Solved Exercises on Three Digit Addition with Regrouping in Grade 2

Master three digit addition with regrouping: carrying tens and hundreds, place value understanding, and problem-solving strategies through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic regrouping
Exercise 1
Add: 247 + 168 = ?
Definition:

Regrouping (Carrying): When adding digits results in 10 or more, we carry the extra ten(s) to the next place value column

Addition method with regrouping:
  1. Add digits starting from the ones place
  2. If sum ≥ 10, write the ones digit and carry the tens to the next column
  3. Continue adding in each column, including carried digits
  4. Write the final answer
Expression
247 + 168
Setup
247
+168
----
Step 1: Add the ones place

7 + 8 = 15

Write 5 in the ones place, carry 1 to the tens place

Step 2: Add the tens place

4 + 6 + 1 (carried) = 11

Write 1 in the tens place, carry 1 to the hundreds place

Step 3: Add the hundreds place

2 + 1 + 1 (carried) = 4

Write 4 in the hundreds place

247 + 168 = 415
Final answer:

247 + 168 = 415

Applied rules:

• Place value: Each column represents ones, tens, hundreds

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

• Sequential addition: Work from right to left

Ones

7 + 8 = 15 (1 ten, 5 ones)

→
Carry

Carry 1 ten to tens column

2 Double regrouping
Exercise 2
Add: 379 + 264 = ?
Definition:

Double regrouping: When adding digits in both ones and tens places results in 10 or more, we carry to both the next columns

Expression
379 + 264
Setup
379
+264
----
Step 1: Add the ones place

9 + 4 = 13

Write 3 in the ones place, carry 1 to the tens place

Step 2: Add the tens place

7 + 6 + 1 (carried) = 14

Write 4 in the tens place, carry 1 to the hundreds place

Step 3: Add the hundreds place

3 + 2 + 1 (carried) = 6

Write 6 in the hundreds place

379 + 264 = 643
Final answer:

379 + 264 = 643

Applied rules:

• Double carrying: Both ones and tens columns require regrouping

• Sequential addition: Continue carrying to next columns

• Place value: Each column represents specific value

Ones

9 + 4 = 13 (1 ten, 3 ones)

→
Tens

7 + 6 + 1 = 14 (1 hundred, 4 tens)

3 Triple regrouping
Exercise 3
Add: 589 + 476 = ?
Definition:

Triple regrouping: When adding digits results in carrying across all three place values

Expression
589 + 476
Setup
589
+476
----
Step 1: Add the ones place

9 + 6 = 15

Write 5 in the ones place, carry 1 to the tens place

Step 2: Add the tens place

8 + 7 + 1 (carried) = 16

Write 6 in the tens place, carry 1 to the hundreds place

Step 3: Add the hundreds place

5 + 4 + 1 (carried) = 10

Write 0 in the hundreds place, carry 1 to thousands place

Step 4: Write the thousands place

Carried 1 goes to thousands place

589 + 476 = 1065
Final answer:

589 + 476 = 1065

Applied rules:

• Triple carrying: Ones, tens, and hundreds columns all require regrouping

• Thousands place: When hundreds sum ≥ 10, add thousands place

• Sequential addition: Carry continues to higher place values

Rules and methods, laws,...
Hundreds + Tens + Ones
Place Value Addition
Rule 1
Ones + Ones
Start from rightmost column
Rule 2
If ≥ 10, carry to next
Regroup when sum ≥ 10
Rule 3
Include carried digits
Add previous carries
Key definitions:

Regrouping: Exchanging 10 units of one place value for 1 unit of the next higher place value

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

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

Complete methodology:
  1. Align numbers: Place ones under ones, tens under tens, hundreds under hundreds
  2. Add from right to left: Start with ones place, then tens, then hundreds
  3. Check for regrouping: If sum ≥ 10, write ones digit and carry tens
  4. Include carried digits: Add any carried digits to the next column
  5. Repeat: Continue for each place value column
Tip 1: Draw lines to separate place value columns.
Tip 2: Circle the carried digit to make it visible.
Tip 3: Check your work by adding in reverse order.
Tip 4: Count up to verify your answer makes sense.
Common errors: Forgetting to carry, adding carried digits incorrectly, misaligning columns.
Exam preparation: Practice with various combinations, check work systematically.
Formulas to know by heart:

• Place value: H T O (Hundreds, Tens, Ones)

• Regrouping rule: 10 ones = 1 ten, 10 tens = 1 hundred

• Carrying rule: Write ones digit, carry tens digit

• Addition sequence: Right to left (O → T → H)

Solution: Exercises 4 to 5
4 Word problem
Exercise 4
Sarah has 287 stickers. Her friend gives her 156 more stickers. How many stickers does Sarah have now?
Definition:

Word problem: A mathematical problem presented in a real-world context requiring translation to arithmetic

Problem
287 + 156
Setup
287
+156
----
Solution
443
Step 1: Identify the operation

"gives her more stickers" means addition

So we need to add 287 + 156

Step 2: Add the ones place

7 + 6 = 13

Write 3 in the ones place, carry 1 to the tens place

Step 3: Add the tens place

8 + 5 + 1 (carried) = 14

Write 4 in the tens place, carry 1 to the hundreds place

Step 4: Add the hundreds place

2 + 1 + 1 (carried) = 4

Write 4 in the hundreds place

Sarah has 443 stickers
Final answer:

Sarah has 443 stickers.

Applied rules:

• Word translation: Convert words to mathematical operations

• Regrouping: Apply carrying when sum ≥ 10

• Contextual answer: Include units in the final answer

5 Mixed regrouping
Exercise 5
Add: 428 + 395 = ?
Definition:

Mixed regrouping: Addition where only some place value columns require regrouping

Expression
428 + 395
Setup
428
+395
----
Result
823
Step 1: Add the ones place

8 + 5 = 13

Write 3 in the ones place, carry 1 to the tens place

Step 2: Add the tens place

2 + 9 + 1 (carried) = 12

Write 2 in the tens place, carry 1 to the hundreds place

Step 3: Add the hundreds place

4 + 3 + 1 (carried) = 8

Write 8 in the hundreds place

Step 4: Verify the answer

Estimate: 400 + 400 ≈ 800, so 823 is reasonable

428 + 395 = 823
Final answer:

428 + 395 = 823

Applied rules:

• Selective regrouping: Only regroup when sum ≥ 10

• Verification: Estimate to check reasonableness

• Sequential addition: Maintain place value alignment

Detailed Rules, Methods, Definitions, and Formulas
H T O + H T O = H T O
Place Value Addition
Key definitions:

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

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

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

Three-Digit Number: A number with hundreds, tens, and ones places (e.g., 456)

Complete methodology:
  1. Align numbers vertically: Match ones with ones, tens with tens, hundreds with hundreds
  2. Add from right to left: Start with the ones place, then move to tens, then hundreds
  3. Check for regrouping: If the sum in any column is 10 or greater, carry the tens digit to the next column
  4. Include carried digits: Add any carried digits to the next column's sum
  5. Repeat for each column: Continue the process for all place value columns
  6. Write the final answer: Combine all digits from each column
Tip 1: Always start adding from the rightmost column (ones place).
Tip 2: Circle or highlight carried digits to keep track of them.
Tip 3: Use estimation to check if your answer is reasonable (round numbers and add).
Tip 4: Draw vertical lines to separate place value columns for better organization.
Tip 5: Practice with place value blocks to visualize the regrouping process.
Common errors: Forgetting to carry, adding carried digits incorrectly, misaligning columns, forgetting to add carried digits to the next column.
Key concepts: Understanding that 10 ones equal 1 ten, and 10 tens equal 1 hundred is crucial for regrouping.
Essential formulas and rules:

• Place value positions: H (Hundreds) T (Tens) O (Ones)

• Regrouping rule: When sum ≥ 10, write ones digit and carry tens digit

• Carrying principle: 10 ones = 1 ten, 10 tens = 1 hundred

• Addition sequence: Ones → Tens → Hundreds (right to left)

• Verification method: Estimate the sum to check reasonableness

Examples of Regrouping
Visual Representations
No Regrouping

234 + 125

4+5=9, 3+2=5, 2+1=3

Answer: 359

With Regrouping

287 + 156

7+6=13 (write 3, carry 1)

8+5+1=14 (write 4, carry 1)

2+1+1=4

Answer: 443

Questions & Answers

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

Answer: Great question! The reason we carry is because of our base-10 number system. Each place value can only hold digits 0-9:

  • The ones place can only hold digits 0-9
  • If we get 10 or more in the ones place, we need to convert 10 ones into 1 ten
  • This 1 ten gets moved (carried) to the tens column

Think of it like money: if you have 15 pennies, you can trade 10 pennies for 1 dime. You now have 1 dime and 5 pennies.

Example: In 27 + 15, when we add 7 + 5 = 12, we can't put "12" in the ones place because it takes two digits. So we put the 2 in ones place and carry the 1 to tens place.

Question: My child is struggling with remembering to add the carried number. Do you have any tips to help them remember?

Answer: Yes, here are several effective strategies to help your child remember to add carried numbers:

  • Circle the carry: Have your child circle or draw a circle around the carried number to make it stand out
  • Say it out loud: Encourage saying "and carry 1" or "plus the carry" when adding each column
  • Physical movement: Point to the carried number while adding the next column
  • Use color: Write carried numbers in a different color to make them more visible
  • Practice with manipulatives: Use base-10 blocks to physically show the carrying process

Start with simpler problems and gradually increase difficulty. Consistent practice with visual cues will help build the habit.

Question: Sometimes I forget which direction to go when adding. Should I go left to right or right to left?

Answer: Always go from right to left when adding! This is important for regrouping:

  • Start with the ones place (rightmost column)
  • Then go to the tens place (middle column)
  • Finally go to the hundreds place (leftmost column)

This order is important because when you add the ones place, you might need to carry to the tens place. If you went left to right, you wouldn't know if you needed to change the tens place later.

Remember: Right to Left - Ones, Tens, Hundreds!