Solved Exercises on Two-Digit Addition with Regrouping in Grade 2

Master two-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:
\(27 + 35\)
Definition:

Regrouping (Carrying): When adding ones and the sum is 10 or more, carry the tens to the tens column

Addition method:
  1. Add the ones column first
  2. If ones sum ≥ 10, carry the tens to the tens column
  3. Add the tens column including any carried amount
  4. Write the final answer
Expression
\(27 + 35\)
Setup
27
+35
--
Result
\(62\)
Step 1: Add the ones column

\(7 + 5 = 12\)

Step 2: Regroup because 12 ≥ 10

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

Step 3: Add the tens column

\(2 + 3 + 1\) (carried) \(= 6\)

Step 4: Write the final answer

Combine tens and ones: \(62\)

\(27 + 35 = 62\)
Final answer:

\(27 + 35 = 62\)

Applied rules:

• Place Value: Ones and tens columns must be aligned

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

• Addition: Add each column separately starting from right

2 Multiple regrouping
Exercise 2
Add:
\(48 + 27\)
Definition:

Multiple regrouping: When adding ones results in 10 or more, we must regroup/carry

Expression
\(48 + 27\)
Setup
48
+27
--
Result
\(75\)
Step 1: Add the ones column

\(8 + 7 = 15\)

Step 2: Regroup because 15 ≥ 10

Write down 5 in ones place, carry 1 to tens column

Step 3: Add the tens column

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

Step 4: Write the final answer

Combine tens and ones: \(75\)

\(48 + 27 = 75\)
Final answer:

\(48 + 27 = 75\)

Applied rules:

• Regrouping: Any sum of 10 or more in ones column requires carrying

• Place Value: Each digit represents its place value

• Addition: Always add from right to left

3 Verification
Exercise 3
Add:
\(56 + 19\)
Definition:

Verification: Check your answer by using another method

Expression
\(56 + 19\)
Setup
56
+19
--
Result
\(75\)
Step 1: Add the ones column

\(6 + 9 = 15\)

Step 2: Regroup because 15 ≥ 10

Write down 5 in ones place, carry 1 to tens column

Step 3: Add the tens column

\(5 + 1 + 1\) (carried) \(= 7\)

Step 4: Write the final answer

Combine tens and ones: \(75\)

Step 5: Verify the answer

Estimate: \(56 ≈ 60\), \(19 ≈ 20\), so \(60 + 20 = 80\). Our answer \(75\) is close!

\(56 + 19 = 75\)
Final answer:

\(56 + 19 = 75\)

Applied rules:

• Regrouping: Always carry when ones sum ≥ 10

• Verification: Estimate to check reasonableness

• Place Value: Keep digits in correct columns

Rules and methods, laws,...
\(27 + 35 = 62\)
Two-Digit Addition with Regrouping
Step 1
Add Ones
Add digits in ones column
Step 2
Regroup
Carry tens if sum ≥ 10
Step 3
Add Tens
Add digits in tens column
Key definitions:

Regrouping: Exchanging 10 ones for 1 ten when adding

Place Value: Each digit has a value based on its position

Carrying: Moving extra tens to the next column

Complete methodology:
  1. Align numbers: Put ones under ones, tens under tens
  2. Add ones: Start from the rightmost column
  3. Check for regrouping: If sum ≥ 10, carry to tens column
  4. Add tens: Include any carried tens
  5. Write answer: Combine tens and ones
Tip 1: Always start adding from the ones column.
Tip 2: Remember to add carried tens to the tens column.
Tip 3: Check your answer by estimating.
Common errors: Forgetting to carry, misaligning columns, adding from left to right.
Key concepts: Place value, regrouping, carrying, column alignment.
Rules to remember:

• Alignment: Ones under ones, tens under tens

• Start from right: Add ones column first

• Regroup when needed: Carry tens if ones sum ≥ 10

• Include carries: Add carried tens to tens column

• Check your work: Verify with estimation

Solution: Exercises 4 to 5
4 Word problem
Exercise 4
Sarah has 38 stickers and Tom has 45 stickers. How many stickers do they have altogether?
Definition:

Word problems: Real-life situations requiring mathematical operations

Problem
\(38 + 45\)
Setup
38
+45
--
Result
\(83\)
Step 1: Identify the operation

"Altogether" means addition: \(38 + 45\)

Step 2: Add the ones column

\(8 + 5 = 13\)

Step 3: Regroup because 13 ≥ 10

Write down 3 in ones place, carry 1 to tens column

Step 4: Add the tens column

\(3 + 4 + 1\) (carried) \(= 8\)

Step 5: Write the final answer

They have 83 stickers altogether.

\(38 + 45 = 83\)
Final answer:

Sarah and Tom have 83 stickers altogether.

Applied rules:

• Word Problem Strategy: Identify key words indicating operation

• Regrouping: Carry when ones sum ≥ 10

• Context: Answer in context of the problem

5 Mixed review
Exercise 5
Add:
\(64 + 28\)
Definition:

Mixed review: Practice combining different skills learned

Expression
\(64 + 28\)
Setup
64
+28
--
Result
\(92\)
Step 1: Add the ones column

\(4 + 8 = 12\)

Step 2: Regroup because 12 ≥ 10

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

Step 3: Add the tens column

\(6 + 2 + 1\) (carried) \(= 9\)

Step 4: Write the final answer

Combine tens and ones: \(92\)

Step 5: Verify with estimation

Estimate: \(64 ≈ 60\), \(28 ≈ 30\), so \(60 + 30 = 90\). Our answer \(92\) is reasonable!

\(64 + 28 = 92\)
Final answer:

\(64 + 28 = 92\)

Applied rules:

• Regrouping: Always carry when ones sum ≥ 10

• Verification: Use estimation to check reasonableness

• Place Value: Keep digits in correct columns

Comprehensive Guide to Two-Digit Addition with Regrouping
\(AB + CD = EF\)
Where B+D ≥ 10 requires regrouping
Key definitions:

Regrouping: The process of exchanging 10 units of one place value for 1 unit of the next higher place value

Carrying: Moving the extra tens from the ones column to the tens column

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

Complete methodology:
  1. Set up the problem: Write numbers vertically with ones under ones and tens under tens
  2. Add the ones column: Add the digits in the ones place
  3. Check for regrouping: If the sum is 10 or greater, write down the ones digit and carry the tens digit
  4. Add the tens column: Add the digits in the tens place plus any carried tens
  5. Write the final answer: Combine the tens and ones digits
Tip 1: Always start from the ones column when adding.
Tip 2: Draw lines to separate columns for better organization.
Tip 3: Circle the number you're carrying to keep track.
Tip 4: Practice with manipulatives like base-ten blocks to visualize regrouping.
Common errors: Forgetting to carry, adding carried tens incorrectly, misaligning columns.
Success strategies: Practice regularly, check work, use visual aids, estimate answers.
Essential rules:

• Column alignment: Ones under ones, tens under tens

• Right-to-left addition: Always start from the rightmost column

• Regrouping condition: When ones sum ≥ 10, carry to tens column

• Include carries: Add any carried tens to the tens column

• Verification: Always check your answer using estimation

Questions & Answers

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

Answer: Great question! We carry because of our place value system. In the decimal system:

  • Each place can only hold digits 0-9
  • When we have 10 or more ones, we group them into tens
  • For example, if we get 12 ones, that's really 1 ten and 2 ones

Think of it like money: if you have 12 one-dollar bills, you could trade 10 of them for a ten-dollar bill. Now you have 1 ten-dollar bill and 2 one-dollar bills. That's exactly what carrying does!

In \(27 + 35\), when we add \(7 + 5 = 12\), we're saying we have 12 ones. We write 2 in the ones place and carry 1 to the tens place because 12 ones = 1 ten + 2 ones.

Question: My child struggles with remembering to add the carried number. What's the best way to help them remember?

Answer: Here are several effective strategies to help with remembering to carry:

  • Circle the carry: Have your child circle the number they're carrying to make it stand out
  • Write it small: Write the carried number in a smaller size above the tens column
  • Count aloud: "Now I add the tens: 2 + 3 plus the 1 I carried..."
  • Use manipulatives: Base-ten blocks help visualize the carrying process

Another helpful tip is to have your child say the full equation after carrying: "I have 2 in the tens column, plus 3 in the tens column, plus the 1 I carried, which equals 6."

Practice with smaller problems first, then gradually increase difficulty as the concept becomes automatic.

Question: Does the carrying rule apply to bigger numbers too, like hundreds?

Answer: Yes, absolutely! The carrying principle works for numbers of any size. It's the same pattern:

  • When ones column adds to ≥ 10, carry to tens column
  • When tens column adds to ≥ 10, carry to hundreds column
  • When hundreds column adds to ≥ 10, carry to thousands column
  • This continues for larger place values

For example, in \(156 + 278\):
Ones: \(6 + 8 = 14\), write 4, carry 1
Tens: \(5 + 7 + 1\) (carried) \(= 13\), write 3, carry 1
Hundreds: \(1 + 2 + 1\) (carried) \(= 4\)
Answer: \(434\)

The same place value principles apply regardless of how many digits you're adding!