Expanded Form with Regrouping for Grade 1

Master expanded form with regrouping: place value understanding, step-by-step methods, and detailed solutions through these 5 exercises.

Expanded Form with Regrouping

Visual Guide to Understanding Place Value Regrouping

🔄
Regrouping
1 ten = 10 ones
🔟
Tens Place
Groups of 10
1️⃣
Ones Place
Individual units
📝
Expanded Form
Break numbers into parts
1
Identify Need for Regrouping
2
Convert 1 Ten to 10 Ones
3
Adjust Place Values
4
Complete Operation
42 = 40 + 2
→
30 + 12
→
Regroup: 1 ten → 10 ones
Worksheet: Exercises 1 to 3 with Regrouping
1 Basic Regrouping
Exercise 1
Solve: 42 - 17 using expanded form with regrouping
Definition:

Regrouping: Converting 1 ten into 10 ones when needed for subtraction

Regrouping Method:
  1. Write both numbers in expanded form
  2. Check if ones in minuend ≥ ones in subtrahend
  3. If not, regroup by converting 1 ten to 10 ones
  4. Subtract the ones, then subtract the tens
  5. Combine results to get final answer
Step 1: Write in expanded form

42 = 40 + 2

17 = 10 + 7

Step 2: Check if regrouping is needed

We need to subtract: (40 + 2) - (10 + 7)

Check: 2 ones < 7 ones, so we need to regroup!

Step 3: Regroup 42

Take 1 ten from 40, convert to 10 ones

42 = 40 + 2 = 30 + 10 + 2 = 30 + 12

Step 4: Subtract ones

12 ones - 7 ones = 5 ones

Step 5: Subtract tens

30 tens - 10 tens = 20 tens

Step 6: Combine results

20 + 5 = 25

42 - 17 = 25
Final Answer:

42 - 17 = 25

Applied Rules:

• Regrouping: When ones in minuend < ones in subtrahend

• Place Value: Tens and ones subtracted separately

• Conversion: 1 ten = 10 ones

2 Intermediate Regrouping
Exercise 2
Solve: 53 - 28 using expanded form with regrouping
Step 1: Write in expanded form

53 = 50 + 3

28 = 20 + 8

Step 2: Check if regrouping is needed

We need to subtract: (50 + 3) - (20 + 8)

Check: 3 ones < 8 ones, so we need to regroup!

Step 3: Regroup 53

Take 1 ten from 50, convert to 10 ones

53 = 50 + 3 = 40 + 10 + 3 = 40 + 13

Step 4: Subtract ones

13 ones - 8 ones = 5 ones

Step 5: Subtract tens

40 tens - 20 tens = 20 tens

Step 6: Combine results

20 + 5 = 25

53 - 28 = 25
Final Answer:

53 - 28 = 25

Applied Rules:

• Regrouping: When ones in minuend < ones in subtrahend

• Place Value: Tens and ones subtracted separately

• Verification: Check by adding: 25 + 28 = 53 ✓

3 Practice Regrouping
Exercise 3
Solve: 61 - 29 using expanded form with regrouping
Step 1: Write in expanded form

61 = 60 + 1

29 = 20 + 9

Step 2: Check if regrouping is needed

We need to subtract: (60 + 1) - (20 + 9)

Check: 1 ones < 9 ones, so we need to regroup!

Step 3: Regroup 61

Take 1 ten from 60, convert to 10 ones

61 = 60 + 1 = 50 + 10 + 1 = 50 + 11

Step 4: Subtract ones

11 ones - 9 ones = 2 ones

Step 5: Subtract tens

50 tens - 20 tens = 30 tens

Step 6: Combine results

30 + 2 = 32

61 - 29 = 32
Final Answer:

61 - 29 = 32

Applied Rules:

• Regrouping: When ones in minuend < ones in subtrahend

• Place Value: Tens and ones subtracted separately

• Verification: Check by adding: 32 + 29 = 61 ✓

Worksheet: Exercises 4 to 5 with Regrouping
4 Advanced Regrouping
Exercise 4
Solve: 72 - 37 using expanded form with regrouping
Step 1: Write in expanded form

72 = 70 + 2

37 = 30 + 7

Step 2: Check if regrouping is needed

We need to subtract: (70 + 2) - (30 + 7)

Check: 2 ones < 7 ones, so we need to regroup!

Step 3: Regroup 72

Take 1 ten from 70, convert to 10 ones

72 = 70 + 2 = 60 + 10 + 2 = 60 + 12

Step 4: Subtract ones

12 ones - 7 ones = 5 ones

Step 5: Subtract tens

60 tens - 30 tens = 30 tens

Step 6: Combine results

30 + 5 = 35

72 - 37 = 35
Final Answer:

72 - 37 = 35

Applied Rules:

• Regrouping: When ones in minuend < ones in subtrahend

• Place Value: Tens and ones subtracted separately

• Verification: Check by adding: 35 + 37 = 72 ✓

5 Challenge Regrouping
Exercise 5
Solve: 84 - 46 using expanded form with regrouping
Step 1: Write in expanded form

84 = 80 + 4

46 = 40 + 6

Step 2: Check if regrouping is needed

We need to subtract: (80 + 4) - (40 + 6)

Check: 4 ones < 6 ones, so we need to regroup!

Step 3: Regroup 84

Take 1 ten from 80, convert to 10 ones

84 = 80 + 4 = 70 + 10 + 4 = 70 + 14

Step 4: Subtract ones

14 ones - 6 ones = 8 ones

Step 5: Subtract tens

70 tens - 40 tens = 30 tens

Step 6: Combine results

30 + 8 = 38

84 - 46 = 38
Final Answer:

84 - 46 = 38

Applied Rules:

• Regrouping: When ones in minuend < ones in subtrahend

• Place Value: Tens and ones subtracted separately

• Verification: Check by adding: 38 + 46 = 84 ✓

Comprehensive Summary: Expanded Form with Regrouping

Complete Guide to Expanded Form with Regrouping

This summary provides a comprehensive overview of expanded form with regrouping, covering all essential concepts, methods, and practice strategies.

Key Definitions
  • Regrouping: Converting 1 ten into 10 ones when needed for subtraction
  • Minuend: The number being subtracted from (the larger number)
  • Subtrahend: The number being subtracted (the smaller number)
  • Difference: The result of subtraction
  • Expanded Form: Writing a number as the sum of its place values
  • Place Value: The value of a digit based on its position
Core Rules & Principles
  • Regrouping Rule: When ones in minuend < ones in subtrahend
  • Conversion Rule: 1 ten = 10 ones
  • Place Value Rule: Tens and ones subtracted separately
  • Value Conservation: Regrouping changes form but not value
  • Verification Rule: Difference + Subtrahend = Minuend
Step-by-Step Method
  1. Identify Numbers: Determine minuend and subtrahend
  2. Write Expanded Forms: Express both numbers as tens + ones
  3. Compare Ones: Check if minuend ones ≥ subtrahend ones
  4. Regroup if Needed: Take 1 ten from tens place, add 10 to ones place
  5. Subtract Ones: Subtract ones from ones
  6. Subtract Tens: Subtract tens from tens
  7. Combine Results: Add tens and ones together
  8. Verify Answer: Add difference to subtrahend to check
Examples & Practice

Simple Examples:

32 - 15: 30+2 → 20+12, then 20+12 - 10+5 = 10+7 = 17

41 - 23: 40+1 → 30+11, then 30+11 - 20+3 = 10+8 = 18

Intermediate Examples:

53 - 27: 50+3 → 40+13, then 40+13 - 20+7 = 20+6 = 26

64 - 38: 60+4 → 50+14, then 50+14 - 30+8 = 20+6 = 26

Advanced Examples:

72 - 45: 70+2 → 60+12, then 60+12 - 40+5 = 20+7 = 27

81 - 59: 80+1 → 70+11, then 70+11 - 50+9 = 20+2 = 22

Tips & Tricks
  • Always Check: Look at ones column first to decide if regrouping is needed
  • Visual Aid: Use base-10 blocks to physically see the regrouping
  • Count Up: After solving, count up from answer to minuend to verify
  • Pattern Recognition: Numbers ending in small ones often need regrouping
  • Verification: Always add your answer to the subtrahend to check
Common Pitfalls
  • Forgetting Regrouping: Not checking if ones subtraction is possible
  • Mixing Places: Subtracting tens from ones or vice versa
  • Incorrect Regrouping: Forgetting to reduce tens by 1 when adding to ones
  • Sign Confusion: Subtracting in wrong order
  • Verification Neglect: Not checking work after solving
Memory Aids
  • "More on Top, Don't Need to Stop": If top ones ≥ bottom ones, no regrouping
  • "More on Bottom, Need to Borrow": If top ones < bottom ones, regroup
  • "Tens Down One, Ones Up Ten": When regrouping, reduce tens by 1, add 10 to ones
  • "Check Your Work": Always verify by addition
  • "One Ten Equals Ten Ones": Remember the conversion rule
Key Takeaways
  • Regrouping is just changing the form, not the value of the number
  • Always subtract like place values (ones from ones, tens from tens)
  • Expanded form helps understand what's really happening during regrouping
  • Verification through addition builds confidence
  • Practice with various problems strengthens regrouping skills

Questions & Answers

Question: Why do we need to regroup in expanded form subtraction? It seems like extra work.

Answer: Regrouping isn't extra work - it's how subtraction actually works! When you have 42 - 17, you're trying to take 7 ones from 2 ones, which is impossible. So you need to regroup: take 1 ten from the 40 (leaving 30) and convert it to 10 ones (adding to the 2 ones to make 12 ones). Now you can subtract: 12 - 7 = 5 ones, and 30 - 10 = 20 tens, giving 25. Regrouping shows what's really happening in subtraction.

Question: How do I know when I need to regroup?

Answer: Always look at the ones place first! If the ones digit in the top number (minuend) is smaller than the ones digit in the bottom number (subtrahend), you need to regroup. For example, in 53 - 28, check: is 3 ones ≥ 8 ones? No, so you must regroup. In 42 - 17, check: is 2 ones ≥ 7 ones? No, so you must regroup. If the top number's ones are greater than or equal to the bottom number's ones, no regrouping is needed.

Question: What happens to the value of the number when I regroup?

Answer: The total value of the number stays exactly the same when you regroup! When you change 42 from 40 + 2 to 30 + 12, you still have the same amount: 42. You're just changing how you represent it to make subtraction possible. It's like having 4 twenty-dollar bills and 2 one-dollar bills, then exchanging one twenty-dollar bill for twenty one-dollar bills. You still have the same total amount of money, just organized differently!