Solved Exercises on Expanded Form Subtraction with Regrouping in Grade 1

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

Expanded Form Subtraction with Regrouping

Visual Guide to Understanding Place Value and Regrouping

šŸ”¢
Place Value
Tens and Ones positions
šŸ”„
Regrouping
Borrowing from tens to ones
šŸ“
Expanded Form
Break numbers into parts
āž–
Subtraction
Taking away parts
1
Write in Expanded Form
2
Check Ones Column
3
Regroup if Needed
4
Subtract Each Place
42 = 40 + 2
ā†’
42 = 30 + 12
ā†’
Regroup: 1 ten to 10 ones
Rules and Methods, Laws,...
42 = 40 + 2
Expanded Form
Key Definitions:

Expanded Form: Writing a number as the sum of its place values (e.g., 42 = 40 + 2)

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

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

Complete Methodology:
  1. Step 1: Write both numbers in expanded form
  2. Step 2: Check if ones in minuend ā‰„ ones in subtrahend
  3. Step 3: If not, regroup by converting 1 ten to 10 ones
  4. Step 4: Subtract the ones, then subtract the tens
  5. Step 5: Combine results to get final answer
Tip 1: Always check if you need to regroup before subtracting ones.
Tip 2: When regrouping, reduce tens by 1 and add 10 to ones.
Tip 3: Count up from the smaller number to check your answer.
Essential Rules:

ā€¢ Regrouping Rule: If ones in minuend < ones in subtrahend, regroup

ā€¢ Place Value: Tens and ones must be subtracted separately

ā€¢ Consistency: Keep track of regrouped amounts

Solution: Exercises 1 to 3
1 Basic Regrouping
Exercise 1
Solve: 42 - 17 using expanded form subtraction with regrouping
Definition:

Expanded Form Subtraction: Breaking numbers into tens and ones to perform subtraction

Subtraction Method:
  1. Write numbers in expanded form
  2. Check if ones can be subtracted
  3. Regroup if necessary
  4. Subtract tens and ones separately
  5. Combine results
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:

ā€¢ Regrouping: When ones in minuend < ones in subtrahend

ā€¢ Place Value: Tens and ones subtracted separately

ā€¢ Conversion: 1 ten = 10 ones

2 Intermediate Regrouping
Exercise 2
Solve: 53 - 28 using expanded form subtraction 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:

ā€¢ Regrouping: When ones in minuend < ones in subtrahend

ā€¢ Place Value: Tens and ones subtracted separately

ā€¢ Verification: Check by adding: 25 + 28 = 53 āœ“

3 Multiple Regrouping Practice
Exercise 3
Solve: 61 - 29 using expanded form subtraction 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:

ā€¢ Regrouping: When ones in minuend < ones in subtrahend

ā€¢ Place Value: Tens and ones subtracted separately

ā€¢ Verification: Check by adding: 32 + 29 = 61 āœ“

Solution: Exercises 4 to 5
4 Challenging Regrouping
Exercise 4
Solve: 72 - 37 using expanded form subtraction 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:

ā€¢ Regrouping: When ones in minuend < ones in subtrahend

ā€¢ Place Value: Tens and ones subtracted separately

ā€¢ Verification: Check by adding: 35 + 37 = 72 āœ“

5 Advanced Regrouping
Exercise 5
Solve: 84 - 46 using expanded form subtraction 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:

ā€¢ Regrouping: When ones in minuend < ones in subtrahend

ā€¢ Place Value: Tens and ones subtracted separately

ā€¢ Verification: Check by adding: 38 + 46 = 84 āœ“

Detailed Course: Expanded Form Subtraction with Regrouping
52 = 50 + 2 ā†’ 40 + 12
Regrouping Process
Key Definitions:

Minuend: The number being subtracted from (the larger number)

Subtrahend: The number being subtracted (the smaller number)

Difference: The result of subtraction

Regrouping: Converting 1 ten into 10 ones when needed

Complete Methodology:
  1. Step 1: Identify the minuend and subtrahend
  2. Step 2: Write both numbers in expanded form
  3. Step 3: Compare the ones digits
  4. Step 4: Regroup if ones in minuend < ones in subtrahend
  5. Step 5: Subtract the ones digits
  6. Step 6: Subtract the tens digits
  7. Step 7: Combine the results
Tip 1: Always check the ones column first to determine if regrouping is needed.
Tip 2: When regrouping, decrease the tens digit by 1 and increase the ones digit by 10.
Tip 3: Use base-10 blocks or drawings to visualize the regrouping process.
Tip 4: Always verify your answer by adding the difference back to the subtrahend.
Common Errors: Forgetting to regroup when needed, subtracting smaller from larger without regrouping, miscounting after regrouping.
Key Points: Place value understanding, consistent regrouping, verification of answers.
Essential Formulas:

ā€¢ Expanded Form: AB = AƗ10 + B

ā€¢ Regrouping: AƗ10 + B = (A-1)Ɨ10 + (B+10) when B < C in subtraction

ā€¢ Verification: Minuend = Subtrahend + Difference

Questions & Answers

Question: I don't understand why we need to regroup when doing expanded form subtraction. Why can't I just subtract the smaller number from the bigger one in the ones place?

Answer: Great question! When you have a situation like 42 - 17, you're trying to subtract 7 ones from 2 ones (2 < 7). Since you can't take 7 from 2, you need to regroup. Think of it like having 2 candies but needing to give away 7 - impossible! So you borrow 1 ten (which is worth 10 ones), giving you 12 ones total. Now you can subtract: 12 - 7 = 5 ones. The regrouping makes the subtraction possible while keeping the total value the same.

Question: How do I know when I need to regroup in expanded form subtraction?

Answer: You need to regroup when the ones digit in the top number (minuend) is smaller than the ones digit in the bottom number (subtrahend). For example, in 53 - 28, the ones in the top number is 3 and in the bottom is 8. Since 3 < 8, you must regroup. In expanded form, you're comparing the ones part: is 3 ones greater than or equal to 8 ones? No, so regrouping is necessary.

Question: After I regroup, how do I make sure I did it correctly?

Answer: There are several ways to check your regrouping:

  • Counting method: Make sure the total value stays the same. If you had 42 (40 + 2), after regrouping you should still have 42 (30 + 12 = 42) āœ“
  • Addition check: Add your answer back to the number you subtracted. If 42 - 17 = 25, then 25 + 17 should equal 42 āœ“
  • Base-10 blocks: Use physical blocks to represent the numbers and see if the regrouping makes sense visually.

The key is ensuring the total value doesn't change during regrouping!