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

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

Solution: Exercises 1 to 3
1 Basic Regrouping Concept
Exercise 1
Solve: 52 - 18 = ? Use place value understanding and regrouping.
5 TENS
50
2 ONES
2
1 TEN
10
8 ONES
8
↓
BORROW 1 TEN
from 5 tens
ADD to ONES
2 + 10 = 12
52
-
18
34
Definition:

Regrouping (Borrowing): Converting 1 ten into 10 ones when the minuend ones are less than the subtrahend ones.

Regrouping method:
  1. Check if minuend ones < subtrahend ones
  2. If yes, borrow 1 ten from the tens place
  3. Convert the borrowed ten to 10 ones
  4. Add to the ones place
  5. Subtract the ones
  6. Subtract the tens (with 1 less from borrowing)
Ones
2 < 8
Borrow
1 ten = 10 ones
New Ones
2 + 10 = 12
Step 1: Check ones column

2 < 8, so we need to regroup

Step 2: Borrow from tens

Take 1 ten from 5 tens, leaving 4 tens

Step 3: Convert to ones

1 ten = 10 ones, add to 2 ones = 12 ones

Step 4: Subtract ones

12 - 8 = 4

Step 5: Subtract tens

4 - 1 = 3

52 - 18 = 34
Final answer:

52 - 18 = 34

Applied rules:

• Regrouping rule: When ones minuend < ones subtrahend, borrow from tens

• Borrowing: 1 ten = 10 ones

• Place value: Maintain correct positioning of digits

2 Column Subtraction With Regrouping
Exercise 2
Solve: 71 - 26 = ? Use column subtraction method with regrouping.
4
11
7
1
-
2
6
4
5
Definition:

Column subtraction with regrouping: Subtracting digits vertically while borrowing from one column to the next.

Ones
1 < 6
Borrow
7→6, 1→11
Subtract
11-6=5, 6-2=4
Step 1: Check ones column

1 < 6, so we need to borrow

Step 2: Borrow from tens

7 tens becomes 6 tens, 1 one becomes 11 ones

Step 3: Subtract ones

11 - 6 = 5

Step 4: Subtract tens

6 - 2 = 4

71 - 26 = 45
Final answer:

71 - 26 = 45

Applied rules:

• Column alignment: Line up numbers by place value

• Borrow placement: Adjust digits appropriately when borrowing

• Subtract borrowed: Account for the borrowed digit in the calculation

3 Mental Regrouping Strategy
Exercise 3
Solve: 63 - 28 = ? Use mental regrouping strategy.
6 TENS
60
3 ONES
3
2 TENS
20
8 ONES
8
↓
MENTAL BORROWING
3 < 8, so borrow
MENTAL SUBTRACTION
13-8=5, 5-2=3
63
-
28
35
Definition:

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

Ones
3 < 8
Borrow Mentally
60→50, 3→13
Mental Calculation
13-8=5, 50-20=30
Step 1: Think of tens and ones

63 = 60 + 3, 28 = 20 + 8

Step 2: Check if borrowing needed

3 < 8, so we need to borrow

Step 3: Borrow mentally

Take 1 ten from 6 tens = 5 tens, add to 3 ones = 13 ones

Step 4: Subtract mentally

13 - 8 = 5, 50 - 20 = 30

Step 5: Combine mentally

30 + 5 = 35

63 - 28 = 35
Final answer:

63 - 28 = 35

Applied rules:

• Mental breakdown: Separate tens and ones mentally

• Regroup mentally: Convert 1 ten to 10 ones in mind

• Recombine: Join adjusted tens and ones after subtraction

Regrouping Subtraction Guide
AB - CD = (A×10 + B) - (C×10 + D) = (A-1-C)×10 + (B+10-D)
Regrouping Formula
Regrouping
Ones Minuend < Onessubtrahend
Borrow from Tens
Borrowing
1 Ten = 10 Ones
Convert to Ones
Column Method
Vertical Subtraction
With Regrouping
REGROUPING RULE
When ones minuend < ones subtrahend
Borrow 1 Ten
Convert to 10 Ones
Solution: Exercises 4 to 5
4 Word Problem Application
Exercise 4
Emma had 84 stickers. She gave 37 stickers to her friend. How many stickers does Emma have now? Use column subtraction with regrouping.
7
14
8
4
-
3
7
4
7
Definition:

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

Initial
84
Given Away
37
Remaining
47
Step 1: Identify the numbers

Emma has 84 stickers, gives away 37

Step 2: Set up the subtraction

84 - 37

Step 3: Check ones column

4 < 7, so we need to borrow

Step 4: Borrow from tens

8 tens becomes 7 tens, 4 ones becomes 14 ones

Step 5: Subtract ones

14 - 7 = 7

Step 6: Subtract tens

7 - 3 = 4

Step 7: State the answer

Emma has 47 stickers remaining

Emma has 47 stickers
Final answer:

Emma has 47 stickers remaining.

Applied rules:

• Problem translation: Convert words to mathematical operations

• Regrouping necessity: When ones minuend < ones subtrahend, regroup is required

• Borrow management: Adjust both tens and ones digits appropriately

5 Advanced Regrouping Problem
Exercise 5
Solve: 92 - 47 = ? Which strategy works best? Explain your thinking.
9 TENS
90
2 ONES
2
4 TENS
40
7 ONES
7
↓
REGROUPING NEEDED
2 < 7
90→80, 2→12
Subtract: 12-7=5, 8-4=4
92
-
47
45
Definition:

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

Problem
92 - 47
Best Strategy
Column Method
Answer
45
Step 1: Analyze the numbers

We have 92 - 47. Both are two-digit numbers.

Step 2: Check for regrouping

2 < 7, so regrouping is needed.

Step 3: Borrow from tens

Take 1 ten from 9 tens = 8 tens, add to 2 ones = 12 ones

Step 4: Subtract ones

12 - 7 = 5

Step 5: Subtract tens

8 - 4 = 4

Step 6: Combine results

4 tens + 5 ones = 45

92 - 47 = 45
Final answer:

92 - 47 = 45. Used column subtraction with regrouping.

Applied rules:

• Regrouping check: Always verify if ones minuend < ones subtrahend

• Borrow adjustment: Reduce tens by 1, increase ones by 10

• Place value maintenance: Keep digits in correct positions

Regrouping Subtraction Properties
(10A + B) - (10C + D) = 10(A-1-C) + (B+10-D)
Where B < D
Key definitions:

Regrouping: The process of converting 1 ten into 10 ones when the minuend ones are less than the subtrahend ones.

Borrowing: Taking 1 ten from the tens place to add to the ones place.

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. Check ones column: Is minuend ones < subtrahend ones?
  2. Check for regrouping: If yes, regroup is needed
  3. Borrow: Take 1 ten from tens place
  4. Convert: Add 10 to the ones place
  5. Subtract ones: Now subtract the ones
  6. Subtract tens: Subtract tens with 1 less from borrowing
Tip 1: Always check if the minuend ones are less than subtrahend ones to determine if regrouping is needed.
Tip 2: Write the adjusted digits clearly to avoid forgetting the borrowing.
Tip 3: Practice with base-10 blocks to visualize the regrouping process.
Tip 4: Always verify your answer by adding the result to the subtrahend to check if it equals the minuend.
Common errors: Forgetting to borrow, borrowing incorrectly, misplacing digits.
Key insight: Regrouping maintains the correct place value and ensures accurate subtraction.
Important rules:

• Regrouping rule: When ones minuend < ones subtrahend, borrow from tens

• Borrowing rule: 1 ten = 10 ones

• Place value: Maintain correct positioning of all digits

• Verification: Always check that the difference makes sense

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

Observation: Regrouping transforms 1 ten into 10 ones for accurate subtraction.

  • Step 1: Check if ones minuend < ones subtrahend
  • Step 2: If needed, borrow 1 ten from tens place
  • Step 3: Add 10 to the ones place
  • Step 4: Subtract the ones
  • Step 5: Subtract the tens (with 1 less from borrowing)
  • Step 6: Write the final answer with correct place values

Questions & Answers

Question: My child struggles to remember to borrow when doing regrouping. How can I help them remember?

Answer: Here are strategies to help with borrowing:

  • Visual reminders: Have them circle or highlight when borrowing is needed
  • Physical actions: Cross out the original digit and write the new one
  • Verbal prompts: Say "borrow 1 ten" out loud when regrouping
  • Color coding: Use different colors for borrowed 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 subtracting?

Answer: Use concrete examples and visual models:

  • Base-10 blocks: Show how 1 ten block can be exchanged for 10 one blocks
  • Grouping concept: Explain that we need enough ones to subtract
  • Real-world analogy: Compare to exchanging a $10 bill for 10 singles
  • Place value emphasis: Reinforce that each position must have enough to subtract

The key is helping students understand that regrouping provides enough to subtract.

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

Answer: Absolutely! Here are engaging activities:

  • Regrouping dice: Roll dice to create problems that require regrouping
  • Borrowing games: Use play money to practice exchanging tens and ones
  • Subtraction 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!