrouping needed
- Always start subtracting from the ones place (rightmost)
- Draw lines under each column to keep digits aligned
- Check each column to see if regrouping is needed
Q: When do I need to regroup in subtraction?
A: You need to regroup when the top digit in any column is smaller than the bottom digit. In 456-123, no regrouping was needed since 6>3, 5>2, and 4>1.
Q: What happens if I don't regroup when needed?
A: You'll get an incorrect answer. For example, in 423-156, if you don't regroup, you'd get 333 instead of the correct answer 267.
Tens place regrouping: When the tens digit in the minuend is smaller than the tens digit in the subtrahend, we borrow from the hundreds column.
Note: This occurs when subtracting tens digits results in needing to borrow from the hundreds column.
- Start from the ones column
- If the top digit is smaller than the bottom digit, borrow from the tens column
- Move to the tens column and check if borrowing is needed
- If the tens digit is smaller after borrowing, borrow from the hundreds column
- Subtract the hundreds column
3 < 6, so borrow 1 from tens: 3 becomes 13, tens decreases from 2 to 1
13 - 6 = 7
After borrowing, 1 < 8, so borrow 1 from hundreds: 1 becomes 11, hundreds decreases from 5 to 4
11 - 8 = 3
After borrowing, 4 - 1 = 3
337
• Borrowing: When top digit < bottom digit, borrow from next higher place value
• Column subtraction: Subtract digits in same place value column
• Borrowing effect: The borrowed digit increases the current place value by 10
• Practice Tip: Check by adding: 337 + 186 = 523 ✓
- 412 - 278 = 134 - Practice with tens regrouping
- 634 - 297 = 337 - Another tens regrouping example
- 521 - 183 = 338 - More tens regrouping practice
- Circle or highlight borrowed digits to keep track
- Count borrowed digits carefully in the next column
- Double-check that you decreased the borrowed-from digit by 1
Q: What if I forget to decrease the borrowed-from digit?
A: You'll get an incorrect answer. For example, in 523-186, forgetting to decrease hundreds from 5 to 4 gives 437 instead of 337.
Q: Can I regroup in multiple columns?
A: Yes! Some problems require regrouping in ones, tens, and hundreds columns simultaneously.
Hundreds place regrouping: When the hundreds digit in the minuend is smaller than the hundreds digit in the subtrahend after previous borrows.
Note: This occurs when we need to borrow from the thousands place (if available) or when the hundreds column requires special attention after lower place value borrows.
- Start from the ones column
- Check if borrowing is needed in each column
- Move to tens column and check if borrowing is needed
- Move to hundreds column and check if borrowing is needed
- Continue to higher place values if necessary
4 < 7, so borrow 1 from tens: 4 becomes 14, tens decreases from 2 to 1
14 - 7 = 7
After borrowing, 1 < 8, so borrow 1 from hundreds: 1 becomes 11, hundreds decreases from 6 to 5
11 - 8 = 3
After borrowing, 5 - 3 = 2
237
• Place value progression: Move from right to left through columns
• Borrowing rule: When top digit < bottom digit, borrow from next column
• Accumulation: Previous borrows affect subsequent columns
• Practice Tip: Check by adding: 237 + 387 = 624 ✓
- 513 - 278 = 235 - Practice with hundreds regrouping
- 724 - 489 = 235 - Another hundreds place example
- 632 - 395 = 237 - More practice with multiple regroups
- Keep track of multiple borrows in the same problem
- Verify your answer by adding the result to the subtrahend
- Work slowly and carefully when multiple columns require regrouping
Q: What if I need to borrow from zero?
A: You must borrow from the next non-zero digit. For example, in 300-123, you'd need to borrow from the hundreds place: 300 becomes 2(10)0, then 29(10).
Q: How do I handle borrowing when hundreds digit is 1?
A: The same way - borrow 1 from hundreds, making it 0, and add 10 to the tens column.
Double regrouping: When regrouping is needed in more than one column during subtraction (e.g., both ones and tens columns).
Note: This occurs when the top digits in multiple place value columns are smaller than the bottom digits, requiring borrowing in each of those columns.
- Start from the ones column, regroup if needed
- Move to the tens column (including any effects from previous borrows), regroup if needed
- Move to the hundreds column, including any effects from previous borrows
2 < 8, so borrow 1 from tens: 2 becomes 12, tens decreases from 3 to 2
12 - 8 = 4
After borrowing, 2 < 7, so borrow 1 from hundreds: 2 becomes 12, hundreds decreases from 5 to 4
12 - 7 = 5
After borrowing, 4 - 2 = 2
254
• Sequential regrouping: Handle one column at a time from right to left
• Borrow inclusion: Previous borrows affect subsequent columns
• Multi-step tracking: Keep track of multiple borrows in the same problem
• Practice Tip: Count borrowed digits carefully to avoid errors
- 421 - 187 = 234 - Practice with double regrouping
- 643 - 298 = 345 - Another double regrouping example
- 531 - 286 = 245 - More double regrouping practice
- Circle each borrowed digit to keep track of them
- Work slowly and carefully when multiple columns require regrouping
- Double-check that you decreased borrowed-from digits by 1
Q: What if I forget a borrowed digit in a double regrouping problem?
A: You'll get an incorrect answer. For example, in 532-278, forgetting to decrease the hundreds digit from 5 to 4 gives 354 instead of 254.
Q: Can I have regrouping in all three columns?
A: Yes! Problems like 300-156 require regrouping in ones, tens, and hundreds columns.
Word problem: A mathematical problem presented in a narrative context that requires identifying the operation and numbers to solve.
Note: Word problems require translating language into mathematical expressions and applying appropriate computational strategies.
- Read the problem carefully and identify key information
- Determine the operation needed (subtraction in this case)
- Set up the mathematical expression with identified numbers
- Solve using appropriate computational strategy (regrouping if needed)
- Check if the answer makes sense in the context of the problem
"Gave" means we need to subtract the numbers
642 - 278 (align by place value)
2 < 8, so borrow 1 from tens: 2 becomes 12, tens decreases from 4 to 3
12 - 8 = 4
After borrowing, 3 < 7, so borrow 1 from hundreds: 3 becomes 13, hundreds decreases from 6 to 5
13 - 7 = 6
After borrowing, 5 - 2 = 3
Sarah has 364 stickers left
364 stickers left
• Contextual understanding: Identify keywords indicating the operation
• Translation: Convert words into mathematical expressions
• Verification: Ensure the answer makes sense in the problem context
• Practice Tip: Check by adding: 364 + 278 = 642 ✓
- Pencils: 563 - 289 = 274 - Practice with different context
- Books: 752 - 386 = 366 - Another word problem example
- Toys: 641 - 297 = 344 - More practice with regrouping
- Look for keywords like "left," "remaining," "difference," or "how many more" for subtraction
- Draw pictures or use manipulatives to visualize the problem
- Always write the answer in the context of the original problem
Q: How do I know if a word problem needs addition or subtraction?
A: Look for keywords: "altogether," "total," "sum," "combined," "in all" suggest addition; "left," "difference," "less," "remains," "gave away" suggest subtraction.
Q: Should I always include the units in my answer?
A: Yes! Always answer word problems with the appropriate units (stickers, dollars, etc.) as specified in the problem.