Multi Digit Addition and Subtraction Worksheets in Grade 3

Practice multi-digit addition and subtraction with regrouping, estimation, and problem-solving through these 5 detailed worksheet exercises.

Worksheet Practice: Addition Problems
1
\(47 + 28\)
2
\(156 + 284\)
3
\(347 + 289\)
4
\(583 + 247\)
5
\(428 + 395\)
Worksheet Practice: Subtraction Problems
6
\(83 - 27\)
7
\(405 - 187\)
8
\(623 - 289\)
9
\(500 - 278\)
10
\(732 - 486\)
Solution: Exercises 1 to 3
1 Addition with carrying
Exercise 1
\(47 + 28\)
Definition:

Carrying (Regrouping): When adding digits in a place value column results in a number 10 or greater, carry the tens digit to the next higher place value

Addition method:
  1. Align numbers by place value (ones under ones, tens under tens)
  2. Start adding from the rightmost place (ones)
  3. If sum ≥ 10, write the ones digit and carry the tens digit to next place
  4. Continue to the left
Original
\(47 + 28\)
Carrying
\(7^{15} + 8\)
Result
\(75\)
Tens
Ones
Tens
Ones
4
7
2
8
↓
1 4
7
2
8

Carry 1 to tens place: 7 + 8 = 15

Step 1: Add ones place

\(7 + 8 = 15\)

Since 15 ≥ 10, write 5 in ones place and carry 1 to tens place

Step 2: Add tens place

\(4 + 2 + 1\) (carried) = 7

Step 3: Write final answer

Tens: 7, Ones: 5

\(47 + 28 = 75\)
Final answer:

\(47 + 28 = 75\)

Applied rules:

• Carrying: When sum ≥ 10, carry the tens digit to next place

• Place value: Each place represents a power of 10

• Addition: Always add digits in the same place value column

2 Addition with multiple carrying
Exercise 2
\(156 + 284\)
Definition:

Multiple carrying: When adding across multiple place values, carry sequentially from right to left

Hunds
Tens
Ones
Hunds
Tens
Ones
1
5
6
2
8
4
↓
1 1
1 5
6
2
8
4

Carry 1 from ones to tens (6+4=10), then carry 1 from tens to hundreds (5+8+1=14)

Step 1: Add ones place

\(6 + 4 = 10\)

Write 0 in ones place, carry 1 to tens place

Step 2: Add tens place

\(5 + 8 + 1\) (carried) = 14

Write 4 in tens place, carry 1 to hundreds place

Step 3: Add hundreds place

\(1 + 2 + 1\) (carried) = 4

Step 4: Write final answer

Hundreds: 4, Tens: 4, Ones: 0

\(156 + 284 = 440\)
Final answer:

\(156 + 284 = 440\)

Applied rules:

• Sequential carrying: Carry from right to left as needed

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

• Systematic approach: Work from right to left, carrying as needed

3 Subtraction with borrowing
Exercise 3
\(83 - 27\)
Definition:

Borrowing (Regrouping): When subtracting, if the top digit is smaller than the bottom digit, borrow 1 from the next higher place value

Tens
Ones
Tens
Ones
8
3
2
7
↓
7
13
2
7

Borrowed 1 ten → 10 ones: 83 → 7^{13}

Step 1: Look at ones place

\(3 < 7\), so we cannot subtract: 3 - 7

Step 2: Regroup from tens place

Borrow 1 ten from 8 tens: 8 tens = 7 tens + 1 ten

Add the borrowed 1 ten to ones: 1 ten = 10 ones

New ones: 3 + 10 = 13 ones

Step 3: Subtract ones

\(13 - 7 = 6\)

Step 4: Subtract tens

\(7 - 2 = 5\)

\(83 - 27 = 56\)
Final answer:

\(83 - 27 = 56\)

Applied rules:

• Regrouping: Borrow 1 from higher place value when needed

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

• Subtraction: Always subtract bottom number from top number

Rules and methods, laws,...
\(\text{If } a + b \geq 10, \text{ then carry } \lfloor(a + b)/10\rfloor \text{ to next place}\)
Carrying Condition
\(\text{If } a < b, \text{ then borrow from next place}\)
Borrowing Condition
Relationship 1
\(10 \text{ ones} = 1 \text{ ten}\)
Place Value Relationship
Relationship 2
\(10 \text{ tens} = 1 \text{ hundred}\)
Place Value Relationship
Relationship 3
\(1 \text{ ten} = 10 \text{ ones}\)
Place Value Relationship
Key definitions:

Carrying: Moving a group of 10 from one place value to the next higher place value in addition

Borrowing: Taking from a higher place value to add to a lower place value in subtraction

Regrouping: Converting between place values to enable operations

Place value: The value of a digit based on its position in the number

Complete methodology:
  1. Align numbers: Match digits by place value
  2. Identify operation: Determine if addition or subtraction
  3. Start from right: Begin with the ones place
  4. Check for carrying/borrowing: If needed, apply appropriate operation
  5. Add each place: Continue working left until all places are done
Tip 1: Always check if carrying or borrowing is needed before starting.
Tip 2: Write small carry digits above the next column to keep track.
Tip 3: Practice with place value charts to visualize the carrying process.
Tip 4: Always verify your answer by estimating or checking with a calculator.
Common errors: Forgetting to include carried digits in next place addition, not reducing higher place value after borrowing.
Success strategies: Practice with visual aids, check each step, verify answers.
Rules to remember:

• Carrying condition: When sum ≥ 10, carry the tens digit

• Borrowing condition: When top digit < bottom digit

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

• Inclusion rule: Always include carried digit in next place value addition

• Reduction rule: When borrowing, reduce the higher place value by 1

• Verification: Estimate to check if answer is reasonable

Solution: Exercises 4 to 5
4 Mixed carrying pattern
Exercise 4
\(583 + 247\)
Definition:

Mixed carrying: When some places require carrying while others don't, handle each place individually

Hunds
Tens
Ones
Hunds
Tens
Ones
5
8
3
2
4
7
↓
1 5
8
3
2
4
7

Carry 1 from ones to tens: 3 + 7 = 10

Step 1: Add ones place

\(3 + 7 = 10\)

Write 0 in ones place, carry 1 to tens place

Step 2: Add tens place

\(8 + 4 + 1\) (carried) = 13

Write 3 in tens place, carry 1 to hundreds place

Step 3: Add hundreds place

\(5 + 2 + 1\) (carried) = 8

Step 4: Write final answer

Hundreds: 8, Tens: 3, Ones: 0

\(583 + 247 = 830\)
Final answer:

\(583 + 247 = 830\)

Applied rules:

• Selective carrying: Only carry when sum ≥ 10 for each specific place

• Sequential processing: Handle carrying one place at a time

• Verification: Check by estimating: 583 ≈ 580, 247 ≈ 250, 580 + 250 = 830 ✓

5 Subtraction with multiple borrowing
Exercise 5
\(405 - 187\)
Definition:

Multiple borrowing: When subtracting across multiple place values, borrow sequentially from left to right

Hunds
Tens
Ones
Hunds
Tens
Ones
4
0
5
1
8
7
↓
3
9
15
1
8
7

Borrowed 1 hundred → 10 tens → 9 tens + 1 ten → 10 ones

Step 1: Look at ones place

\(5 < 7\), so we cannot subtract: 5 - 7

Step 2: Check tens place

Tens place has 0, so we cannot borrow from tens

Step 3: Regroup from hundreds place

Borrow 1 hundred from 4 hundreds: 4 hundreds = 3 hundreds + 1 hundred

Add the borrowed 1 hundred to tens: 1 hundred = 10 tens

New tens: 0 + 10 = 10 tens

Step 4: Regroup from tens place

Take 1 ten from 10 tens: 10 tens = 9 tens + 1 ten

Add the borrowed 1 ten to ones: 1 ten = 10 ones

New ones: 5 + 10 = 15 ones

Step 5: Subtract each place

Ones: \(15 - 7 = 8\)

Tens: \(9 - 8 = 1\)

Hundreds: \(3 - 1 = 2\)

\(405 - 187 = 218\)
Final answer:

\(405 - 187 = 218\)

Applied rules:

• Sequential borrowing: When lower place has 0, borrow from higher place first

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

• Systematic approach: Work from right to left, borrowing as needed

Complete Summary: Multi Digit Addition and Subtraction Worksheets in Grade 3

Key Definitions and Concepts
  • Addition: The operation of combining two or more numbers to find their total or sum.
  • Subtraction: The operation of taking one number away from another to find the difference.
  • Carrying (Regrouping): The process of moving a group of 10 from one place value to the next higher place value when the sum of digits in a column is 10 or greater.
  • Borrowing (Regrouping): The process of converting a higher place value unit into 10 of the next lower place value unit when the top digit is smaller than the bottom digit.
  • Place Value: The value of a digit based on its position in a number (ones, tens, hundreds, thousands).
  • Addends: The numbers being added together in an addition problem.
  • Minuend: The number being subtracted from (the top number in vertical subtraction).
  • Subtrahend: The number being subtracted (the bottom number in vertical subtraction).
  • Sum: The result of an addition problem.
  • Difference: The result of a subtraction problem.
  • Carry Digit: The tens digit that is moved to the next higher place value when carrying occurs.
  • Vertical Addition/Subtraction: Writing numbers vertically with place values aligned to perform operations.
Core Rules and Principles
  • Carrying Rule: When the sum of digits in any place value column is 10 or greater, carry the tens digit to the next higher place value.
  • Borrowing Rule: When the top digit in any place value column is smaller than the bottom digit, borrow 1 from the next higher place value.
  • Place Value Relationships: 10 ones = 1 ten, 10 tens = 1 hundred, 10 hundreds = 1 thousand.
  • Addition Direction: Always add from right to left (ones, tens, hundreds, thousands).
  • Subtraction Direction: Always subtract from right to left (ones, tens, hundreds, thousands).
  • Inclusion Rule: Always include any carried digits in the addition of the next higher place value.
  • Reduction Rule: When borrowing, reduce the higher place value by 1.
  • Verification Rule: Estimate your answer to check if it's reasonable.
Step-by-Step Methods and Procedures

For Addition:

  1. Align Numbers: Write the numbers vertically with place values lined up (ones under ones, tens under tens, etc.).
  2. Start from Right: Begin addition with the ones place.
  3. Add Each Column: Add the digits in the current place value column.
  4. Check for Carrying: If the sum is 10 or greater, write the ones digit and carry the tens digit to next column.
  5. Include Carries: Add any carried digits to the next higher place value column.
  6. Move Left: Move to the next column to the left and repeat steps 3-5.
  7. Verify: Estimate your answer to ensure it's reasonable.

For Subtraction:

  1. Align Numbers: Write the numbers vertically with place values lined up.
  2. Start from Right: Begin subtraction with the ones place.
  3. Check Each Place: For each place value, check if the top digit is greater than or equal to the bottom digit.
  4. Borrow if Needed: If the top digit is smaller, borrow 1 from the next higher place value.
  5. Subtract: Perform the subtraction in that column.
  6. Move Left: Move to the next column to the left and repeat steps 3-5.
  7. Verify: Add the difference to the subtrahend to ensure you get the minuend.
Examples (Simple to Advanced)

Simple Addition: \(24 + 35\)

Ones: 4 + 5 = 9 (no carrying needed)

Tens: 2 + 3 = 5

Answer: 59

Simple Subtraction: \(47 - 23\)

Ones: 7 - 3 = 4

Tens: 4 - 2 = 2

Answer: 24

Medium Addition: \(47 + 28\)

Ones: 7 + 8 = 15, write 5, carry 1

Tens: 4 + 2 + 1 (carried) = 7

Answer: 75

Medium Subtraction: \(83 - 27\)

Ones: 3 < 7, so borrow: 83 → 7^{13}, then 13 - 7 = 6

Tens: 7 - 2 = 5

Answer: 56

Advanced Mixed: \(156 + 284\)

Ones: 6 + 4 = 10, write 0, carry 1

Tens: 5 + 8 + 1 = 14, write 4, carry 1

Hundreds: 1 + 2 + 1 = 4

Answer: 440

Tips, Tricks, and Common Pitfalls
  • Tip 1: Always write numbers vertically to align place values correctly.
  • Tip 2: Write small carry digits above the next column to keep track.
  • Tip 3: Use place value charts to visualize the carrying process.
  • Tip 4: Always estimate your answer to check if it's reasonable.
  • Tip 5: Practice regularly with worksheets to build fluency.
  • Pitfall 1: Forgetting to include carried digits in the next column's addition.
  • Pitfall 2: Not reducing the higher place value by 1 when borrowing.
  • Pitfall 3: Misaligning place values when writing numbers vertically.
  • Pitfall 4: Adding from left to right instead of right to left.
  • Pitfall 5: Subtracting the wrong way (bottom from top instead of top from bottom).
Key Notes and Takeaways for Memorization
  • Memory Aid: "Ten or more, move to the store" - when you get 10 or more, carry the extra to the next place value.
  • Memory Aid: "Right to left" - always add and subtract from right to left.
  • Memory Aid: "Keep the ones, pass the tens" - keep the ones digit, pass the tens digit to the next column.
  • Rule to Remember: If sum ≥ 10, carry the tens digit to the next place value.
  • Rule to Remember: If top digit < bottom digit, borrow from the next place value.
  • Rule to Remember: 10 ones = 1 ten, 10 tens = 1 hundred, 10 hundreds = 1 thousand.
  • Verification Strategy: Round numbers and add/subtract to check if your answer is close.
Understanding for Students

Think of carrying like trading coins: if you have 13 pennies, you can trade 10 pennies for 1 dime. You now have 1 dime and 3 pennies. In addition, when you get 10 or more in any place value, you trade groups of 10 for 1 in the next higher place value. For subtraction, think of borrowing like exchanging: if you have 1 dollar bill and need to give 25 cents, you can exchange your dollar for 4 quarters. In subtraction, when you need more in a place value, you exchange 1 from the next higher place value for 10 of the lower place value!

Questions & Answers

Question: I get confused about when to carry. How do I know if I need to carry?

Answer: You need to carry when the sum of the digits in any place value column is 10 or greater:

  • If you add two digits and get 10, 11, 12, 13, 14, 15, 16, 17, 18, or 19, you must carry
  • For example: 7 + 6 = 13, so you write 3 and carry 1
  • Or: 5 + 8 = 13, so you write 3 and carry 1
  • If you add two digits and get 9 or less, you don't carry
  • For example: 4 + 3 = 7, so you just write 7

Think of it like this: "If I have 10 or more of something, I can make a group of 10 and have some left over!"

Question: Why do I need to add the carried number to the next column? It seems like I'm adding extra.

Answer: The carried number isn't extra - it represents actual value that was created in the previous column:

  • When you add 7 + 6 = 13 in the ones place, you have 13 ones total
  • But 13 ones = 1 ten + 3 ones
  • You write the 3 ones in the ones place
  • You carry the 1 ten to the tens place because that's where tens belong
  • So when you add the tens column, you must include that 1 ten you carried

Think of it like money: if you have 13 dollars in ones, you can change 10 of those dollars for 1 ten-dollar bill. That ten-dollar bill goes with your other tens!

Question: How can I check if my multi-digit addition and subtraction is correct? I want to make sure I didn't make mistakes.

Answer: There are several ways to check your work:

  • Estimation: Round numbers and add to see if your answer is close
  • Reverse operation: Subtract one addend from the sum to see if you get the other addend
  • Calculator: Use a calculator to verify your answer
  • Re-do: Solve the problem again to make sure you get the same answer

Example: If you did 47 + 28 = 75

Estimate: 50 + 30 = 80, and 75 is close to 80 ✓

Check: 75 - 47 = 28 ✓ or 75 - 28 = 47 ✓

Develop the habit of checking your work - it's an important mathematical skill!