Multi-Digit Addition with Regrouping: Solved Exercises for Grade 3

Master multi-digit addition with regrouping: carrying method, place value understanding, and practical applications through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic Regrouping
Exercise 1
Add: 27 + 15
Definition:

Regrouping (Carrying): When adding digits results in a number greater than 9, we carry the tens digit to the next column.

Addition method with regrouping:
  1. Add digits in the ones place
  2. If sum ≥ 10, write the ones digit and carry the tens digit
  3. Add digits in the tens place including any carried digit
  4. Write the final result
2
7
+
1
5
-
-
-
4
2
Step 1: Add ones place

7 + 5 = 12 → Write 2 in ones place, carry 1 to tens place

Step 2: Add tens place with carry

2 + 1 + 1 (carried) = 4 → Write 4 in tens place

Step 3: Write the result

27 + 15 = 42

27 + 15 = 42
Final answer:

27 + 15 = 42

Applied rules:

• Place Value: Each digit has a specific place (ones, tens, hundreds)

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

• Addition Property: Adding carried digits to the next column

Visual Representation
🔢
Ones: 7 + 5 = 12
Write 2, carry 1
➡️
Tens: 2 + 1 + 1 = 4
Write 4
✅
Result: 42
2 Two-Digit Regrouping
Exercise 2
Add: 58 + 37
Definition:

Regrouping in multiple places: When adding larger numbers, regrouping may occur in multiple columns.

5
8
+
3
7
-
-
-
9
5
Step 1: Add ones place

8 + 7 = 15 → Write 5 in ones place, carry 1 to tens place

Step 2: Add tens place with carry

5 + 3 + 1 (carried) = 9 → Write 9 in tens place

Step 3: Write the result

58 + 37 = 95

58 + 37 = 95
Final answer:

58 + 37 = 95

Applied rules:

• Place Value System: Each column represents a power of 10

• Carrying Method: Transfer excess to higher place value

• Sequential Addition: Work from right to left

Visual Representation
ONES
8 + 7 = 15
Write 5, carry 1
TENS
5 + 3 + 1 = 9
Write 9
RESULT
95
3 Three-Digit Regrouping
Exercise 3
Add: 146 + 278
Definition:

Three-digit addition: Extending regrouping to hundreds place when needed.

1
4
6
+
2
7
8
-
-
-
-
4
2
4
Step 1: Add ones place

6 + 8 = 14 → Write 4 in ones place, carry 1 to tens place

Step 2: Add tens place with carry

4 + 7 + 1 (carried) = 12 → Write 2 in tens place, carry 1 to hundreds place

Step 3: Add hundreds place with carry

1 + 2 + 1 (carried) = 4 → Write 4 in hundreds place

Step 4: Write the result

146 + 278 = 424

146 + 278 = 424
Final answer:

146 + 278 = 424

Applied rules:

• Place Value System: Ones, tens, hundreds

• Multiple Regrouping: May occur in multiple columns

• Carry Forward: Always include carried digits in next column

Visual Representation
ONES
6 + 8 = 14
Write 4, carry 1
TENS
4 + 7 + 1 = 12
Write 2, carry 1
HUNDREDS
1 + 2 + 1 = 4
Write 4
Key Concepts and Methods
Regrouping: Sum ≥ 10
When to Carry
Place Value System

• Ones (rightmost digit)

• Tens (second from right)

• Hundreds (third from right)

• Each place is 10 times the value of the place to its right

Carrying Rule: When sum ≥ 10, keep the ones digit and carry the tens digit to the next column.
Sequential Addition: Always work from right to left (ones, tens, hundreds).
Tip 1: Always check your work by adding in reverse or using estimation.
Tip 2: Draw small arrows above columns where you carry to keep track.
Tip 3: Practice with smaller numbers first before moving to larger ones.
Key Definitions:

Regrouping: Converting 10 units of one place value into 1 unit of the next higher place value

Carrying: Moving an extra value from one column to the next when the sum exceeds 9

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

Step-by-Step Method:
  1. Align numbers: Place digits in correct columns (ones under ones, etc.)
  2. Add from right: Start with ones place and move left
  3. Check for regrouping: If sum ≥ 10, carry the tens digit
  4. Include carries: Add carried digits to the next column
  5. Write result: Record the final answer
Solution: Exercises 4 to 5
4 Complex Regrouping
Exercise 4
Add: 389 + 476
Definition:

Complex regrouping: Multiple regroupings may occur in the same problem across different place values.

3
8
9
+
4
7
6
-
-
-
-
8
6
5
Step 1: Add ones place

9 + 6 = 15 → Write 5 in ones place, carry 1 to tens place

Step 2: Add tens place with carry

8 + 7 + 1 (carried) = 16 → Write 6 in tens place, carry 1 to hundreds place

Step 3: Add hundreds place with carry

3 + 4 + 1 (carried) = 8 → Write 8 in hundreds place

Step 4: Write the result

389 + 476 = 865

389 + 476 = 865
Final answer:

389 + 476 = 865

Applied rules:

• Multiple Regrouping: Regrouping can happen in multiple columns

• Carry Management: Always include previous carries in calculations

• Place Value Accuracy: Maintain correct column alignment

Visual Representation
ONES
9 + 6 = 15
Write 5, carry 1
TENS
8 + 7 + 1 = 16
Write 6, carry 1
HUNDREDS
3 + 4 + 1 = 8
Write 8
5 Application Problem
Exercise 5
Sarah collected 247 stickers. Her friend gave her 189 more. How many stickers does Sarah have now?
Definition:

Word problems: Real-world scenarios requiring mathematical operations to solve.

2
4
7
+
1
8
9
-
-
-
-
4
3
6
Step 1: Identify the operation

This is an addition problem: 247 + 189

Step 2: Add ones place

7 + 9 = 16 → Write 6 in ones place, carry 1 to tens place

Step 3: Add tens place with carry

4 + 8 + 1 (carried) = 13 → Write 3 in tens place, carry 1 to hundreds place

Step 4: Add hundreds place with carry

2 + 1 + 1 (carried) = 4 → Write 4 in hundreds place

Step 5: Write the result

Sarah has 436 stickers in total

Sarah has 436 stickers
Final answer:

Sarah has 436 stickers now.

Applied rules:

• Problem Analysis: Identify the operation needed

• Regrouping Method: Apply carrying technique correctly

• Contextual Answer: Provide answer in context of the problem

Problem-Solving Strategy
READ
Understand the problem
PLAN
Identify operation (addition)
SOLVE
Perform calculation
CHECK
Verify answer
Key Laws, Methods, Rules, and Definitions
If sum ≥ 10, carry 1
Carrying Rule
Key definitions:

Regrouping: Converting 10 units of one place value into 1 unit of the next higher place value

Carrying: Moving an extra value from one column to the next when the sum exceeds 9

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

Complete methodology:
  1. Align the numbers: Ensure digits are in correct place value columns
  2. Add from right to left: Start with ones place, then tens, then hundreds
  3. Check for regrouping: If sum ≥ 10, write the ones digit and carry the tens digit
  4. Include carried digits: Add any carried digits to the next column
  5. Continue process: Repeat for each column until complete
  6. Verify result: Check your work by estimating or adding in reverse
Tip 1: Always align numbers properly by place value before starting.
Tip 2: Circle or mark where you carry to avoid forgetting.
Tip 3: Practice mental math for basic facts to speed up the process.
Tip 4: Estimate first to check if your answer makes sense.
Common errors: Forgetting to carry, misaligning numbers, adding carried digits incorrectly.
Practice tips: Start with simple problems, gradually increase difficulty, always check your work.
Essential rules to remember:

• Place Value Alignment: Always align numbers by place value

• Right-to-Left Addition: Start from ones place and move left

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

• Include Carries: Always add carried digits to the next column

• Verification: Check your answer by estimating or using inverse operations

Questions & Answers

Question: I don't understand why we need to "carry" when adding. Why can't we just write the whole number in one place?

Answer: Great question! The reason we carry is because of our place value system. Each place can only hold a single digit (0-9). Think of it like money:

  • If you have 12 pennies, you can't put all 12 in the "pennies" pocket
  • You exchange 10 pennies for 1 dime, keeping 2 pennies
  • So you have 2 pennies and 1 dime

In math, when you get 12 in the ones place, you "exchange" 10 ones for 1 ten, keeping 2 ones. That's why you write 2 in the ones place and carry 1 to the tens place. It's like exchanging coins for bills!

Example: In 27 + 15, when you add 7 + 5 = 12, you can't write "12" in the ones place because that would mean 12 ones. Instead, you write 2 ones and carry 1 ten to the tens column.

Question: My child is having trouble remembering to add the carried number. Any tips to help them remember?

Answer: Here are some effective strategies to help your child remember to add carried numbers:

  • Circle the carry: Have them circle or draw a circle around the number they're carrying so it stands out
  • Say it aloud: Encourage them to say "plus the carry" when they reach the next column
  • Physical marker: Use a small dot or checkmark where they need to remember to add the carry
  • Slow down: Take extra time at the carry step, emphasizing "I carried a 1, so now I need to add it"

Practice with smaller numbers first, then gradually increase complexity. Also, encourage them to check their work by doing a quick estimate (like rounding to nearest 10) to see if their answer makes sense.

Example: If solving 38 + 27, they add 8 + 7 = 15, write 5, carry 1. Then they should pause and say "3 + 2 + 1 (the carry) = 6", giving the answer 65.

Question: Sometimes I have to carry more than once in the same problem. How do I keep track of everything?

Answer: When you have to carry multiple times in one problem, it helps to be very organized! Here's how:

  • Work slowly: Don't rush through each step
  • Mark each carry: Write the carried number clearly above the next column
  • Double-check: After adding each column, make sure you included any carries
  • Go step by step: Focus on one column at a time

Let's take 389 + 476 as an example:
• Add ones: 9 + 6 = 15 → write 5, carry 1
• Add tens: 8 + 7 + 1 (carry) = 16 → write 6, carry 1
• Add hundreds: 3 + 4 + 1 (carry) = 8
• Result: 865

Each time you carry, treat it like adding a new number to that column. The carried number becomes part of the addition in the next column.