Subtraction with Regrouping Practice Problems - Grade 1 Math

Master subtraction with regrouping through interactive practice problems and step-by-step solutions designed for 1st grade students.

Regrouping Practice Problems
1 Regrouping Tens
Exercise 1
Solve: 24 - 7 = ? Use regrouping to solve this subtraction problem.
Definition:

Regrouping: Taking 1 ten and changing it to 10 ones when we need more ones to subtract.

Subtraction with Regrouping: A method used when the top number in the ones place is smaller than the bottom number.

Method for regrouping subtraction:
  1. Look at the ones place: Is the top number smaller than the bottom number?
  2. If yes, take 1 ten from the tens place and add 10 to the ones place
  3. Subtract the ones: ones - ones
  4. Subtract the tens: tens - tens
  5. Write the answer
Step 1: Look at the ones place

4 ones - 7 ones. Since 4 is smaller than 7, we need to regroup.

Step 2: Regroup from tens

Take 1 ten from the 2 tens: 24 becomes 1 ten and 14 ones.

Step 3: Subtract the ones

14 ones - 7 ones = 7 ones

Step 4: Subtract the tens

1 ten - 0 tens = 1 ten

Step 5: Write the answer

1 ten and 7 ones = 17

2
4
-
0
7
1
14
-
0
7
=
1
7
24 - 7 = 17!
Final result:

24 - 7 = 17

Applied rules:

• Regrouping rule: When top number is smaller, borrow from tens

• Place value: 1 ten = 10 ones

• Subtraction principle: Take away the smaller number from the larger

2 Regrouping Practice
Exercise 2
Solve: 32 - 5 = ? Use regrouping to solve this subtraction problem.
Definition:

Regrouping: The process of exchanging 1 ten for 10 ones when needed for subtraction.

Step 1: Look at the ones place

2 ones - 5 ones. Since 2 is smaller than 5, we need to regroup.

Step 2: Regroup from tens

Take 1 ten from the 3 tens: 32 becomes 2 tens and 12 ones.

Step 3: Subtract the ones

12 ones - 5 ones = 7 ones

Step 4: Subtract the tens

2 tens - 0 tens = 2 tens

Step 5: Write the answer

2 tens and 7 ones = 27

3
2
-
0
5
2
12
-
0
5
=
2
7
32 - 5 = 27!
Final result:

32 - 5 = 27

Applied rules:

• Regrouping rule: When top number is smaller, borrow from tens

• Place value: 1 ten = 10 ones

• Subtraction principle: Take away the smaller number from the larger

3 Advanced Regrouping
Exercise 3
Solve: 41 - 8 = ? Use regrouping to solve this subtraction problem.
Definition:

Regrouping: Changing 1 ten to 10 ones when the top ones digit is smaller than the bottom ones digit.

Step 1: Look at the ones place

1 one - 8 ones. Since 1 is smaller than 8, we need to regroup.

Step 2: Regroup from tens

Take 1 ten from the 4 tens: 41 becomes 3 tens and 11 ones.

Step 3: Subtract the ones

11 ones - 8 ones = 3 ones

Step 4: Subtract the tens

3 tens - 0 tens = 3 tens

Step 5: Write the answer

3 tens and 3 ones = 33

4
1
-
0
8
3
11
-
0
8
=
3
3
41 - 8 = 33!
Final result:

41 - 8 = 33

Applied rules:

• Regrouping rule: When top number is smaller, borrow from tens

• Place value: 1 ten = 10 ones

• Subtraction principle: Take away the smaller number from the larger

Detailed Summary: Subtraction with Regrouping Concepts
Complete Learning Summary
Definitions of Key Concepts

Regrouping: The process of taking 1 ten and converting it to 10 ones when the top number in the ones place is smaller than the bottom number in the ones place.

Subtraction with Regrouping: A method used to subtract numbers when the top digit in the ones place is smaller than the bottom digit in the ones place.

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

Ones Place: The rightmost digit in a number that represents single units.

Core Rules and Principles

Regrouping Rule: When the top number in the ones place is smaller than the bottom number in the ones place, you must regroup from the tens place.

Place Value Rule: 1 ten is equal to 10 ones (1 ten = 10 ones).

Subtraction Principle: You can only subtract a smaller number from a larger number in each place value.

Exchange Rule: When you take 1 ten from the tens place, you add 10 ones to the ones place.

Step-by-Step Methods and Procedures

General Regrouping Process:

  1. Look at the ones place: Is the top number smaller than the bottom number?
  2. If yes, take 1 ten from the tens place and add 10 to the ones place
  3. Subtract the ones: ones - ones
  4. Subtract the tens: tens - tens
  5. Write the final answer

Checking Your Work:

  1. Add your answer to the number you subtracted
  2. The result should equal the original number
  3. For example: 24 - 7 = 17, so 17 + 7 should equal 24

Alternative Approach:

  1. Draw tens and ones to visualize the problem
  2. Break apart a ten to get more ones
  3. Take away the required amount
  4. Count what remains
Examples: Simple to Advanced

Simple Example: 15 - 7 = ?

Since 5 < 7, regroup: 15 becomes 0 tens and 15 ones. Then 15 - 7 = 8.

Intermediate Example: 23 - 8 = ?

Since 3 < 8, regroup: 23 becomes 1 ten and 13 ones. Then 13 - 8 = 5, 1 - 0 = 1. Answer: 15.

Advanced Example: 52 - 6 = ?

Since 2 < 6, regroup: 52 becomes 4 tens and 12 ones. Then 12 - 6 = 6, 4 - 0 = 4. Answer: 46.

Tips, Tricks, and Common Pitfalls

Tips:

  • Always check if you need to regroup BEFORE subtracting
  • Remember: 1 ten = 10 ones
  • Count backwards from the larger number to check your answer
  • Use your fingers or objects to visualize the regrouping
  • Circle the number you need to regroup to remind yourself

Common Pitfalls:

  • Forgetting to reduce the tens place after regrouping
  • Subtracting the smaller number from the larger regardless of position
  • Not recognizing when regrouping is needed
  • Mixing up tens and ones after regrouping
  • Subtracting digits in the wrong order
Key Notes for Memorization

Memory Aids:

  • "Need more? Go next door!" (borrow from the tens place)

Remember: Regrouping is like trading 1 ten-dollar bill for 10 one-dollar bills. The total value stays the same, but it's easier to work with when you need more ones!

Practice Tips & Applications
Subtraction Strategies
Regrouping Effectively
Key definitions:

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

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

Subtraction: Taking one number away from another

Effective practice techniques:
  1. Visual representation: Draw tens and ones to see the regrouping
  2. Step-by-step approach: Always follow the same sequence of steps
  3. Check your work: Add the answer to the subtracted number
  4. Pattern recognition: Notice when regrouping is needed
  5. Regular practice: Work with different numbers to build fluency
Tip 1: Look at the ones place first to determine if regrouping is needed.
Tip 2: Remember that 1 ten equals 10 ones when regrouping.
Tip 3: Always reduce the tens place by 1 after regrouping.
Tip 4: Check your answer by adding it to the number you subtracted.
Common applications: Money calculations, measuring differences, comparing quantities.
Learning benefits: Develops number sense, place value understanding, and problem-solving skills.
Best practices to remember:

• Always check if regrouping is needed before subtracting

• Remember to reduce the tens place after regrouping

• Verify your answer by adding it back to the subtracted number

• Practice regularly to build fluency

• Use visual aids when starting out

Real World Connections & Advanced Applications
Real World Math
Connecting Regrouping to Life
Practical applications:

Money management: Calculating change when buying items

Time calculations: Finding the difference between times

Measurement: Comparing lengths, weights, or capacities

Extending the concept:
  1. Apply regrouping to larger numbers (hundreds, thousands)
  2. Connect to addition and subtraction word problems
  3. Link to estimation and rounding concepts
  4. Integrate with measurement and data problems
  5. Build foundation for multi-digit operations
Story connection: "If you have 24 candies and eat 7, how many are left?" (24 - 7 = 17)
Home connection: Practice with toys, coins, or other objects when regrouping.
Game connection: Board games often involve moving backward, which uses subtraction.
Foundation building: These skills prepare for more advanced arithmetic operations.
Transferability: Skills learned apply to many mathematical and real-world situations.
Advanced connections:

• Multi-digit subtraction with multiple regrouping steps

• Addition with regrouping (carrying)

• Mental math strategies

• Estimation and approximation

• Word problem solving strategies

Questions & Answers

Question: Why do I need to regroup? Can't I just subtract the smaller number from the bigger number?

Answer: Great question! You CAN subtract the smaller number from the bigger number, but only when looking at each place value separately. In 24 - 7:

  • Looking at ones: 4 - 7, but 4 is smaller than 7, so we can't subtract normally
  • We need to regroup: take 1 ten (which is 10 ones) and add it to the 4 ones
  • Now we have 14 ones - 7 ones = 7 ones
  • Then we subtract the tens: 1 ten - 0 tens = 1 ten

Regrouping helps us break down the problem so we can subtract properly in each place value.

Question: How can I help my child practice regrouping at home?

Answer: Here are effective ways to practice regrouping at home:

  • Use physical objects: Counters, beans, or coins to represent tens and ones
  • Draw pictures: Draw tens sticks and ones dots to visualize the regrouping
  • Play games: Create subtraction games with dice or cards
  • Real-world practice: Use money, cooking measurements, or shopping scenarios
  • Step-by-step approach: Practice one step at a time before combining

Start with simple problems and gradually increase difficulty as your child gains confidence.

Question: What strategies work best for teaching regrouping to first graders?

Answer: Effective strategies for teaching regrouping include:

  • Concrete manipulatives: Use base-ten blocks or other physical objects first
  • Visual representations: Draw tens and ones to show the regrouping process
  • Story contexts: Connect to real-world scenarios like sharing or spending
  • Step-by-step instruction: Break down the process into clear, manageable steps
  • Repetitive practice: Provide multiple opportunities with varied problems

Emphasize the concept that 1 ten equals 10 ones, and use consistent language to describe the regrouping process.