Solved Exercises on Two-Digit Addition With Regrouping in 2nd Grade

Master two-digit addition with regrouping: place value understanding, carrying, and column addition within 100 through these 5 detailed exercises with visual methods.

Solution: Exercises 1 to 3
1 Basic Regrouping Concept
Exercise 1
Solve: 28 + 15 = ? Use place value understanding and regrouping.
2 TENS
20
8 ONES
8
1 TEN
10
5 ONES
5
↓
CARRY 1 TEN
from 13 ONES
3 ONES LEFT
8 + 5 = 13
28
+
15
43
Definition:

Regrouping: Converting 10 ones into 1 ten when the sum of ones exceeds 9.

Regrouping method:
  1. Add the ones column
  2. If sum ≥ 10, regroup 10 ones as 1 ten
  3. Write remaining ones in the ones place
  4. Carry the ten to the tens column
  5. Add the tens column including the carried ten
Ones
8 + 5
Regroup
13 = 10 + 3
Carry
1 ten
Step 1: Add ones column

8 + 5 = 13 ones

Step 2: Regroup

13 ones = 1 ten + 3 ones

Step 3: Write ones

Write 3 in the ones place

Step 4: Carry tens

Carry 1 ten to the tens column

Step 5: Add tens column

2 + 1 + 1 (carried) = 4 tens

28 + 15 = 43
Final answer:

28 + 15 = 43

Applied rules:

• Regrouping rule: When ones sum ≥ 10, convert to tens and ones

• Carrying: Move extra tens to the tens column

• Place value: Maintain correct positioning of digits

2 Column Addition With Regrouping
Exercise 2
Solve: 39 + 27 = ? Use column addition method with regrouping.
1
3
9
+
2
7
6
6
Definition:

Column addition with regrouping: Adding digits vertically while carrying excess from one column to the next.

Ones
9 + 7 = 16
Regroup
16 = 10 + 6
Carry
1 to tens
Step 1: Add ones column

9 + 7 = 16

Step 2: Regroup ones

16 ones = 1 ten + 6 ones

Step 3: Write 6 in ones place

Put 6 in the ones column

Step 4: Carry 1 to tens column

Put 1 above the tens column

Step 5: Add tens column

3 + 2 + 1 (carried) = 6

39 + 27 = 66
Final answer:

39 + 27 = 66

Applied rules:

• Column alignment: Line up numbers by place value

• Carry placement: Put carried digit above the next column

• Include carried: Add carried digit to the next column

3 Mental Regrouping Strategy
Exercise 3
Solve: 58 + 24 = ? Use mental regrouping strategy.
5 TENS
50
8 ONES
8
2 TENS
20
4 ONES
4
↓
MENTAL REGROUPING
8 + 4 = 12
12 = 10 + 2
Carry 1 ten
58
+
24
82
Definition:

Mental regrouping: Performing regrouping mentally by breaking numbers into tens and ones.

Ones
8 + 4
Regroup
12 = 10 + 2
Mental Carry
Add 1 to tens
Step 1: Think of tens and ones

58 = 50 + 8, 24 = 20 + 4

Step 2: Add ones mentally

8 + 4 = 12

Step 3: Regroup mentally

12 = 10 + 2, so carry 1 ten

Step 4: Add tens mentally

50 + 20 + 10 (carried) = 80

Step 5: Combine mentally

80 + 2 = 82

58 + 24 = 82
Final answer:

58 + 24 = 82

Applied rules:

• Mental breakdown: Separate tens and ones mentally

• Regroup mentally: Convert excess ones to tens in mind

• Recombine: Join adjusted tens and remaining ones

Regrouping Addition Guide
AB + CD = (A×10 + B) + (C×10 + D) = (A+C+carry)×10 + (B+D-10)
Regrouping Formula
Regrouping
Ones ≥ 10
Convert to Tens
Carrying
Extra Ten
Move to Tens
Column Method
Vertical Addition
With Regrouping
REGROUPING RULE
When ones ≥ 10
Convert to
1 Ten + Rest
Solution: Exercises 4 to 5
4 Word Problem Application
Exercise 4
Emma has 47 stickers. Her friend gives her 36 more stickers. How many stickers does Emma have now? Use column addition with regrouping.
1
4
7
+
3
6
8
3
Definition:

Word problem solving: Translating real-world scenarios into mathematical operations requiring regrouping.

Initial
47
Added
36
Total
83
Step 1: Identify the numbers

Emma has 47 stickers, gets 36 more

Step 2: Set up the addition

47 + 36

Step 3: Add ones column

7 + 6 = 13

Step 4: Regroup

13 ones = 1 ten + 3 ones

Step 5: Carry and add tens

4 + 3 + 1 (carried) = 8 tens

Step 6: State the answer

Emma has 83 stickers in total

Emma has 83 stickers
Final answer:

Emma has 83 stickers altogether.

Applied rules:

• Problem translation: Convert words to mathematical operations

• Regrouping necessity: When ones sum ≥ 10, regroup is required

• Carry management: Include carried digit in tens addition

5 Advanced Regrouping Problem
Exercise 5
Solve: 76 + 18 = ? Which strategy works best? Explain your thinking.
7 TENS
70
6 ONES
6
1 TEN
10
8 ONES
8
↓
REGROUPING NEEDED
6 + 8 = 14
14 = 10 + 4
Carry 1 ten
76
+
18
94
Definition:

Advanced regrouping: Problems where regrouping is necessary and requires careful attention to place value.

Problem
76 + 18
Best Strategy
Column Method
Answer
94
Step 1: Analyze the numbers

We have 76 + 18. Both are two-digit numbers.

Step 2: Check for regrouping

6 + 8 = 14, which is ≥ 10, so regrouping is needed.

Step 3: Regroup ones

14 ones = 1 ten + 4 ones

Step 4: Add tens column

7 + 1 + 1 (carried) = 9 tens

Step 5: Combine results

9 tens + 4 ones = 94

76 + 18 = 94
Final answer:

76 + 18 = 94. Used column addition with regrouping.

Applied rules:

• Regrouping check: Always verify if ones sum ≥ 10

• Carry inclusion: Include carried digit in tens addition

• Place value maintenance: Keep digits in correct positions

Regrouping Addition Properties
(10A + B) + (10C + D) = 10(A+C+E) + (B+D-10)
Where E=1 if B+D≥10
Key definitions:

Regrouping: The process of converting 10 ones into 1 ten when the sum of the ones column equals or exceeds 10.

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

Two-digit number: A number with tens and ones places (e.g., 23, 45, 78).

Place value: The value of a digit based on its position (tens place or ones place).

Regrouping method steps:
  1. Add ones column: Calculate the sum of the ones digits
  2. Check for regrouping: If sum ≥ 10, regroup is needed
  3. Regroup: Convert 10 ones to 1 ten
  4. Carry: Move the extra ten to the tens column
  5. Add tens: Include the carried ten in the tens addition
Tip 1: Always check if the ones sum is 10 or more to determine if regrouping is needed.
Tip 2: Write the carried digit clearly above the tens column to avoid forgetting it.
Tip 3: Practice with base-10 blocks to visualize the regrouping process.
Tip 4: Always verify your answer by checking the place value of each digit.
Common errors: Forgetting to carry, carrying to wrong column, misplacing digits.
Key insight: Regrouping maintains the correct place value and ensures accurate addition.
Important rules:

• Regrouping rule: When ones sum ≥ 10, convert to tens and ones

• Carrying rule: Move extra tens to the tens column

• Place value: Maintain correct positioning of all digits

• Verification: Always check that the sum makes sense

Regrouping Process Chart
Two-Digit Addition With Regrouping Steps
Visual representation of the regrouping process:
AB = A TENS
+ B ONES
CD = C TENS
+ D ONES
IF B+D ≥ 10
THEN CARRY 1

Observation: Regrouping transforms excess ones into tens for accurate addition.

  • Step 1: Add ones column and check if sum ≥ 10
  • Step 2: If needed, regroup 10 ones as 1 ten
  • Step 3: Carry the ten to the tens column
  • Step 4: Add tens column including the carried ten
  • Step 5: Write the final answer with correct place values

Questions & Answers

Question: My child struggles to remember to carry the extra ten when doing regrouping. How can I help them remember?

Answer: Here are strategies to help with carrying:

  • Visual reminders: Have them circle or highlight the carried digit
  • Physical actions: Point to the carried digit when adding the tens column
  • Verbal prompts: Say "don't forget to add the carried ten" out loud
  • Color coding: Use different colors for carried digits

Practice with manipulatives like base-10 blocks to make the concept concrete.

Question: How can I help students understand why we need to regroup when adding?

Answer: Use concrete examples and visual models:

  • Base-10 blocks: Show how 10 ones can be exchanged for 1 ten block
  • Grouping concept: Explain that we can only write 0-9 in each place
  • Real-world analogy: Compare to exchanging 10 singles for a $10 bill
  • Place value emphasis: Reinforce that each position has a maximum of 9

The key is helping students understand that regrouping maintains proper place value.

Question: Are there any games or activities that can help practice two-digit addition with regrouping?

Answer: Absolutely! Here are engaging activities:

  • Regrouping dice: Roll dice to create problems that require regrouping
  • Trading games: Use play money to practice exchanging tens and ones
  • Addition bingo: Create bingo cards with regrouping problems
  • Math relay races: Team challenges with multi-step regrouping problems

Make it hands-on and competitive - children learn best when actively engaged!