Solved Exercises on Three-Digit Subtraction With Regrouping in Grade 2

Master three-digit subtraction with regrouping: place value, column subtraction, and borrowing concepts through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Single regrouping
Exercise 1
Calculate:
\(423 - 157\)
Definition:

Regrouping (borrowing): When the top digit in a column is smaller than the bottom digit, we borrow from the next higher place value

Regrouping method:
  1. Line up numbers by place value (ones under ones, tens under tens, hundreds under hundreds)
  2. Subtract ones column: \(3 - 7\), since 3 < 7, borrow 1 from tens column (3 becomes 13, 2 becomes 1), so \(13 - 7 = 6\)
  3. Subtract tens column: \(1 - 5\), since 1 < 5, borrow 1 from hundreds column (1 becomes 11, 4 becomes 3), so \(11 - 5 = 6\)
  4. Subtract hundreds column: \(3 - 1 = 2\)
  5. Write the answer: \(266\)
Expression
\(423 - 157\)
Column subtraction with regrouping
\(\begin{array}{r} 423 \\ - 157 \\ \hline 266 \end{array}\)
Result
\(266\)
Step 1: Line up by place value

\(\begin{array}{r} H \ T \ O \\ 4 \ 2 \ 3 \\ - 1 \ 5 \ 7 \\ \hline \end{array}\)

Step 2: Subtract ones column

\(3 - 7\): Since 3 < 7, borrow 1 from tens column (2 becomes 1, 3 becomes 13), so \(13 - 7 = 6\)

Step 3: Subtract tens column

\(1 - 5\): Since 1 < 5, borrow 1 from hundreds column (4 becomes 3, 1 becomes 11), so \(11 - 5 = 6\)

Step 4: Subtract hundreds column

\(3 - 1 = 2\)

\(423 - 157 = 266\)
Final answer:

\(423 - 157 = 266\)

Applied rules:

• Place value: Align digits by their place values (hundreds, tens, ones)

• Regrouping rule: When top digit < bottom digit, borrow 1 from next column

• Borrow effect: Borrowed column decreases by 1, borrowing column increases by 10

2 Regrouping in two columns
Exercise 2
Calculate:
\(502 - 186\)
Definition:

Multiple regrouping: When regrouping is needed in more than one column during the same subtraction

Expression
\(502 - 186\)
Column subtraction with regrouping
\(\begin{array}{r} 502 \\ - 186 \\ \hline 316 \end{array}\)
Result
\(316\)
Step 1: Line up by place value

\(\begin{array}{r} H \ T \ O \\ 5 \ 0 \ 2 \\ - 1 \ 8 \ 6 \\ \hline \end{array}\)

Step 2: Subtract ones column

\(2 - 6\): Since 2 < 6, borrow 1 from tens column (0 becomes 10, 2 becomes 12), so \(12 - 6 = 6\)

Step 3: Subtract tens column

\(0 - 8\): Since 0 < 8, borrow 1 from hundreds column (5 becomes 4, 0 becomes 10), so \(10 - 8 = 2\)

Step 4: Subtract hundreds column

\(4 - 1 = 3\)

\(502 - 186 = 316\)
Final answer:

\(502 - 186 = 316\)

Applied rules:

• Multiple regrouping: Regroup in each column where top digit < bottom digit

• Sequential borrowing: Borrow from next higher column when needed

• Zero handling: When borrowing from zero, continue to the next non-zero column

3 Regrouping with zeros
Exercise 3
Calculate:
\(600 - 247\)
Definition:

Regrouping with zeros: When subtracting requires regrouping and one or more of the numbers contain zeros

Expression
\(600 - 247\)
Column subtraction with regrouping
\(\begin{array}{r} 600 \\ - 247 \\ \hline 353 \end{array}\)
Result
\(353\)
Step 1: Line up by place value

\(\begin{array}{r} H \ T \ O \\ 6 \ 0 \ 0 \\ - 2 \ 4 \ 7 \\ \hline \end{array}\)

Step 2: Subtract ones column

\(0 - 7\): Since 0 < 7, borrow 1 from tens column, but tens is 0, so borrow from hundreds (6 becomes 5, 0 becomes 10, then borrow 1 from tens: 10 becomes 9, 0 becomes 10), so \(10 - 7 = 3\)

Step 3: Subtract tens column

\(9 - 4 = 5\)

Step 4: Subtract hundreds column

\(5 - 2 = 3\)

\(600 - 247 = 353\)
Final answer:

\(600 - 247 = 353\)

Applied rules:

• Zero handling: When borrowing from zero, continue to the next non-zero column

• Chain borrowing: Borrow sequentially through zeros to reach a non-zero digit

• Place value preservation: Maintain correct place value after regrouping

Three-Digit Subtraction With Regrouping Strategies
\(\begin{array}{r} H \ T \ O \\ 4 \ 2 \ 3 \\ - 1 \ 5 \ 7 \\ \hline 2 \ 6 \ 6 \end{array}\)
Regrouping Process
Rule 1
Borrow When Needed
When top digit < bottom digit
Rule 2
Decrease Higher Column
Subtract 1 from borrowed column
Rule 3
Increase Current Column
Add 10 to borrowing column
Key definitions:

Three-digit number: A number with three digits representing hundreds, tens, and ones places

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

Regrouping (borrowing): Moving a group of ten from one place value to the next lower place value

Subtraction with regrouping methodology:
  1. Align numbers: Put numbers in columns by place value
  2. Subtract ones column: If top digit < bottom digit, borrow 1 from tens column
  3. Subtract tens column: If top digit < bottom digit, borrow 1 from hundreds column
  4. Subtract hundreds column: Subtract the digits
  5. Write the answer: Combine the results from each column
Tip 1: Always borrow when the top digit is smaller than the bottom digit.
Tip 2: Remember to decrease the borrowed column by 1 and increase the borrowing column by 10.
Tip 3: Work from right to left (ones → tens → hundreds).
Tip 4: Circle or mark borrowed digits to keep track of them.
Common errors: Forgetting to borrow, borrowing incorrectly, decreasing the wrong column.
Success strategies: Use lined paper, mark borrows clearly, check each step.
Three-digit subtraction with regrouping rules:

• Borrowing condition: \(3 < 7\) → borrow from tens

• Borrow effect: \(2 - 1 = 1\), \(3 + 10 = 13\)

• Sequential processing: Process each column before moving to the next

• Zero handling: When borrowing from zero, continue to next non-zero column

Solution: Exercises 4 to 5
4 Multiple regrouping
Exercise 4
Calculate:
\(703 - 268\)
Definition:

Multiple regrouping: When regrouping occurs in more than one column during the same subtraction

Expression
\(703 - 268\)
Column subtraction with regrouping
\(\begin{array}{r} 703 \\ - 268 \\ \hline 435 \end{array}\)
Result
\(435\)
Step 1: Line up by place value

\(\begin{array}{r} H \ T \ O \\ 7 \ 0 \ 3 \\ - 2 \ 6 \ 8 \\ \hline \end{array}\)

Step 2: Subtract ones column

\(3 - 8\): Since 3 < 8, borrow 1 from tens column, but tens is 0, so borrow from hundreds (7 becomes 6, 0 becomes 10, then borrow 1 from tens: 10 becomes 9, 3 becomes 13), so \(13 - 8 = 5\)

Step 3: Subtract tens column

\(9 - 6 = 3\)

Step 4: Subtract hundreds column

\(6 - 2 = 4\)

\(703 - 268 = 435\)
Final answer:

\(703 - 268 = 435\)

Applied rules:

• Multiple regrouping: Regroup in each column where top digit < bottom digit

• Chain borrowing: Borrow sequentially through zeros to reach a non-zero digit

• Sequential processing: Process each column from right to left

5 Real-world application
Exercise 5
A store had 520 toys in stock. They sold 184 toys during the week. How many toys are left in stock?
Definition:

Word problem: A real-world scenario that requires mathematical calculation to solve

Problem
Started: 520, Sold: 184, Left: ?
Equation
520 - 184 = ?
Result
336
Step 1: Identify the numbers

Starting toys = 520, Toys sold = 184

Step 2: Set up the subtraction

We need to find the remaining toys, so we subtract: 520 - 184

Step 3: Line up by place value

\(\begin{array}{r} H \ T \ O \\ 5 \ 2 \ 0 \\ - 1 \ 8 \ 4 \\ \hline \end{array}\)

Step 4: Subtract each column with regrouping

Ones: \(0 - 4\): Since 0 < 4, borrow 1 from tens (2 becomes 1, 0 becomes 10), so \(10 - 4 = 6\)

Tens: \(1 - 8\): Since 1 < 8, borrow 1 from hundreds (5 becomes 4, 1 becomes 11), so \(11 - 8 = 3\)

Hundreds: \(4 - 1 = 3\)

336 toys are left in stock.
Final answer:

336 toys are left in stock.

Applied rules:

• Real-world application: Connect math to everyday situations

• Problem-solving: Identify what needs to be calculated

• Regrouping: Apply borrowing rules when top digit < bottom digit

Three-Digit Subtraction With Regrouping Laws, Methods, and Definitions
\(\begin{array}{r} H \ T \ O \\ a \ b \ c \\ - d \ e \ f \\ \hline g \ h \ i \end{array}\)
General Form of Three-Digit Subtraction with Regrouping
Key definitions:

Three-digit number: A number with three digits representing hundreds, tens, and ones places

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

Regrouping (borrowing): Moving a group of ten from one place value to the next lower place value when the top digit is smaller than the bottom digit

Three-digit subtraction with regrouping methodology:
  1. Align numbers: Put numbers in columns by place value
  2. Subtract ones column: If top digit < bottom digit, borrow 1 from tens column
  3. Subtract tens column: If top digit < bottom digit, borrow 1 from hundreds column
  4. Subtract hundreds column: Subtract the digits
  5. Write the answer: Combine the results from each column
Tip 1: Always borrow when the top digit is smaller than the bottom digit.
Tip 2: Remember to decrease the borrowed column by 1 and increase the borrowing column by 10.
Tip 3: Work from right to left (ones → tens → hundreds).

Tip 4: Circle or mark borrowed digits to keep track of them.
Common errors: Forgetting to borrow, borrowing incorrectly, decreasing the wrong column.
Success strategies: Use lined paper, mark borrows clearly, check each step.
Three-digit subtraction with regrouping formulas:

• Borrowing condition: If top digit < bottom digit, borrow from next higher column

• Borrow effect: Decrease borrowed column by 1, increase borrowing column by 10

• Sequential processing: Process columns from right to left

• Multiple regrouping: Apply borrowing rules to each column independently

Exercise with Visualization: Regrouping Process
Exercise 6: Regrouping Visualization
Consider the regrouping process in three-digit subtraction:
\(f_1(x) = x\) (before regrouping)
\(f_2(x) = x + 10\) (after borrowing)
\(f_3(x) = x - 1\) (decreased column)

Analysis: The chart shows how regrouping works in three-digit subtraction.

  • \(f_1(x) = x\) (original value before regrouping)
  • \(f_2(x) = x + 10\) (value increased after borrowing)
  • \(f_3(x) = x - 1\) (value decreased after lending)

Questions & Answers

Question: When do I need to regroup in three-digit subtraction?

Answer: You need to regroup (or borrow) whenever the top digit in a column is smaller than the bottom digit. Here's how to recognize it:

  • Ones column: If the top ones digit is smaller than the bottom ones digit (like 3 < 7)
  • Tens column: If the top tens digit is smaller than the bottom tens digit
  • Hundreds column: If the top hundreds digit is smaller than the bottom hundreds digit

For example, in 423 - 157:

  • Ones: 3 - 7, since 3 < 7, we need to regroup
  • Tens: 2 - 5, since 2 < 5, we need to regroup
  • Hundreds: 4 - 1, since 4 > 1, no regrouping needed

Remember: regrouping only happens when the top digit is smaller than the bottom digit!

Question: I sometimes forget to decrease the column I borrowed from. How can I remember to do this?

Answer: This is a very common mistake! Here are some strategies to help you remember:

  1. Cross out the original digit: Cross out the digit you're borrowing from and write the new value above it
  2. Mark it clearly: Put a small checkmark or circle to remind you that you've borrowed from that column
  3. Say it out loud: When borrowing, say "I'm borrowing from here, so this becomes one less"
  4. Visual marking: Write the new value slightly above the original digit

For example, in 423 - 157:

When borrowing from the tens column (2), cross out the 2 and write 1 above it:

\(\begin{array}{r} 4\cancel{2}^1 3 \\ - 157 \\ \hline \end{array}\)

Now when you subtract the tens column, you'll remember to use 1 instead of 2: \(1 - 5\), which requires borrowing from the hundreds column.

With practice, this will become automatic!

Question: My child sometimes borrows from the wrong column. How can I help them understand where to borrow from?

Answer: This is a common source of confusion! Here's how to help your child understand:

Borrowing Rule: When the top digit is smaller than the bottom digit in a column, you "borrow" from the next higher place value column.

Direction: Always borrow from the column to the left (the next higher place value):

  • If borrowing for the ones column, take from the tens column
  • If borrowing for the tens column, take from the hundreds column

Think of it as: "When I need more in this column, I take from the column that's worth more."

For example, in 502 - 186:

  • Ones: 2 - 6, since 2 < 6, borrow from tens column (0 becomes 10, 2 becomes 12)
  • Tens: 0 - 8, since 0 < 8, borrow from hundreds column (5 becomes 4, 0 becomes 10)

Use physical objects like base-10 blocks to show this concept visually! You can also use the phrase "going left to get more" to help remember the direction.