Solved Exercises on Using Place Value with Regrouping in Grade 2

Master place value regrouping: tens and ones, addition and subtraction within 100 with regrouping through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Addition with regrouping
Exercise 1
Add using place value strategies with regrouping:
38 + 27
Definition:

Regrouping in addition: Converting 10 or more ones into a new ten when adding

Addition method with regrouping:
  1. Break each number into tens and ones
  2. Add the tens together
  3. Add the ones together
  4. Check if ones sum to 10 or more
  5. If yes, regroup: convert 10 ones to 1 ten
  6. Add the regrouped ten to the tens total
  7. Combine the final tens and ones
Expression
38 + 27
Break apart
30 + 8 + 20 + 7
Result
65
Step 1: Break numbers into tens and ones

38 = 30 + 8 (3 tens and 8 ones)

27 = 20 + 7 (2 tens and 7 ones)

Step 2: Add the tens together

30 + 20 = 50

Step 3: Add the ones together

8 + 7 = 15 ones

Step 4: Check if regrouping is needed

15 ones ≥ 10, so we need to regroup!

Step 5: Regroup the ones

15 ones = 1 ten + 5 ones

Add this extra ten to our tens: 50 + 10 = 60

Step 6: Combine the results

60 + 5 = 65

38 + 27 = 65
Final answer:

38 + 27 = 65

Applied rules:

• Regrouping: When ones add to 10 or more, convert to tens

• Place value: Separate tens and ones to make addition easier

• Combining: Add the final tens and ones together

Addition with Regrouping Visual
📊
Tens Place

38 → 3 tens

27 → 2 tens

Total: 3 + 2 = 5 tens = 50

Ones Place

38 → 8 ones

27 → 7 ones

Total: 8 + 7 = 15 ones

Regroup: 15 = 1 ten + 5 ones

Final Calculation

New tens: 50 + 10 = 60

Final ones: 5

Answer: 60 + 5 = 65

2 Subtraction with regrouping
Exercise 2
Subtract using place value strategies with regrouping:
52 - 37
Definition:

Regrouping in subtraction: Borrowing 1 ten from the tens place to add 10 ones to the ones place when needed

Expression
52 - 37
Break apart
50 + 2 - 30 - 7
Result
15
Step 1: Break numbers into tens and ones

52 = 50 + 2 (5 tens and 2 ones)

37 = 30 + 7 (3 tens and 7 ones)

Step 2: Check if we can subtract ones

2 ones - 7 ones: We cannot subtract 7 from 2!

We need to regroup!

Step 3: Regroup the tens

Borrow 1 ten from 5 tens: 50 becomes 40

Add 10 to the ones: 2 + 10 = 12 ones

Now we have: 40 + 12 - 30 - 7

Step 4: Subtract the tens

40 - 30 = 10

Step 5: Subtract the ones

12 - 7 = 5

Step 6: Combine the results

10 + 5 = 15

52 - 37 = 15
Final answer:

52 - 37 = 15

Applied rules:

• Regrouping: When ones in minuend are less than ones in subtrahend, borrow from tens

• Place value: Separate tens and ones for easier calculation

• Subtraction: Subtract tens from tens and ones from ones

Subtraction with Regrouping
📊
Original Numbers

52 → 5 tens + 2 ones

37 → 3 tens + 7 ones

Regrouping Needed

2 ones < 7 ones → Borrow 1 ten

52 → 4 tens + 12 ones

Final Calculation

Tens: 4 - 3 = 1 ten

Ones: 12 - 7 = 5 ones

Answer: 15

3 Mixed operations with regrouping
Exercise 3
Solve using place value strategies with regrouping:
46 + 28 - 19
Definition:

Mixed operations with regrouping: Performing addition and subtraction in sequence using place value strategies with regrouping when needed

Expression
46 + 28 - 19
Step 1
46 + 28 = 74
Step 2
74 - 19 = 55
Step 1: Add 46 + 28

46 = 40 + 6 (4 tens and 6 ones)

28 = 20 + 8 (2 tens and 8 ones)

Tens: 40 + 20 = 60

Ones: 6 + 8 = 14 (regroup: 1 ten + 4 ones)

60 + 10 = 70, plus 4 ones = 74

Step 2: Subtract 74 - 19

74 = 70 + 4 (7 tens and 4 ones)

19 = 10 + 9 (1 ten and 9 ones)

Check ones: 4 < 9 → need to regroup

74 = 60 + 14 (6 tens and 14 ones)

Tens: 60 - 10 = 50

Ones: 14 - 9 = 5

50 + 5 = 55

Step 3: Final result

46 + 28 - 19 = 55

46 + 28 - 19 = 55
Final answer:

46 + 28 - 19 = 55

Applied rules:

• Order of operations: Perform operations from left to right

• Place value: Break numbers into tens and ones for each operation

• Regrouping: Apply when necessary in both addition and subtraction

Mixed Operations with Regrouping
📊
Step 1: Addition

46 + 28

40 + 6 + 20 + 8

= 60 + 14 = 74

Step 2: Subtraction

74 - 19

70 + 4 - 10 - 9

Regroup: 60 + 14 - 10 - 9

= 50 + 5 = 55

Final Answer

46 + 28 - 19 = 55

Complete Summary: Using Place Value with Regrouping
AB ± CD = (A×10 + B) ± (C×10 + D)
Place Value Operations Formula
Key definitions:

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

Tens place: The second digit from the right, representing groups of ten

Ones place: The rightmost digit, representing individual units

Regrouping: Converting between tens and ones when performing operations

Minuend: The number being subtracted from (top number)

Subtrahend: The number being subtracted (bottom number)

Expanded form: Writing a number as the sum of its place values (e.g., 45 = 40 + 5)

Complete methodology:
  1. Recognize the operation: Determine if addition or subtraction is needed
  2. Break apart numbers: Write each number in expanded form (tens + ones)
  3. For addition: Add tens with tens and ones with ones
  4. For subtraction: Check if regrouping is needed
  5. Regroup if necessary: Convert between tens and ones when needed
  6. Combine results: Add the final tens and ones together
Tip 1: Always write out the expanded form (tens + ones) to visualize the problem.
Tip 2: In addition, if ones add to 10 or more, regroup into tens.
Tip 3: In subtraction, if ones in minuend are less than ones in subtrahend, regroup.
Tip 4: Use base-10 blocks or drawings to physically represent tens and ones.
Tip 5: Remember that 1 ten = 10 ones when regrouping.
Common errors: Adding tens to ones, forgetting to regroup when needed, borrowing incorrectly.
Key concepts: 1 ten = 10 ones, only operate on like place values, regrouping preserves value.
Memorization tips: "More than 9 ones? Make a new ten!" for addition. "Not enough ones? Borrow from tens!" for subtraction.
Essential rules to remember:

• Place value formula: Two-digit number AB = A×10 + B

• Addition rule: (T₁ + O₁) + (T₂ + O₂) = (T₁ + T₂) + (O₁ + O₂)

• Subtraction rule: (T₁ + O₁) - (T₂ + O₂) = (T₁ - T₂) + (O₁ - O₂)

• Regrouping rules: When O₁ + O₂ ≥ 10 in addition or O₁ < O₂ in subtraction

• Like place values: Only operate on tens with tens and ones with ones

Examples progression
Addition with regrouping:

38 + 27 = (30 + 8) + (20 + 7) = (30 + 20) + (8 + 7) = 50 + 15 = 50 + 10 + 5 = 65

Subtraction with regrouping:

52 - 37 = (50 + 2) - (30 + 7) = (40 + 12) - (30 + 7) = (40 - 30) + (12 - 7) = 10 + 5 = 15

Mixed operations with regrouping:

46 + 28 - 19 = 74 - 19 = (70 + 4) - (10 + 9) = (60 + 14) - (10 + 9) = 55

Solution: Exercises 4 to 5
4 Word problem with regrouping
Exercise 4
Tom had 53 marbles. He gave 28 marbles to his friend and then found 19 more marbles. How many marbles does Tom have now?
Definition:

Word problems: Real-life situations requiring mathematical operations using place value strategies with regrouping

Expression
53 - 28 + 19
Step 1
53 - 28 = 25
Step 2
25 + 19 = 44
Step 1: Identify the operations in the problem

Tom starts with 53 marbles

He gives away 28 marbles (subtraction)

He finds 19 more marbles (addition)

This is a mixed operation: 53 - 28 + 19

Step 2: Subtract 53 - 28

53 = 50 + 3 (5 tens and 3 ones)

28 = 20 + 8 (2 tens and 8 ones)

Check ones: 3 < 8 → need to regroup

53 = 40 + 13 (4 tens and 13 ones)

Tens: 40 - 20 = 20

Ones: 13 - 8 = 5

20 + 5 = 25 marbles after giving some away

Step 3: Add 25 + 19

25 = 20 + 5 (2 tens and 5 ones)

19 = 10 + 9 (1 ten and 9 ones)

Tens: 20 + 10 = 30

Ones: 5 + 9 = 14 (regroup: 1 ten + 4 ones)

30 + 10 = 40, plus 4 ones = 44 marbles total

Step 4: State the final answer in context

Tom has 44 marbles now.

Tom has 44 marbles now.
Final answer:

Tom has 44 marbles now.

Applied rules:

• Problem solving: Identify operations needed from context

• Place value: Break numbers into tens and ones

• Regrouping: Apply when necessary in both operations

Word Problem Strategy
📊
Given Information

Started with: 53 marbles

Gave away: 28 marbles

Found: 19 more marbles

Operations: Subtraction, then Addition

Step 1: Subtraction

53 - 28

53 = 40 + 13

28 = 20 + 8

Result: 25 marbles

Step 2: Addition

25 + 19

25 = 20 + 5

19 = 10 + 9

Ones: 5 + 9 = 14 (regroup)

Result: 44 marbles

5 Multi-step place value with regrouping problem
Exercise 5
A school library has 64 books. They donate 29 books to another school and then receive 37 new books. Later, they lend 18 books to students. How many books are in the library now?
Definition:

Multi-step problems: Problems requiring multiple operations solved sequentially using place value strategies with regrouping

Expression
64 - 29 + 37 - 18
Step 1
64 - 29 = 35
Step 2
35 + 37 = 72
Step 3
72 - 18 = 54
Step 1: Identify the sequence of operations

Start with 64 books

Donate 29 books (subtract)

Receive 37 books (add)

Lend 18 books (subtract)

Expression: 64 - 29 + 37 - 18

Step 2: Subtract 64 - 29

64 = 60 + 4 (6 tens and 4 ones)

29 = 20 + 9 (2 tens and 9 ones)

Check ones: 4 < 9 → need to regroup

64 = 50 + 14 (5 tens and 14 ones)

Tens: 50 - 20 = 30

Ones: 14 - 9 = 5

30 + 5 = 35 books after donation

Step 3: Add 35 + 37

35 = 30 + 5 (3 tens and 5 ones)

37 = 30 + 7 (3 tens and 7 ones)

Tens: 30 + 30 = 60

Ones: 5 + 7 = 12 (regroup: 1 ten + 2 ones)

60 + 10 = 70, plus 2 ones = 72 books after receiving new ones

Step 4: Subtract 72 - 18

72 = 70 + 2 (7 tens and 2 ones)

18 = 10 + 8 (1 ten and 8 ones)

Check ones: 2 < 8 → need to regroup

72 = 60 + 12 (6 tens and 12 ones)

Tens: 60 - 10 = 50

Ones: 12 - 8 = 4

50 + 4 = 54 books remaining

Step 5: Final answer in context

The library has 54 books now.

The library has 54 books now.
Final answer:

The library has 54 books now.

Applied rules:

• Order of operations: Work from left to right for mixed operations

• Place value: Break each number into tens and ones

• Regrouping: Apply when necessary in each operation

Multi-Step Problem Strategy
📊
Initial Books

Start: 64 books

Step 1: Donate

64 - 29

64 = 50 + 14

29 = 20 + 9

Result: 35 books

Step 2: Receive

35 + 37

35 = 30 + 5

37 = 30 + 7

Ones: 5 + 7 = 12 (regroup)

Result: 72 books

Step 3: Lend

72 - 18

72 = 60 + 12

18 = 10 + 8

Result: 54 books

Questions & Answers

Question: I don't understand when I need to regroup. Can you explain?

Answer: Great question! You need to regroup in two situations:

  • In addition: When the ones add to 10 or more (like 8 + 7 = 15)
  • In subtraction: When the top number's ones are less than the bottom number's ones (like 2 ones vs 7 ones)

Think of regrouping as "making exchanges": 10 ones = 1 ten, or borrowing 1 ten = 10 ones.

Question: My child sometimes forgets to regroup when they should. How can I help them remember?

Answer: Here are some strategies to help your child remember when to regroup:

  • Have them always check the ones first: "Do I have enough ones to subtract?" or "Will my ones add to 10 or more?"
  • Create a chant: "More on the floor, go next door" (for subtraction) or "More than 9, make a new ten" (for addition)
  • Use physical manipulatives like base-10 blocks to visualize the process
  • Draw circles around the ones in both numbers and compare them before starting

Practice with simple problems first: 32 - 15, 41 - 18, 28 + 17, etc., before moving to larger numbers.

Remind them that regrouping doesn't change the value, just how it's written!

Question: I want to get faster at place value operations with regrouping. Are there any shortcuts I can learn?

Answer: Once you master the basics, here are some mental math shortcuts for advanced learners:

  • Compensation: Instead of 43 - 19, think 44 - 20 (add 1 to both numbers)
  • Make tens: In 27 + 8, think 27 + 3 + 5 = 30 + 5 = 35
  • Patterns: Notice that adding 9 is like adding 10 and subtracting 1

But remember, these shortcuts work because of place value! Always understand the underlying concept first.

Practice with timed drills once you're comfortable with the basic strategies to build speed and accuracy.