Multi-Digit Subtraction Word Problems Worksheets

Master multi-digit subtraction word problems through 5 detailed exercises with step-by-step solutions, rules, and visual examples.

Solution: Exercises 1 to 3
1 Library Books
Exercise 1
The school library had 847 books. Students borrowed 235 books. How many books are left in the library?

Problem Context:

This is a subtraction problem because we need to find how many books REMAIN after some were borrowed.

Key Information:

  • Starting number of books: 847
  • Books borrowed: 235
  • Question: How many books are LEFT?

Operation:

We need to SUBTRACT the borrowed books from the total books: 847 - 235

Set Up Problem:
847
-235
Ones Place Check:
7 > 5 (No need to borrow)
Tens Place Check:
4 > 3 (No need to borrow)
Hundreds Place Check:
8 > 2 (No need to borrow)
Direct Subtraction:
Ones: 7 - 5 = 2
Tens: 4 - 3 = 1
Hundreds: 8 - 2 = 6
Calculate:
Answer: 612 books
Step 1: Identify what we know

The library started with 847 books and 235 were borrowed.

Step 2: Determine what we need to find

We need to find how many books are LEFT in the library.

Step 3: Choose the operation

Since books were taken away, we use subtraction: 847 - 235

Step 4: Solve the subtraction

847 - 235 = 612

Step 5: Answer the question

There are 612 books left in the library.

847 - 235 = 612 books left
Final answer:

There are 612 books left in the library.

Applied rules:

• Keywords: "left", "remain", "how many are left" indicate subtraction

• Context Clue: Something being taken away suggests subtraction

• Place Value: Align numbers correctly when solving

2 Fish Tank
Exercise 2
A fish tank had 520 fish. The owner gave away 186 fish to friends. How many fish are remaining in the tank?

Problem Context:

This is a subtraction problem because fish were given away, so we need to find how many are left.

Key Information:

  • Initial number of fish: 520
  • Fish given away: 186
  • Question: How many fish are REMAINING?

Operation:

We need to SUBTRACT the given fish from the total fish: 520 - 186

Set Up Problem:
520
-186
Ones Place Check:
0 < 6 (Need to borrow)
Tens Place Check:
1 < 8 (Need to borrow, but zero can't give!)
Hundreds Place Check:
5 > 1 (Can borrow from here)
Regrouping Process:
5→4 hundreds, 2→12 tens, 0→10 ones
Final Subtraction:
Ones: 10 - 6 = 4
Tens: 11 - 8 = 3
Hundreds: 4 - 1 = 3
Calculate:
Answer: 334 fish
Step 1: Identify what we know

The fish tank started with 520 fish and 186 were given away.

Step 2: Determine what we need to find

We need to find how many fish are REMAINING in the tank.

Step 3: Choose the operation

Since fish were given away, we use subtraction: 520 - 186

Step 4: Solve the subtraction (with regrouping)

520 - 186 = 334

Step 5: Answer the question

There are 334 fish remaining in the tank.

520 - 186 = 334 fish remaining
Final answer:

There are 334 fish remaining in the tank.

Applied rules:

• Keywords: "remaining", "given away", "how many are left" indicate subtraction

• Regrouping: When top number < bottom number, borrow from higher place value

• Zero Handling: When borrowing from zero, go to next non-zero place value

3 Apple Orchard
Exercise 3
An apple orchard grew 7,425 apples this year. The farmers sold 2,198 apples at the market. How many apples do they have left to sell?

Problem Context:

This is a subtraction problem because apples were sold, so we need to find how many are left to sell.

Key Information:

  • Total apples grown: 7,425
  • Apples sold: 2,198
  • Question: How many apples are LEFT to sell?

Operation:

We need to SUBTRACT the sold apples from the total apples: 7,425 - 2,198

Set Up Problem:
7,425
-2,198
Ones Place Check:
5 < 8 (Need to borrow)
Tens Place Check:
1 < 9 (Need to borrow after regrouping)
Hundreds Place Check:
3 > 1 (Can borrow from here after regrouping)
Regrouping Process:
7→6 thousands, 4→3 hundreds, 2→12 tens, 5→15 ones
Final Subtraction:
Ones: 15 - 8 = 7
Tens: 11 - 9 = 2
Hundreds: 3 - 1 = 2
Thousands: 6 - 2 = 4
Calculate:
Answer: 5,227 apples
Step 1: Identify what we know

The orchard grew 7,425 apples and sold 2,198 apples.

Step 2: Determine what we need to find

We need to find how many apples are LEFT to sell.

Step 3: Choose the operation

Since apples were sold, we use subtraction: 7,425 - 2,198

Step 4: Solve the subtraction (with regrouping)

7,425 - 2,198 = 5,227

Step 5: Answer the question

The farmers have 5,227 apples left to sell.

7,425 - 2,198 = 5,227 apples left
Final answer:

The farmers have 5,227 apples left to sell.

Applied rules:

• Keywords: "left to sell", "how many remain", "sold" indicate subtraction

• Four-Digit Subtraction: Same principles apply to larger numbers

• Regrouping Chain: May need to regroup across multiple place values

Rules and Methods for Word Problems
Starting Amount - Amount Taken Away = Remaining Amount
Subtraction Word Problem Formula
Rule 1
Read Carefully
Identify key information and numbers
Rule 2
Find Keywords
Look for words that indicate subtraction
Rule 3
Set Up Problem
Write the subtraction equation
Key Terms:

Word Problem: A math problem presented in the form of a story or real-world situation

Key Information: The important numbers and facts needed to solve the problem

Keywords: Words that suggest which operation to use (subtract, add, multiply, divide)

Context: The real-world situation described in the problem

Subtraction Keywords: Words like "left," "remaining," "how many are left," "less than," "gave away," "sold," "borrowed," "used," etc.

Complete Word Problem Method:
  1. Read the problem carefully: Understand what is happening in the story
  2. Identify key information: Find the numbers and important facts
  3. Look for keywords: Find words that suggest subtraction
  4. Determine what to find: What is the question asking?
  5. Set up the equation: Write the subtraction problem
  6. Solve the subtraction: Use proper subtraction methods
  7. Answer the question: Write a complete sentence with the answer
Tip 1: Circle or underline important numbers in the problem.
Tip 2: Look for keywords like "left," "remaining," "how many are left," "less than."
Tip 3: Draw pictures or models to represent the problem.
Tip 4: Always answer with a complete sentence that addresses the question.
Common errors: Misreading the question, using the wrong operation, forgetting to regroup when needed, not answering the specific question asked.
Success strategies: Read twice, identify keywords, set up equation, solve carefully, check answer makes sense in context.
Essential Rules:

• Read Thoroughly: Understand the context before solving

• Keyword Recognition: Identify words that suggest subtraction

• Information Extraction: Pull out relevant numbers and facts

• Equation Setup: Write the correct subtraction problem

• Proper Execution: Use correct subtraction methods including regrouping

• Complete Answer: Answer the specific question in context

Solution: Exercises 4 to 5
4 Car Mileage
Exercise 4
Mr. Johnson's car had 24,560 miles on it. He drove 12,847 miles during his vacation. What is the new mileage on his car?

Problem Context:

This is an addition problem because miles are being ADDED to the car's total mileage.

Key Information:

  • Starting mileage: 24,560 miles
  • Miles driven: 12,847 miles
  • Question: What is the NEW mileage?

Operation:

We need to ADD the driven miles to the starting mileage: 24,560 + 12,847

Wait! This is Addition:
24,560
+12,847
Ones Place:
0 + 7 = 7
Tens Place:
6 + 4 = 10 (carry 1)
Hundreds Place:
5 + 8 + 1 = 14 (carry 1)
Thousands Place:
4 + 2 + 1 = 7
Ten-Thousands Place:
2 + 1 = 3
Calculate:
Answer: 37,407 miles
Step 1: Identify what we know

The car had 24,560 miles and Mr. Johnson drove 12,847 more miles.

Step 2: Determine what we need to find

We need to find the NEW total mileage on the car.

Step 3: Choose the operation

Since miles are being ADDED to the total, we use addition: 24,560 + 12,847

Step 4: Solve the addition

24,560 + 12,847 = 37,407

Step 5: Answer the question

The new mileage on his car is 37,407 miles.

24,560 + 12,847 = 37,407 miles
Final answer:

The new mileage on his car is 37,407 miles.

Applied rules:

• Context Matters: "Drove" means adding miles, not subtracting

• Keyword Analysis: "What is the new..." often indicates addition

• Problem Understanding: Always consider the real-world context

5 Savings Account
Exercise 5
Sarah had $3,250 in her savings account. She withdrew $876 for a family vacation. How much money does she have left in her account?

Problem Context:

This is a subtraction problem because money was withdrawn, so we need to find how much remains.

Key Information:

  • Starting amount: $3,250
  • Amount withdrawn: $876
  • Question: How much money is LEFT in the account?

Operation:

We need to SUBTRACT the withdrawn amount from the starting amount: $3,250 - $876

Set Up Problem:
$3,250
-$876
Ones Place Check:
0 < 6 (Need to borrow)
Tens Place Check:
4 < 7 (Need to borrow after regrouping)
Hundreds Place Check:
1 < 8 (Need to borrow after regrouping)
Thousands Place Check:
3 > 0 (Can borrow from here)
Regrouping Process:
3→2 thousands, 2→12 hundreds, 5→14 tens, 0→10 ones
Final Subtraction:
Ones: 10 - 6 = 4
Tens: 14 - 7 = 7
Hundreds: 11 - 8 = 3
Thousands: 2 - 0 = 2
Calculate:
Answer: $2,374
Step 1: Identify what we know

Sarah had $3,250 in her account and withdrew $876.

Step 2: Determine what we need to find

We need to find how much money is LEFT in her account.

Step 3: Choose the operation

Since money was withdrawn, we use subtraction: $3,250 - $876

Step 4: Solve the subtraction (with regrouping)

$3,250 - $876 = $2,374

Step 5: Answer the question

Sarah has $2,374 left in her account.

$3,250 - $876 = $2,374
Final answer:

Sarah has $2,374 left in her account.

Applied rules:

• Keywords: "withdrawn", "left", "remaining" indicate subtraction

• Money Problems: Same subtraction principles apply

• Regrouping Chain: May need to regroup across multiple place values

Comprehensive Guide: Laws, Methods, Rules, Definitions
Original Amount - Change Amount = Final Amount
Word Problem Subtraction Formula
Key definitions:

Word Problem: A mathematical problem presented in a narrative format describing a real-world situation.

Context: The real-world scenario that gives meaning to the numbers and operations in the problem.

Keywords: Words that indicate which mathematical operation to perform (addition, subtraction, multiplication, division).

Subtraction Keywords: Words like "left," "remaining," "how many are left," "less than," "gave away," "sold," "borrowed," "used," "withdrawn," "taken away," etc.

Key Information: The important numbers and facts needed to solve the problem.

Complete methodology:
  1. Read carefully: Understand the story and what is happening
  2. Identify key information: Circle or note important numbers and facts
  3. Look for keywords: Find words that suggest the operation needed
  4. Determine the question: Understand what the problem is asking for
  5. Set up the equation: Write the mathematical expression
  6. Solve the math: Perform the calculation correctly
  7. Check context: Make sure the answer makes sense in the story
  8. Answer completely: Provide the answer in a complete sentence
Tip 1: Always read the problem twice to catch all details.
Tip 2: Draw pictures or models to visualize the problem.
Tip 3: Be careful with keywords - sometimes "more" can mean addition, but "more than" might mean subtraction.
Tip 4: Always check if your answer makes sense in the context of the problem.
Tip 5: Practice identifying subtraction keywords: left, remaining, difference, less, fewer, gave away, sold, spent, etc.
Common errors: Misidentifying the operation needed, using wrong numbers, making calculation errors, not answering the specific question asked, forgetting to regroup when necessary.
Success strategies: Read slowly, identify keywords, organize information, check work, ensure answer fits the context.
Essential rules to know:

• Context Understanding: Always consider the real-world situation described

• Keyword Recognition: Learn to identify words that suggest subtraction

• Information Organization: Separate known facts from the unknown

• Operation Selection: Choose the correct mathematical operation

• Calculation Accuracy: Perform math operations correctly including regrouping

• Answer Verification: Check that the answer makes sense in context

• Complete Response: Answer the question fully and in context

Complete Summary: Multi-Digit Subtraction Word Problems

Key Concepts and Definitions

Word Problems: Mathematical problems presented in narrative form that describe real-world situations requiring calculations to solve.

Subtraction Word Problems: Word problems that require finding the difference between two quantities, typically involving situations where something is taken away, lost, used, or decreased.

Context: The real-world scenario that gives meaning to the numbers and operations in the problem.

Keywords: Words that indicate which mathematical operation to perform, helping identify when subtraction is needed.

Key Information: The important numbers, facts, and details needed to solve the problem.

Core Rules and Principles

Rule 1 - Context Understanding: Always read the entire problem to understand the real-world situation being described.

Rule 2 - Keyword Recognition: Identify words that suggest subtraction operations (left, remaining, difference, less than, fewer, gave away, sold, used, etc.).

Rule 3 - Information Extraction: Separate the given information from what needs to be found.

Rule 4 - Operation Selection: Choose subtraction when quantities are being reduced, taken away, or compared for differences.

Rule 5 - Proper Calculation: Apply correct subtraction methods, including regrouping when necessary.

Rule 6 - Answer Verification: Ensure the solution makes sense within the problem's context.

Step-by-Step Methods and Procedures

  1. Read Thoroughly: Understand the story and what is happening in the real-world situation.
  2. Identify Key Information: Circle or highlight important numbers and facts mentioned in the problem.
  3. Look for Keywords: Find words that indicate subtraction is needed (left, remaining, difference, etc.).
  4. Determine the Question: Understand specifically what the problem is asking for.
  5. Set Up the Equation: Write the subtraction problem using the identified numbers.
  6. Solve Carefully: Perform the subtraction, including regrouping if necessary.
  7. Check Your Work: Verify that the answer makes sense in the context of the problem.
  8. Answer Completely: Provide the answer in a complete sentence that addresses the question.

Examples: From Simple to Advanced

Simple Example: "The library had 847 books. Students borrowed 235 books. How many books are left?"

• Keywords: "borrowed", "left" → subtraction needed

• Equation: 847 - 235 = 612

• Answer: 612 books are left

Intermediate Example: "A fish tank had 520 fish. The owner gave away 186 fish. How many fish are remaining?"

• Keywords: "gave away", "remaining" → subtraction needed

• Equation: 520 - 186 = 334 (requires regrouping)

• Answer: 334 fish are remaining

Advanced Example: "An apple orchard grew 7,425 apples. The farmers sold 2,198 apples. How many apples do they have left?"

• Keywords: "sold", "left" → subtraction needed

• Equation: 7,425 - 2,198 = 5,227 (four-digit subtraction with regrouping)

• Answer: 5,227 apples are left

Tips, Tricks, and Common Pitfalls

Tips:

  • Circle or underline important numbers in the problem
  • Look for keywords like "left," "remaining," "difference," "less than," "gave away," "sold," "used," "withdrawn"
  • Draw pictures or models to visualize the problem
  • Always check if your answer makes sense in the real-world context
  • Answer with a complete sentence that addresses the question
  • Remember that "more" doesn't always mean addition - pay attention to context

Common Mistakes:

  • Choosing the wrong operation (using addition instead of subtraction)
  • Misreading the problem and using incorrect numbers
  • Forgetting to regroup when needed in the calculation
  • Not answering the specific question that was asked
  • Making calculation errors due to rushing
  • Ignoring the context and providing an unrealistic answer

Key Notes for Memorization

Memory Aid: "Take Away Words Mean Subtract!" - When you see words like "left," "remaining," "difference," "fewer," or "less," think subtraction.

Context is King: Always consider the real-world situation - sometimes the same words can mean different operations depending on context.

Process Over Speed: Read carefully, identify information, set up equation, solve, and check - don't rush!

Keywords List: Left, remaining, difference, less than, fewer, gave away, sold, used, spent, withdrawn, taken away, reduced, decreased.

Verification Strategy: Add your answer to the smaller number to see if you get the larger number - this checks your subtraction.

Questions & Answers

Question: Sometimes I see the word "more" in a problem and I think it means addition, but sometimes it means subtraction. How do I know the difference?

Answer: Great observation! The word "more" can indeed mean different things depending on the context:

  • "More" as addition: "Sarah has 5 apples. John has 3 more apples than Sarah. How many does John have?" → 5 + 3 = 8
  • "More" as comparison (subtraction): "Sarah has 8 apples. John has 3 more apples than Sarah. How many does Sarah have?" → This is a subtraction problem: 8 - 3 = 5
  • "How many more" means subtraction: "Sarah has 8 apples, John has 5. How many more apples does Sarah have?" → 8 - 5 = 3

The key is to look at the entire sentence and ask: "What am I trying to find?" If you're finding a total or combined amount, it's usually addition. If you're finding a difference or comparing amounts, it's usually subtraction.

Question: How do I know when I need to regroup in a word problem? Should I figure that out before I start subtracting?

Answer: You don't need to decide about regrouping before starting - you discover it as you work through the problem:

  • Start setting up your subtraction problem by aligning the numbers
  • Look at the ones place first: is the top number ≥ bottom number?
  • If yes, subtract directly. If no, you'll need to regroup
  • Continue checking each place value as you move left

For example, in 520 - 186:

  • Ones place: 0 < 6, so regrouping is needed
  • Tens place: 1 < 8 (after regrouping), so more regrouping needed
  • Hundreds place: 4 > 1 (after regrouping), so no more regrouping needed

The word problem itself doesn't tell you about regrouping - that's determined by the numbers you're working with!

Question: How can I help my students who struggle with reading comprehension affect their ability to solve word problems?

Answer: Here are effective strategies for students with reading challenges:

  • Vocabulary building: Create a word wall with common math terms and their meanings
  • Visual scaffolding: Use drawings, diagrams, or physical objects to represent the problem
  • Chunking: Break the problem into smaller parts and read one sentence at a time
  • Highlighting: Teach students to highlight or circle numbers and key words
  • Rephrasing: Have students restate the problem in their own words
  • Pattern recognition: Group similar problem types together for practice

Consider providing the same problem in multiple formats - written, visual, and verbal - to accommodate different learning styles. Also, encourage students to draw pictures or act out the problem to better understand the context.