Solved Exercises on Subtraction Word Problems with 3-Digit Numbers in 1st Grade

Master 3-digit subtraction word problems: advanced concepts and problem solving through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 3-Digit Take-Away Problem
Exercise 1
Solve the 3-digit problem:
"The school library had 345 books. They donated 123 books to another school. How many books does the library have now?"
Definition:

3-Digit Take-Away Problem: A subtraction problem where the minuend and subtrahend are both 3-digit numbers. The result is also a 3-digit number.

3-Digit subtraction method:
  1. Align numbers by place value (hundreds, tens, ones)
  2. Subtract ones place: 5 - 3 = 2
  3. Subtract tens place: 4 - 2 = 2
  4. Subtract hundreds place: 3 - 1 = 2
"The school library had 345 books. They donated 123 books to another school. How many books does the library have now?"
1
Starting amount: 345 books
2
Books donated: 123 books
3
Equation: 345 - 123 = ?
4
Subtract by place value: 345 - 123 = 222
345 books
300
40
5
Donated 123
100
20
3
Remain 222
200
20
2
Step 1: Identify the starting amount

The library started with 345 books

Step 2: Identify the amount taken away

They donated 123 books to another school

Step 3: Subtract by place value

Hundreds: 3 - 1 = 2, Tens: 4 - 2 = 2, Ones: 5 - 3 = 2

\(345 - 123 = 222\)
Final answer:

The library has 222 books now.

Applied rules:

• Place value: Align numbers by hundreds, tens, and ones

• Subtract by place: Subtract hundreds from hundreds, tens from tens, ones from ones

• Take-away structure: Start amount - taken amount = remaining

2 3-Digit Comparison Problem
Exercise 2
Solve the comparison problem:
"Tom has 467 marbles. Sarah has 234 marbles. How many more marbles does Tom have than Sarah?"
Definition:

3-Digit Comparison Problem: A subtraction problem that finds the difference between two 3-digit amounts. It asks how much more or less one quantity is than another.

"Tom has 467 marbles. Sarah has 234 marbles. How many more marbles does Tom have than Sarah?"
1
Larger amount: Tom has 467 marbles
2
Smaller amount: Sarah has 234 marbles
3
Equation: 467 - 234 = ?
4
Subtract by place value: 467 - 234 = 233
Tom: 467
400
60
7
Sarah: 234
200
30
4
Difference: 233
200
30
3
Step 1: Identify the two quantities

Tom has 467 marbles, Sarah has 234 marbles

Step 2: Determine which is larger

Tom has more marbles than Sarah

Step 3: Subtract by place value

Hundreds: 4 - 2 = 2, Tens: 6 - 3 = 3, Ones: 7 - 4 = 3

\(467 - 234 = 233\)
Final answer:

Tom has 233 more marbles than Sarah.

Applied rules:

• Comparison structure: Larger amount - smaller amount = difference

• Keywords: "more than", "less than", "difference" indicate comparison

• Place value: Align numbers by hundreds, tens, and ones

3 3-Digit Missing Addend Problem
Exercise 3
Solve the missing addend problem:
"A farmer harvested some vegetables. He sold 156 at the market and now has 289 left. How many vegetables did he harvest?"
Definition:

3-Digit Missing Addend Problem: A subtraction problem where you know the result after subtraction and one of the numbers, but need to find the original 3-digit amount.

"A farmer harvested some vegetables. He sold 156 at the market and now has 289 left. How many vegetables did he harvest?"
1
Amount taken away: Farmer sold 156 vegetables
2
Amount remaining: 289 vegetables left
3
Original amount: ? - 156 = 289
4
Solution: 289 + 156 = 445
Harvested ?
400
40
5
Sold 156
100
50
6
Left: 289
200
80
9
Step 1: Identify what happened

The farmer sold 156 vegetables and has 289 left

Step 2: Set up the relationship

Original amount - 156 = 289

Step 3: Find the original amount

To find the original, add: 289 + 156 = 445

\(445 - 156 = 289\)
Final answer:

The farmer harvested 445 vegetables.

Applied rules:

• Missing addend structure: Original - taken = remaining

• Reverse operation: To find original, add remaining + taken

• Keywords: "at first", "some", "originally" indicate missing addend

Features of 3-Digit Subtraction Problems
\( \text{Hundreds} \mid \text{Tens} \mid \text{Ones} \)
Place Value Structure
Place Value Understanding

Working with hundreds, tens, and ones places.

  • Identify hundreds, tens, and ones in each number
  • Subtract digits in the same place value positions
  • Understand the value of each digit in its position
  • Example: In 345, 3 is 300, 4 is 40, 5 is 5
Alignment Strategy

Properly aligning numbers by place value.

  • Line up hundreds under hundreds
  • Line up tens under tens
  • Line up ones under ones
  • Example: 345 - 123 aligns as 3-1, 4-2, 5-3
Regrouping Concept

Understanding when borrowing is needed.

  • When a digit in the minuend is smaller than the corresponding digit in the subtrahend
  • Borrow from the next higher place value
  • Example: In 305 - 127, need to borrow for ones place
  • Not needed in these examples since minuend digits are larger
Mental Math Strategies

Techniques for solving 3-digit subtraction mentally.

  • Subtract hundreds first, then tens, then ones
  • Round numbers to make subtraction easier
  • Use known facts to solve larger problems
  • Example: 400 - 200 = 200, so 405 - 203 = 202
3-Digit Subtraction Characteristics:
  • Numbers range from 100 to 999
  • Three place values to consider
  • Requires careful alignment
  • May involve regrouping/borrowing
3-Digit Subtraction Tips:

• Always align: Hundreds, tens, and ones in their correct columns

• Check your work: Add the result back to the subtrahend to verify

• Understand place value: Each digit represents hundreds, tens, or ones

• Use estimation: Round to check if your answer is reasonable

3-Digit Subtraction Problem Solving Strategies
\( \text{Place Value} \rightarrow \text{Subtract by Place} \rightarrow \text{Combine Results} \)
Step-by-Step Approach
3-Digit Subtraction Process
Step 1: Identify the numbers - Recognize the minuend and subtrahend
Step 2: Align by place value - Match hundreds, tens, and ones
Step 3: Subtract each place value - Start with ones, then tens, then hundreds
Step 4: Combine results - Put the hundreds, tens, and ones together
Step 5: Verify your answer - Add the result back to the subtrahend
Key Strategies for 3-Digit Numbers:
  • Place value breakdown: Separate into hundreds, tens, and ones
  • Column alignment: Ensure proper vertical alignment
  • Sequential subtraction: Ones, tens, then hundreds
  • Verification: Check by adding the result back
Tip 1: Always write numbers vertically with proper alignment.
Tip 2: Check each place value separately before combining.
Tip 3: Estimate first to ensure your answer is reasonable.
Tip 4: Always verify by adding the result to the subtrahend.
Common challenges: Misaligning numbers, forgetting place value, making computational errors.
Success strategies: Proper alignment, careful computation, verification checks.
3-digit subtraction concepts:

• Place value: Each digit has a specific value based on its position

• Alignment: Critical for accurate computation

• Sequential processing: Work from right to left (ones to hundreds)

• Verification: Always check your work

Detailed Summary: 3-Digit Subtraction Word Problems
Complete Learning Guide
Definition of 3-Digit Subtraction Word Problems: Mathematical problems that involve subtracting 3-digit numbers (from 100 to 999) in real-world contexts. These problems require understanding of place value and proper alignment of hundreds, tens, and ones.
Key Terms:
  • 3-Digit Number: A number between 100 and 999
  • Minuend: The number being subtracted from
  • Subtrahend: The number being subtracted
  • Difference: The result of subtraction
  • Place Value: The value of a digit based on its position (hundreds, tens, ones)
  • Regrouping: Borrowing from a higher place value when needed
Core Rules of 3-Digit Subtraction:
  • Place Value Alignment: Always align numbers by hundreds, tens, and ones
  • Subtract by Place: Subtract digits in the same place value positions
  • Sequential Processing: Work from right to left (ones, tens, hundreds)
  • Verification: Add the result to the subtrahend to check
3-Digit Subtraction Process:
  1. Align numbers: Match hundreds, tens, and ones columns
  2. Subtract ones: Subtract the rightmost digits
  3. Subtract tens: Subtract the middle digits
  4. Subtract hundreds: Subtract the leftmost digits
  5. Combine results: Put the results together
Examples (Advanced):
  • Take-Away: "345 - 123 = 222" (subtract by place: 3-1=2, 4-2=2, 5-3=2)
  • Comparison: "467 - 234 = 233" (Tom has 233 more than Sarah)
  • Missing Addend: "289 + 156 = 445" (to find original: add remaining + taken)
Tips and Tricks:
  • Always align numbers by place value before subtracting
  • Work from right to left: ones, tens, hundreds
  • Check your work by adding the result to the subtrahend
  • Estimate first to ensure your answer is reasonable
  • Remember that each digit has a specific place value
Common Pitfalls:
  • Misaligning numbers by place value
  • Subtracting in the wrong order
  • Forgetting to account for place value
  • Not checking if the answer is reasonable
Memory Aids:
  • "Align by place value: hundreds, tens, ones"
  • "Work from right to left: ones, tens, hundreds"
  • "Check by adding: result + subtrahend = minuend"
  • "Each digit has a place value: hundreds, tens, ones"
Checking Your Work: Always verify your answer by adding the difference back to the subtrahend to see if you get the minuend.

Questions & Answers

Question: These numbers are so big! How do I subtract 345 - 123? It seems too hard.

Answer: These numbers might look big, but they're actually made up of smaller parts! Here's how to make it easier:

  • Break it down: Think of 345 as 300 + 40 + 5 and 123 as 100 + 20 + 3
  • Subtract each part: 300 - 100 = 200, 40 - 20 = 20, 5 - 3 = 2
  • Put it together: 200 + 20 + 2 = 222
  • Line them up: Write the numbers vertically so hundreds, tens, and ones align

Example:
345
- 123
-----
222

You're just doing 3 - 1 = 2, 4 - 2 = 2, 5 - 3 = 2!

Question: Why do I need to line up the numbers? Can't I just subtract them any way?

Answer: Great question! Lining up numbers is super important because of place value:

  • Place value: The position of each digit tells its value (hundreds, tens, ones)
  • Same place: You can only subtract hundreds from hundreds, tens from tens, and ones from ones
  • Example: In 345 - 123, you subtract 3 (hundreds) from 1 (hundreds), not from 3 (ones)
  • Accuracy: Proper alignment prevents mistakes

If you don't line up properly, you might subtract 3 (ones) from 1 (hundreds), which would give you the wrong answer!

Always align: hundreds under hundreds, tens under tens, ones under ones!

Question: What if the bottom number is bigger in one place? Like 305 - 127, how do I do 5 - 7?

Answer: Excellent question! When the bottom number is bigger in a place, you need to "borrow" from the next higher place. This is called regrouping:

  • Borrowing: Take 1 from the next higher place value
  • For 305 - 127: You can't do 5 - 7 in the ones place
  • Borrow 1 ten: Since there are 0 tens, you go to the hundreds
  • Exchange: Take 1 hundred and make it 10 tens, then take 1 ten and make it 10 ones

So 305 becomes 2 hundreds, 9 tens, and 15 ones (295 + 10 ones = 295 + 15 = 305)

Now you can do 15 - 7 = 8 in the ones place!

This is called regrouping or borrowing, and it helps when the top number is smaller than the bottom number in a place value.