Solved Exercises on Using Place Value to Add and Subtract Worksheets in Grade 2

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

Worksheet Solution: Exercises 1 to 3
1 Addition with place value
Exercise 1
Add using place value strategies:
46 + 28
Definition:

Place value addition: Adding numbers by breaking them into tens and ones, then combining like place values

Addition method:
  1. Break each number into tens and ones
  2. Add the tens together
  3. Add the ones together
  4. Regroup if ones sum to 10 or more
  5. Combine the results
Expression
46 + 28
Break apart
40 + 6 + 20 + 8
Result
74
Step 1: Break numbers into tens and ones

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

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

Step 2: Add the tens together

40 + 20 = 60

Step 3: Add the ones together

6 + 8 = 14

Step 4: Regroup the ones

14 ones = 1 ten + 4 ones

Add this extra ten to our tens: 60 + 10 = 70

Step 5: Combine the results

70 + 4 = 74

46 + 28 = 74
Final answer:

46 + 28 = 74

Applied rules:

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

• Like place values: Only add tens to tens and ones to ones

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

Place Value Addition Visual
📊
Tens Place

46 → 4 tens

28 → 2 tens

Total: 4 + 2 = 6 tens = 60

Ones Place

46 → 6 ones

28 → 8 ones

Total: 6 + 8 = 14 ones

Regroup: 14 = 1 ten + 4 ones

Final Calculation

New tens: 60 + 10 = 70

Final ones: 4

Answer: 70 + 4 = 74

2 Subtraction with regrouping
Exercise 2
Subtract using place value strategies:
53 - 27
Definition:

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

Expression
53 - 27
Break apart
50 + 3 - 20 - 7
Result
26
Step 1: Break numbers into tens and ones

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

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

Step 2: Check if we can subtract ones

3 ones - 7 ones: We cannot subtract 7 from 3!

We need to regroup!

Step 3: Regroup the tens

Borrow 1 ten from 5 tens: 50 becomes 40

Add 10 to the ones: 3 + 10 = 13 ones

Now we have: 40 + 13 - 20 - 7

Step 4: Subtract the tens

40 - 20 = 20

Step 5: Subtract the ones

13 - 7 = 6

Step 6: Combine the results

20 + 6 = 26

53 - 27 = 26
Final answer:

53 - 27 = 26

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

53 → 5 tens + 3 ones

27 → 2 tens + 7 ones

Regrouping Needed

3 ones < 7 ones → Borrow 1 ten

53 → 4 tens + 13 ones

Final Calculation

Tens: 4 - 2 = 2 tens

Ones: 13 - 7 = 6 ones

Answer: 26

3 Mixed operations
Exercise 3
Solve using place value strategies:
45 + 18 - 26
Definition:

Mixed operations: Performing addition and subtraction in sequence using place value strategies

Expression
45 + 18 - 26
Step 1
45 + 18 = 63
Step 2
63 - 26 = 37
Step 1: Add 45 + 18

45 = 40 + 5 (4 tens and 5 ones)

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

Tens: 40 + 10 = 50

Ones: 5 + 8 = 13 (regroup: 1 ten + 3 ones)

50 + 10 = 60, plus 3 ones = 63

Step 2: Subtract 63 - 26

63 = 60 + 3 (6 tens and 3 ones)

26 = 20 + 6 (2 tens and 6 ones)

Check ones: 3 < 6 → need to regroup

63 = 50 + 13 (5 tens and 13 ones)

Tens: 50 - 20 = 30

Ones: 13 - 6 = 7

30 + 7 = 37

Step 3: Final result

45 + 18 - 26 = 37

45 + 18 - 26 = 37
Final answer:

45 + 18 - 26 = 37

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 Strategy
📊
Step 1: Addition

45 + 18

40 + 5 + 10 + 8

= 50 + 13 = 63

Step 2: Subtraction

63 - 26

60 + 3 - 20 - 6

Regroup: 50 + 13 - 20 - 6

= 30 + 7 = 37

Final Answer

45 + 18 - 26 = 37

Complete Summary: Using Place Value to Add and Subtract Worksheets
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: Check your addition by subtracting one addend from the sum.
Tip 6: Check your subtraction by adding the result to the subtrahend.
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
Simple addition (no regrouping):

34 + 25 = (30 + 4) + (20 + 5) = (30 + 20) + (4 + 5) = 50 + 9 = 59

Addition with regrouping:

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

Simple subtraction (no regrouping):

46 - 23 = (40 + 6) - (20 + 3) = (40 - 20) + (6 - 3) = 20 + 3 = 23

Subtraction with regrouping:

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

Worksheet Solution: Exercises 4 to 5
4 Word problem with mixed operations
Exercise 4
Sarah collected 58 seashells at the beach. She gave 24 to her friend and then found 19 more. How many seashells does Sarah have now?
Definition:

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

Expression
58 - 24 + 19
Step 1
58 - 24 = 34
Step 2
34 + 19 = 53
Step 1: Identify the operations in the problem

Sarah starts with 58 seashells

She gives away 24 seashells (subtraction)

She finds 19 more seashells (addition)

This is a mixed operation: 58 - 24 + 19

Step 2: Subtract 58 - 24

58 = 50 + 8 (5 tens and 8 ones)

24 = 20 + 4 (2 tens and 4 ones)

Tens: 50 - 20 = 30

Ones: 8 - 4 = 4

30 + 4 = 34 seashells after giving some away

Step 3: Add 34 + 19

34 = 30 + 4 (3 tens and 4 ones)

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

Tens: 30 + 10 = 40

Ones: 4 + 9 = 13 (regroup: 1 ten + 3 ones)

40 + 10 = 50, plus 3 ones = 53 seashells total

Step 4: State the final answer in context

Sarah has 53 seashells now.

Sarah has 53 seashells now.
Final answer:

Sarah has 53 seashells 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: 58 seashells

Gave away: 24 seashells

Found: 19 more seashells

Operations: Subtraction, then Addition

Step 1: Subtraction

58 - 24

58 = 50 + 8

24 = 20 + 4

Result: 34 seashells

Step 2: Addition

34 + 19

34 = 30 + 4

19 = 10 + 9

Ones: 4 + 9 = 13 (regroup)

Result: 53 seashells

5 Multi-step place value worksheet problem
Exercise 5
A school library has 72 books. They donate 28 books to another school and then receive 35 new books. Later, they lend 19 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

Expression
72 - 28 + 35 - 19
Step 1
72 - 28 = 44
Step 2
44 + 35 = 79
Step 3
79 - 19 = 60
Step 1: Identify the sequence of operations

Start with 72 books

Donate 28 books (subtract)

Receive 35 books (add)

Lend 19 books (subtract)

Expression: 72 - 28 + 35 - 19

Step 2: Subtract 72 - 28

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

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

Check ones: 2 < 8 → need to regroup

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

Tens: 60 - 20 = 40

Ones: 12 - 8 = 4

40 + 4 = 44 books after donation

Step 3: Add 44 + 35

44 = 40 + 4 (4 tens and 4 ones)

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

Tens: 40 + 30 = 70

Ones: 4 + 5 = 9

70 + 9 = 79 books after receiving new ones

Step 4: Subtract 79 - 19

79 = 70 + 9 (7 tens and 9 ones)

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

Tens: 70 - 10 = 60

Ones: 9 - 9 = 0

60 + 0 = 60 books remaining

Step 5: Final answer in context

The library has 60 books now.

The library has 60 books now.
Final answer:

The library has 60 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: 72 books

Step 1: Donate

72 - 28

72 = 60 + 12

28 = 20 + 8

Result: 44 books

Step 2: Receive

44 + 35

44 = 40 + 4

35 = 30 + 5

Result: 79 books

Step 3: Lend

79 - 19

79 = 70 + 9

19 = 10 + 9

Result: 60 books

Questions & Answers

Question: I get confused when I have to add and subtract in the same problem. How do I know what order to do them?

Answer: Great question! When you have both addition and subtraction in the same problem, work from left to right. For example, in 45 + 18 - 26:

  • First, do 45 + 18 = 63
  • Then, do 63 - 26 = 37

Just like reading words from left to right, solve math problems from left to right too! This ensures you get the correct answer.

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. Are there any shortcuts I can learn?

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

  • Adding multiples of 10: Just add the tens digits and keep zeros (e.g., 40 + 30 = 70)
  • Subtracting multiples of 10: Just subtract the tens digits and keep zeros (e.g., 80 - 30 = 50)
  • Compensation: Instead of 43 - 19, think 44 - 20 (add 1 to both numbers)
  • 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.