Three-digit subtraction word problem: A math problem that requires subtracting three-digit numbers, often involving regrouping across zeros.
- Read the problem carefully
- Identify the starting amount (minuend)
- Identify the amount being taken away (subtrahend)
- Set up the subtraction with place values aligned
- Subtract starting from the ones place (regroup across zeros if needed)
- Check your answer
Library had 805 books (minuend), 267 books were borrowed (subtrahend)
805 - 267 = ?
| Hundreds | Tens | Ones |
|---|---|---|
| 8 | 0 | 5 |
| - 2 | - 6 | - 7 |
We cannot subtract 7 from 5, so we need to borrow from tens place
But the tens place is 0, so we must first borrow from hundreds place
8 hundreds becomes 7 hundreds, 0 tens becomes 10 tens
Now we can borrow from tens: 10 tens becomes 9 tens, 5 ones becomes 15 ones
15 - 7 = 8 ones
9 tens - 6 tens = 3 tens
7 hundreds - 2 hundreds = 5 hundreds
There are 538 books left in the library.
• Regrouping across zeros: When the tens place is 0, borrow from hundreds first, then from tens
• Place Value: Align digits by their place values when subtracting
• Checking: Difference + Subtrahend = Minuend (538 + 267 = 805 ✓)
Multi-step subtraction word problem: A problem requiring multiple subtraction operations to reach the final answer.
Last month: 284 cars, This month: 196 cars
Total sold: 284 + 196 = 480 cars
700 - 480 = ?
| Hundreds | Tens | Ones |
|---|---|---|
| 7 | 0 | 0 |
| - 4 | - 8 | - 0 |
0 - 0 = 0 ones
We cannot subtract 8 from 0, so we borrow from hundreds place
7 hundreds becomes 6 hundreds, 0 tens becomes 10 tens
10 - 8 = 2 tens
6 hundreds - 4 hundreds = 2 hundreds
There are 220 cars left unsold.
• Multi-step problems: Break complex problems into smaller steps
• Regrouping across zeros: When subtracting and encountering zeros, borrow from higher place values
• Verification: Add all parts to verify the total: 220 + 284 + 196 = 700 ✓
Complex multi-step subtraction: A problem involving multiple subtractions over several days or periods.
Friday: 342, Saturday: 289, Sunday: 156
Total sold: 342 + 289 + 156 = 787 tickets
900 - 787 = ?
| Hundreds | Tens | Ones |
|---|---|---|
| 9 | 0 | 0 |
| - 7 | - 8 | - 7 |
We cannot subtract 7 from 0, so we borrow from tens place
But tens place is 0, so first borrow from hundreds: 9 hundreds becomes 8 hundreds, 0 tens becomes 10 tens
Now borrow from tens: 10 tens becomes 9 tens, 0 ones becomes 10 ones
10 - 7 = 3 ones
9 tens - 8 tens = 1 ten
8 hundreds - 7 hundreds = 1 hundred
There are 113 seats still available.
• Multiple operations: First add all the amounts being subtracted, then subtract from the total
• Regrouping across zeros: When the tens place is 0, borrow from hundreds first
• Verification: Add the result to the total subtracted to check: 113 + 787 = 900 ✓
Subtraction: Taking away one number from another to find the difference.
Minuend: The number being subtracted from (larger number).
Subtrahend: The number being subtracted (smaller number).
Difference: The result of the subtraction operation.
Word Problem: A math question written in sentences that tells a story.
Regrouping/Borrowing: Taking from a higher place value when the top digit is smaller than the bottom digit.
Regrouping Across Zeros: Special technique when borrowing from a place value that contains zero.
Multi-step Problem: A problem requiring multiple operations to reach the solution.
Place Value: The value of a digit based on its position (ones, tens, hundreds, thousands).
Subtraction Rule: Minuend - Subtrahend = Difference
Order Matters: We always subtract the smaller number from the larger number.
Checking Rule: Difference + Subtrahend = Minuend (always verify your answer).
Borrowing Rule: When the top digit is smaller than the bottom digit, borrow 1 from the next place value.
Regrouping Across Zeros Rule: When the next place value is zero, continue borrowing from the next non-zero place value.
Zero Rule: Any number minus zero equals itself (e.g., 500 - 0 = 500).
Same Number Rule: Any number minus itself equals zero (e.g., 375 - 375 = 0).
Commutative Property: Subtraction is NOT commutative (a - b ≠ b - a).
- Read Carefully: Read the whole problem slowly and understand what's happening
- Identify Information: Find the starting amount and what is being taken away
- Determine Operation: Look for clue words that indicate subtraction is needed
- Organize Data: For multi-step problems, identify all amounts being subtracted
- Align Place Values: Write numbers vertically with proper alignment
- Subtract Ones First: Start with the ones place and work left
- Regroup if Needed: If top digit is smaller, borrow from next place value
- Handle Zeros: When encountering zeros, borrow from the next non-zero place value
- Check: Add your answer to the subtrahend to verify you get the minuend
- Answer Question: Make sure your answer matches what the problem asked
Simple Regrouping: 452 - 137 = 315 (regroup once from tens to ones)
Across Zeros: 800 - 245 = 555 (regroup from hundreds to tens, then tens to ones)
Three-Digit Across Zeros: 705 - 268 = 437 (regroup across tens zero)
Multi-step: Store had 1000 items, sold 234 on Mon, 156 on Tue, 98 on Wed → 1000-(234+156+98)=512
Word Clues: "left," "remain," "how many more," "difference," "take away," "give," "sell," "away," "lose," "used," "cost," "available," "unsold"
Count Backwards: Start with the bigger number and count backwards by the smaller number.
Use Base Ten Blocks: Physical or drawn blocks to represent hundreds, tens, and ones.
Draw Place Value Charts: Boxes for hundreds, tens, and ones to organize the numbers.
Zero Regrouping: When you see a zero in the tens place, remember to go to the hundreds place first.
Check with Addition: Always add your answer to the number you took away to verify.
Look for Keywords: Words like "left," "remaining," "less," "fewer" mean subtraction.
Borrowing Reminder: When borrowing across zeros, each place value decreases by 1.
Multi-step Strategy: Add all the amounts being subtracted first, then subtract from the total.
Wrong Order: Subtracting the big number from the small number (e.g., 267 - 805 instead of 805 - 267).
Missing Keywords: Not recognizing words that indicate subtraction is needed.
Forgetting to Borrow: Not borrowing when the top digit is smaller than the bottom digit.
Incorrect Zero Regrouping: When borrowing across zeros, not properly adjusting all place values.
Multi-step Mistakes: Adding incorrect numbers together before subtracting.
Not Checking: Forgetting to verify the answer makes sense in the context.
Ignoring Context: Getting the math right but not answering the question asked.
Place Value Errors: Misaligning digits when setting up the problem.
Formula to Remember: Total - Taken Away = What's Left
Always Bigger - Smaller: Subtract the smaller number from the bigger number.
Check Your Work: Difference + Subtrahend = Minuend
Keywords List: left, remain, fewer, less, take away, give, sell, cost, spend, lose, away, used, available, unsold, remaining
Zero Regrouping Rule: When you see a zero in the tens place, borrow from hundreds first.
Multi-step Strategy: Add all subtractions together first, then subtract from the total.
Fact Families: Know that 805 - 267 = 538 means 538 + 267 = 805
Level 1: Subtract with pictures and objects (concrete)
Level 2: Subtract using number lines (visual)
Level 3: Single-digit mental subtraction (abstract)
Level 4: Two-digit subtraction without borrowing
Level 5: Two-digit subtraction with borrowing
Level 6: Three-digit subtraction without borrowing
Level 7: Three-digit subtraction with borrowing
Level 8: Three-digit subtraction with regrouping across zeros
Level 9: Multi-step word problems
Level 10: Four-digit subtraction with regrouping
Common Core: CCSS.MATH.CONTENT.3.NBT.A.2 - Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
Operations: Fluently add and subtract within 1000 using strategies based on place value.
Place Value: Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones.
Problem Types: One- and two-step word problems involving addition and subtraction.
Strategies: Mental math, place value decomposition, properties of operations.
Relating Operations: Understanding that subtraction is the inverse of addition.
Estimation: Using rounding to estimate solutions and assess reasonableness.
Minuend: The number being subtracted from (larger number)
Subtrahend: The number being subtracted (smaller number)
Difference: The result of the subtraction operation
Word problem: A mathematical problem expressed in ordinary language
Borrowing/Regrouping: Taking 1 from a higher place value when the top digit is smaller
Regrouping Across Zeros: Special technique when borrowing from a place value that contains zero
- Read the problem: Understand the context and what is being asked
- Identify numbers: Find the starting amount and amount being taken away
- Choose operation: Determine if subtraction is needed
- Align place values: Write numbers vertically with proper alignment
- Regroup across zeros if needed: Handle zeros appropriately
- Solve: Perform the subtraction calculation
- Check: Verify the answer makes sense in the context
• Subtraction finds the difference between two numbers
• The minuend is always greater than or equal to the subtrahend
• Word problems require careful reading to identify operations
• Checking: Difference + Subtrahend = Minuend
• Key words indicating subtraction: left, fewer, less, take away, remain, away, lost, gave, used, sold, cost, available, remaining
• When regrouping across zeros: 1 hundred = 10 tens, 1 ten = 10 ones
• Multi-step problems: Add all subtractions together first, then subtract from the total
Questions & Answers
Question: How do I subtract when there are zeros in the number, like 800 - 245?
Answer: When you have zeros in the number you're subtracting from, you need to regroup across the zeros. For 800 - 245:
- Start with the ones place: 0 - 5, but you can't subtract 5 from 0
- You need to borrow from the tens place, but it's also 0
- So you go to the hundreds place: 8 hundreds becomes 7 hundreds
- The 0 tens becomes 10 tens
- Now you can borrow from tens: 10 tens becomes 9 tens, 0 ones becomes 10 ones
- Now subtract: 10 - 5 = 5, 9 - 4 = 5, 7 - 2 = 5
- So 800 - 245 = 555
Question: My grade 3 child struggles with multi-step subtraction word problems. Any strategies?
Answer: Multi-step problems can be challenging! Try these strategies:
- Break it down: Identify each part of the problem separately
- Use a table: Organize information in columns (Day/Sale/Amount)
- Combine first: Add all the amounts being subtracted before doing the final subtraction
- Draw models: Use bar models to visualize the relationships
- Practice step-by-step: Do one operation at a time before combining
- Check reasonableness: Does the answer make sense in the context?
For example: If a store starts with 1000 items and sells 234, 156, and 98, add 234+156+98=488, then subtract 1000-488=512.
Question: I sometimes forget to regroup when I need to. How can I remember?
Answer: Here's a helpful memory technique:
- Compare digits: Before subtracting, compare each pair of digits in the same place value
- Red light rule: If the top number is smaller than the bottom number, you need to regroup
- Think of money: If you have $2 but need to pay $5, you need to "break" a larger bill
- Circle the problem: Circle any place where the top digit is smaller than the bottom
- Check your work: After subtracting, add your answer to the number you took away to see if you get the original number
For example: In 805 - 267, check: 5<7 (need to regroup), 0<6 (need to regroup), 8>2 (no regrouping needed).