Addition with Regrouping | Solved Exercises | Mathematics Grade 3 Addition, Subtraction, and Estimation

Solution: Exercises 1 to 3

1 Basic Regrouping

Exercise 1

Add: 27 + 15

Definition:

Regrouping: When the sum in a place value column is 10 or more, carry the extra to the next higher place value

Addition with regrouping method:

Add the ones place: 7 + 5 = 12
Write the ones digit (2) below the line
Carry the tens digit (1) to the tens column
Add the tens column: 2 + 1 + 1 (carried) = 4

Ones Column

7 + 5 = 12

Carry

1 to tens

Tens Column

2+1+1=4

Step 1: Add the ones place

7 + 5 = 12 (which is 1 ten and 2 ones)

Step 2: Write the ones digit and carry the tens

Write 2 in the ones place, carry 1 to the tens column

Step 3: Add the tens column

2 + 1 + 1 (carried) = 4 tens

27 + 15 = 42

Final answer:

27 + 15 = 42

Applied rules:

• Regrouping rule: When sum ≥ 10, carry the tens digit to the next column

• Place value: Keep digits in correct columns

• Addition algorithm: Add from right to left, carrying when needed

2 Two-Digit Addition with Regrouping

Exercise 2

Add: 48 + 37

Definition:

Carrying: Moving excess from one place value to the next higher place value

Ones Column

8 + 7 = 15

Carry

1 to tens

Tens Column

4+3+1=8

Step 1: Add the ones place

8 + 7 = 15 (which is 1 ten and 5 ones)

Step 2: Write 5 in ones place, carry 1 to tens

Write 5 below the line, carry 1 above the tens column

Step 3: Add the tens column including the carried 1

4 + 3 + 1 (carried) = 8 tens

48 + 37 = 85

Final answer:

48 + 37 = 85

Applied rules:

• Regrouping threshold: When sum is 10 or more, regroup

• Carry value: The tens digit of the sum goes to the next column

• Column addition: Add all values in each column

3 Three-Digit Addition with Regrouping

Exercise 3

Add: 164 + 278

Definition:

Multiple regrouping: When regrouping is needed in more than one place value column

Ones Column

4+8=12

Tens Column

6+7+1=14

Hundreds Column

1+2+1=4

Step 1: Add the ones column

4 + 8 = 12 → Write 2, carry 1 to tens

Step 2: Add the tens column including carry

6 + 7 + 1 (carried) = 14 → Write 4, carry 1 to hundreds

Step 3: Add the hundreds column including carry

1 + 2 + 1 (carried) = 4 hundreds

164 + 278 = 442

Final answer:

164 + 278 = 442

Applied rules:

• Sequential regrouping: Regroup in each column as needed

• Carry forward: Each carried digit affects the next column

• Place value alignment: Keep digits properly aligned in columns

Solution: Exercises 4 to 5

4 Addition with Multiple Regroupings

Exercise 4

Add: 289 + 375

Definition:

Double regrouping: When regrouping occurs in both ones and tens columns

Ones Column

9+5=14

Tens Column

8+7+1=16

Hundreds Column

2+3+1=6

Step 1: Add the ones column

9 + 5 = 14 → Write 4, carry 1 to tens

Step 2: Add the tens column including carry

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

Step 3: Add the hundreds column including carry

2 + 3 + 1 (carried) = 6 hundreds

289 + 375 = 664

Final answer:

289 + 375 = 664

Applied rules:

• Multiple regrouping: Can occur in multiple columns of the same problem

• Sequential processing: Handle each column from right to left

• Carry accumulation: Each carry affects the next column's sum

5 Word Problem with Regrouping

Exercise 5

Sam has 156 marbles. His friend gives him 287 more. How many marbles does Sam have now?

Definition:

Word problem: A real-world scenario that requires mathematical operations to solve

Set up problem

156 + 287

Ones Column

6+7=13

Tens Column

5+8+1=14

Hundreds Column

1+2+1=4

Step 1: Identify the operation needed

Sam has 156 marbles and gets 287 more, so we add: 156 + 287

Step 2: Add the ones column

6 + 7 = 13 → Write 3, carry 1 to tens

Step 3: Add the tens column including carry

5 + 8 + 1 (carried) = 14 → Write 4, carry 1 to hundreds

Step 4: Add the hundreds column including carry

1 + 2 + 1 (carried) = 4 hundreds

156 + 287 = 443

Final answer:

Sam has 443 marbles now

Applied rules:

• Problem translation: Convert words to mathematical expression

• Regrouping application: Apply standard algorithm to solve

• Contextual answer: Provide answer in context of the problem

Rules and methods, laws,...

Regrouping Process

Addition Algorithm

Rule 1

Sum ≥ 10

Carry the tens digit

Rule 2

Add from right

Process columns leftward

Rule 3

Place Value

Keep digits aligned

Rule 4

Verify Sum

Check reasonableness

Rule 5

Multiple Carries

Continue process

Rule 6

Double Check

Review calculations

Key Tip: Always check if the sum in each column is 10 or more before moving to the next column.

Strategy: Use base-10 blocks or drawings to visualize regrouping when first learning.

Addition with Regrouping Comprehensive Guide

Addition Process

Understanding Regrouping

Key definitions:

Regrouping: The process of converting 10 units of a lower place value into 1 unit of the next higher place value

Carrying: Moving the extra value from one column to the next higher column during addition

Place Value: The value of a digit based on its position in a number (ones, tens, hundreds, etc.)

Addition with regrouping methodology:

Align numbers: Place values in the same columns
Add from right: Start with ones place, move left
Check sum: If sum ≥ 10, regroup
Carry over: Move extra to next column
Repeat: Continue for all columns

Tip 1: Always check if the sum in each column is 10 or more before moving to the next column.

Tip 2: Use small marks above columns to indicate carries.

Tip 3: Estimate the answer first to check if your result is reasonable.

Tip 4: Practice with visual aids like base-10 blocks to understand the concept.

Common errors: Forgetting to carry, misaligning numbers, adding across instead of down.

Success strategies: Practice regularly, use visual aids, check work carefully.

Essential regrouping rules:

• Regrouping threshold: When the sum in a column is 10 or greater, regroup

• Carry value: Only carry the tens digit of the sum to the next column

• Column processing: Process each column completely before moving to the next

• Place value: Maintain proper alignment of digits in columns

• Verification: Estimate and check if the answer makes sense

Additional Exercises 6-8

6 Money Addition with Regrouping

Exercise 6

Add: $3.87 + $2.56

Definition:

Money addition: Adding amounts with dollars and cents, following the same regrouping rules

Cents Column

7+6=13

Dollars Column

3+2+1=6

Final Amount

$6.43

Step 1: Align decimal points

Line up the decimal points when adding money: $3.87 + $2.56

Step 2: Add the cents (rightmost digits)

7 + 6 = 13 → Write 3, carry 1 to dollars

Step 3: Add the dollars including carry

3 + 2 + 1 (carried) = 6 dollars

$3.87 + $2.56 = $6.43

Final answer:

$3.87 + $2.56 = $6.43

7 Distance Addition with Regrouping

Exercise 7

A car traveled 248 miles on Monday and 176 miles on Tuesday. How many miles did it travel in total?

Definition:

Distance addition: Adding measurements with the same units, requiring regrouping when necessary

Set up problem

248 + 176

Ones Column

8+6=14

Tens Column

4+7+1=12

Hundreds Column

2+1+1=4

Step 1: Identify the operation

Total distance = Monday's distance + Tuesday's distance = 248 + 176

Step 2: Add the ones column

8 + 6 = 14 → Write 4, carry 1 to tens

Step 3: Add the tens column including carry

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

Step 4: Add the hundreds column including carry

2 + 1 + 1 (carried) = 4 hundreds

248 + 176 = 424

Final answer:

The car traveled 424 miles in total

8 Population Addition with Regrouping

Exercise 8

Add: 4,372 + 2,859

Definition:

Large number addition: Applying regrouping rules to numbers with thousands place and beyond

Ones Column

2+9=11

Tens Column

7+5+1=13

Hundreds Column

3+8+1=12

Thousands Column

4+2+1=7

Step 1: Add the ones column

2 + 9 = 11 → Write 1, carry 1 to tens

Step 2: Add the tens column including carry

7 + 5 + 1 (carried) = 13 → Write 3, carry 1 to hundreds

Step 3: Add the hundreds column including carry

3 + 8 + 1 (carried) = 12 → Write 2, carry 1 to thousands

Step 4: Add the thousands column including carry

4 + 2 + 1 (carried) = 7 thousands

4,372 + 2,859 = 7,231

Final answer:

4,372 + 2,859 = 7,231

Solution: Exercises 9 to 10

9 Multi-Step Addition with Regrouping

Exercise 9

In a garden, there are 158 red flowers, 274 yellow flowers, and 96 blue flowers. How many flowers are there in total?

Definition:

Multi-addend addition: Adding three or more numbers together, applying regrouping rules to each column

Set up problem

158+274+96

Ones Column

8+4+6=18

Tens Column

5+7+9+1=22

Hundreds Column

1+2+0+2=5

Step 1: Add the ones column

8 + 4 + 6 = 18 → Write 8, carry 1 to tens

Step 2: Add the tens column including carry

5 + 7 + 9 + 1 (carried) = 22 → Write 2, carry 2 to hundreds

Step 3: Add the hundreds column including carry

1 + 2 + 0 + 2 (carried) = 5 hundreds

158 + 274 + 96 = 528

Final answer:

There are 528 flowers in total

10 Mixed Operations with Regrouping

Exercise 10

A store sold 347 items on Monday. On Tuesday, they sold 289 more items. On Wednesday, they sold 156 more items. How many items did they sell in total?

Definition:

Multi-day total: Adding multiple quantities across different time periods

Set up problem

347+289+156

Ones Column

7+9+6=22

Tens Column

4+8+5+2=19

Hundreds Column

3+2+1+1=7

Step 1: Add the ones column

7 + 9 + 6 = 22 → Write 2, carry 2 to tens

Step 2: Add the tens column including carry

4 + 8 + 5 + 2 (carried) = 19 → Write 9, carry 1 to hundreds

Step 3: Add the hundreds column including carry

3 + 2 + 1 + 1 (carried) = 7 hundreds

347 + 289 + 156 = 792

Final answer:

The store sold 792 items in total

Visual Infographic: Addition with Regrouping

Regrouping Addition Flowchart

Step 1: Align Numbers

📏 Line up place values
1️⃣ Ones under ones
1️⃣ Tens under tens
1️⃣ Hundreds under hundreds

Step 2: Add Ones Column

➕ Add the rightmost digits
🤔 Is sum ≥ 10?
✅ Yes: write ones digit, carry tens
❌ No: just write the sum

Step 3: Continue Leftward

➕ Add tens column (include carry)
🤔 Is sum ≥ 10?
✅ Repeat regrouping process
🔄 Move to next column

Step 4: Final Check

📊 Is answer reasonable?
💡 Estimate first
✅ Verify with subtraction
🎯 Does it match context?

Regrouping Algorithm

Align

Add Ones

Carry if ≥10

Move Left

Regrouping Example: 27 + 15

27
+15
---
42
(7+5=12, write 2, carry 1)
(2+1+1=4 in tens place)

Remember: When sum ≥ 10, regroup by carrying!

Questions & Answers

ThirdGradeTeacher

Elementary Educator

Question: How do I teach my students to understand why we need to regroup in addition? Many of them just follow the steps without understanding the concept behind it.

MathEducationExpert

PhD in Elementary Mathematics Education

Answer: Understanding comes through concrete representation before abstract procedures:

Start with base-10 blocks: Have students physically trade 10 ones for 1 ten when they have more than 9 ones
Use place value mats to organize blocks and show the "trading" process
Connect to real-world examples: "If you have 12 candies and want to put them in bags of 10, you'd have 1 full bag and 2 left over"
Draw visual representations showing groups of 10 becoming a single unit in the next place value

Once students understand the concept with manipulatives, gradually transition to the abstract algorithm. The key is ensuring they understand that regrouping is just renaming the same quantity in a more convenient form.

ParentHelpingKid

Parent of 3rd Grader

Question: My child sometimes forgets to include the carried number when adding the next column. What strategies can help them remember?

StudentSupportCoach

Educational Specialist

Answer: Here are several effective strategies to help your child remember to include carried numbers:

Have them circle or highlight the carried number to make it stand out visually
Encourage them to say the carried number out loud as they write it: "I'm carrying the 1 to the tens place"
Teach them to point to the carried number while adding the next column: "1, plus 2, plus 3 equals 6"
Practice with problems that require carrying in every column to build the habit
Use different colored pencils for carried numbers to make them more noticeable

Consistent practice and visual cues will help make including carried numbers automatic over time.

Solved Exercises on Addition with Regrouping in Grade 3

Regrouping Addition Flowchart

Questions & Answers