Solved Exercises on Two-Digit Subtraction Without Regrouping in 2nd Grade

Master two-digit subtraction without regrouping: place value understanding, column subtraction, and mental strategies within 100 through these 5 detailed exercises with visual methods.

Solution: Exercises 1 to 3
1 Basic Place Value Subtraction
Exercise 1
Solve: 47 - 23 = ? Use place value understanding.
4 TENS
40
7 ONES
7
2 TENS
20
3 ONES
3
47
-
23
24
Definition:

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

Place value method:
  1. Separate tens and ones in each number
  2. Subtract the tens
  3. Subtract the ones
  4. Combine the results
Tens
40 - 20
Ones
7 - 3
Total
20 + 4
Step 1: Separate place values

47 = 4 tens + 7 ones, 23 = 2 tens + 3 ones

Step 2: Subtract tens

4 tens - 2 tens = 2 tens (20)

Step 3: Subtract ones

7 ones - 3 ones = 4 ones (4)

Step 4: Combine

20 + 4 = 24

47 - 23 = 24
Final answer:

47 - 23 = 24

Applied rules:

• Place value rule: Always subtract tens with tens and ones with ones

• No borrowing: Minuend ones ≥ subtrahend ones, minuend tens ≥ subtrahend tens

• Column subtraction: Align numbers by place value

2 Column Subtraction Method
Exercise 2
Solve: 68 - 35 = ? Use column subtraction method.
6
8
-
3
5
3
3
Definition:

Column subtraction: Writing numbers vertically and subtracting digits in the same place value columns.

Align
68
Subtract Ones
8 - 5 = 3
Subtract Tens
6 - 3 = 3
Step 1: Write numbers in columns

68 and 35 aligned by place value

Step 2: Subtract ones column

8 - 5 = 3

Step 3: Subtract tens column

6 - 3 = 3

Step 4: Write the answer

33

68 - 35 = 33
Final answer:

68 - 35 = 33

Applied rules:

• Alignment rule: Line up numbers by place value

• Column subtraction: Subtract digits in the same place value column

• No borrowing: Each minuend digit ≥ corresponding subtrahend digit

3 Mental Subtraction Strategy
Exercise 3
Solve: 56 - 24 = ? Use mental subtraction strategy.
5 TENS
50
6 ONES
6
2 TENS
20
4 ONES
4
56
-
24
32
Definition:

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

Tens
50 - 20
Ones
6 - 4
Total
30 + 2
Step 1: Think of tens

50 - 20 = 30

Step 2: Think of ones

6 - 4 = 2

Step 3: Combine mentally

30 + 2 = 32

56 - 24 = 32
Final answer:

56 - 24 = 32

Applied rules:

• Mental breakdown: Separate tens and ones mentally

• Subtract separately: Subtract tens and ones independently

• Recombine: Join the differences together

Two-Digit Subtraction Guide
AB - CD = (A×10 + B) - (C×10 + D) = (A-C)×10 + (B-D)
Place Value Formula
Place Value
Tens - Ones
Separate and Subtract
Column Method
Vertical Alignment
Subtract by Columns
No Regrouping
Minuend > Subtrahend
No Borrowing Needed
AB = A TENS
- C TENS
CD = B ONES
- D ONES
Solution: Exercises 4 to 5
4 Word Problem Application
Exercise 4
Sarah had 79 stickers. She gave 32 stickers to her friend. How many stickers does Sarah have now? Use column subtraction.
7
9
-
3
2
4
7
Definition:

Word problem solving: Translating real-world scenarios into mathematical operations and applying appropriate strategies.

Initial
79
Given Away
32
Remaining
47
Step 1: Identify the numbers

Sarah has 79 stickers, gives away 32

Step 2: Set up the subtraction

79 - 32

Step 3: Subtract ones column

9 - 2 = 7

Step 4: Subtract tens column

7 - 3 = 4

Step 5: State the answer

Sarah has 47 stickers remaining

Sarah has 47 stickers
Final answer:

Sarah has 47 stickers remaining.

Applied rules:

• Problem translation: Convert words to mathematical operations

• Column alignment: Properly align numbers by place value

• Context answer: Include units in the final answer

5 Advanced Two-Digit Subtraction
Exercise 5
Solve: 87 - 43 = ? Which strategy works best? Explain your thinking.
8 TENS
80
7 ONES
7
4 TENS
40
3 ONES
3
87
-
43
44
Definition:

Strategy selection: Choosing the most efficient method based on the numbers involved and personal preference.

Problem
87 - 43
Best Strategy
Column Method
Answer
44
Step 1: Analyze the numbers

We have 87 - 43. Both are two-digit numbers.

Step 2: Check if regrouping is needed

8 ≥ 4 (tens) and 7 ≥ 3 (ones), so no regrouping is needed.

Step 3: Choose strategy

Column subtraction works well for this problem.

Step 4: Subtract ones

7 - 3 = 4

Step 5: Subtract tens

8 - 4 = 4

87 - 43 = 44
Final answer:

87 - 43 = 44. Used column subtraction method.

Applied rules:

• Strategy flexibility: Multiple methods can solve the same problem

• Verification: Check that minuend digits ≥ subtrahend digits

• Method efficiency: Choose the approach that feels most comfortable

Two-Digit Subtraction Properties
(10A + B) - (10C + D) = 10(A-C) + (B-D)
Expanded Form Formula
Key definitions:

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).

Without regrouping: Subtraction where the minuend digits are greater than or equal to the subtrahend digits in each place value.

Column subtraction: Vertical method of subtracting numbers by place value columns.

Subtraction method selection:
  1. Place value method: Break numbers into tens and ones
  2. Column method: Align numbers vertically and subtract by columns
  3. Mental method: Perform calculations mentally using place value
  4. Verification: Check that minuend digits ≥ subtrahend digits
Tip 1: Always align numbers by place value when using column subtraction.
Tip 2: Subtract ones first, then tens when working column by column.
Tip 3: Check that minuend digits are greater than or equal to subtrahend digits to ensure no regrouping is needed.
Tip 4: Use place value understanding to verify your answer.
Common errors: Misaligning numbers, subtracting smaller from larger incorrectly.
Key insight: Understanding place value is fundamental to all subtraction methods.
Important rules:

• Column subtraction: 47 - 23 = 24 (4 tens - 2 tens, 7 ones - 3 ones)

• Place value: 68 = 60 + 8, 35 = 30 + 5, so 68 - 35 = 33

• No regrouping: 56 - 24 = 32 (since 5 ≥ 2 and 6 ≥ 4)

• Verification: Always check that minuend digits ≥ subtrahend digits

Subtraction Method Comparison Chart
Two-Digit Subtraction Methods
Visual comparison of different subtraction methods:
Method 1
Place Value
Method 2
Column
Method 3
Mental

Observation: All methods lead to the same answer but through different processes.

  • Place value: Break numbers into tens and ones, then subtract separately
  • Column method: Align numbers vertically, subtract by place value columns
  • Mental method: Perform calculations mentally using place value understanding
  • Each method reinforces place value concepts and number relationships

Questions & Answers

Question: My child often forgets to align numbers properly when doing column subtraction. How can I help them remember?

Answer: Here are strategies to help with alignment:

  • Visual cues: Use lined paper or draw boxes to contain each digit
  • Place value emphasis: Remind them that ones go under ones, tens go under tens
  • Color coding: Use different colors for tens and ones columns
  • Slow and deliberate: Encourage taking time to write neatly

Practice with grid paper initially to establish proper alignment habits.

Question: How can I help students understand why we subtract tens with tens and ones with ones?

Answer: Use concrete analogies and visual representations:

  • Money analogy: You can't subtract dollars from cents - they're different units
  • Base-10 blocks: Show how tens and ones are separate quantities
  • Grouping concept: We subtract like things from like things (apples from apples)
  • Place value understanding: Emphasize that position determines value

The key is helping students understand that tens and ones represent different quantities.

Question: Are there any games or activities that can help practice two-digit subtraction without regrouping?

Answer: Absolutely! Here are engaging activities:

  • Place value dice: Roll dice to generate two-digit numbers to subtract
  • Subtraction war: Card game where players compete to solve problems fastest
  • Shopping scenarios: Use toy store prices for real-world practice
  • Math relay races: Team challenges with multi-step problems

Make it competitive and fun - children learn best when they're engaged and motivated!