Subtraction with Regrouping Twice: 10 Solved Exercises

Master subtraction with regrouping twice: borrowing from tens and hundreds, place value understanding, and step-by-step solutions.

Solution: Exercises 1 to 5
1 Subtraction with regrouping twice
Exercise 1
Calculate:
\(523 - 178\)
Definition:

Subtraction with regrouping twice: When subtracting, if the digit in the ones place of the top number is smaller than the bottom number, and the tens place also needs to be borrowed from, we regroup twice.

Subtraction method:
  1. Start from the ones place
  2. If the top digit is smaller than the bottom, regroup from the next place value
  3. Repeat if needed for the tens place
  4. Continue with the remaining digits
H
H
T
O
5
2
3
-
1
7
8
-
Step 1: Ones place: 3 < 8, so we need to regroup. Since tens place has only 2, we need to regroup from hundreds first.
↓
4
1
13
-
↓
4
1
12
3
Step 1: Regroup from hundreds to tens

523 becomes 4 hundreds, 12 tens, 3 ones (since 1 hundred = 10 tens)

Step 2: Regroup from tens to ones

Now we have 4 hundreds, 11 tens, 13 ones (since 1 ten = 10 ones)

Step 3: Subtract each place value

Ones: 13 - 8 = 5

Tens: 11 - 7 = 4

Hundreds: 4 - 1 = 3

\(523 - 178 = 345\)
Final answer:

\(523 - 178 = 345\)

Applied rules:

• Regrouping: When top digit is smaller, borrow from next higher place value

• Place value: 1 hundred = 10 tens, 1 ten = 10 ones

• Subtraction: Subtract each place value separately

2 Subtraction with regrouping twice
Exercise 2
Calculate:
\(612 - 287\)
H
H
T
O
6
1
2
-
2
8
7
-
Step 1: Ones place: 2 < 7, so we need to regroup. Since tens place has only 1, we need to regroup from hundreds first.
↓
5
1
2
-
↓
5
0
12
2
Step 1: Regroup from hundreds to tens

612 becomes 5 hundreds, 11 tens, 2 ones (since 1 hundred = 10 tens)

Step 2: Regroup from tens to ones

Now we have 5 hundreds, 10 tens, 12 ones (since 1 ten = 10 ones)

Step 3: Subtract each place value

Ones: 12 - 7 = 5

Tens: 10 - 8 = 2

Hundreds: 5 - 2 = 3

\(612 - 287 = 325\)
Final answer:

\(612 - 287 = 325\)

Applied rules:

• Regrouping: When top digit is smaller, borrow from next higher place value

• Place value: 1 hundred = 10 tens, 1 ten = 10 ones

• Subtraction: Subtract each place value separately

3 Subtraction with regrouping twice
Exercise 3
Calculate:
\(703 - 268\)
H
H
T
O
7
0
3
-
2
6
8
-
Step 1: Ones place: 3 < 8, so we need to regroup. Since tens place has 0, we need to regroup from hundreds first.
↓
6
0
3
-
↓
6
9
13
3
Step 1: Regroup from hundreds to tens

703 becomes 6 hundreds, 10 tens, 3 ones (since 1 hundred = 10 tens)

Step 2: Regroup from tens to ones

Now we have 6 hundreds, 9 tens, 13 ones (since 1 ten = 10 ones)

Step 3: Subtract each place value

Ones: 13 - 8 = 5

Tens: 9 - 6 = 3

Hundreds: 6 - 2 = 4

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

\(703 - 268 = 435\)

Applied rules:

• Regrouping: When top digit is smaller, borrow from next higher place value

• Place value: 1 hundred = 10 tens, 1 ten = 10 ones

• Subtraction: Subtract each place value separately

Solution: Exercises 4 to 7
4 Subtraction with regrouping twice
Exercise 4
Calculate:
\(801 - 376\)
H
H
T
O
8
0
1
-
3
7
6
-
Step 1: Ones place: 1 < 6, so we need to regroup. Since tens place has 0, we need to regroup from hundreds first.
↓
7
0
1
-
↓
7
9
11
1
Step 1: Regroup from hundreds to tens

801 becomes 7 hundreds, 10 tens, 1 one (since 1 hundred = 10 tens)

Step 2: Regroup from tens to ones

Now we have 7 hundreds, 9 tens, 11 ones (since 1 ten = 10 ones)

Step 3: Subtract each place value

Ones: 11 - 6 = 5

Tens: 9 - 7 = 2

Hundreds: 7 - 3 = 4

\(801 - 376 = 425\)
Final answer:

\(801 - 376 = 425\)

Applied rules:

• Regrouping: When top digit is smaller, borrow from next higher place value

• Place value: 1 hundred = 10 tens, 1 ten = 10 ones

• Subtraction: Subtract each place value separately

5 Subtraction with regrouping twice
Exercise 5
Calculate:
\(902 - 458\)
H
H
T
O
9
0
2
-
4
5
8
-
Step 1: Ones place: 2 < 8, so we need to regroup. Since tens place has 0, we need to regroup from hundreds first.
↓
8
0
2
-
↓
8
9
12
2
Step 1: Regroup from hundreds to tens

902 becomes 8 hundreds, 10 tens, 2 ones (since 1 hundred = 10 tens)

Step 2: Regroup from tens to ones

Now we have 8 hundreds, 9 tens, 12 ones (since 1 ten = 10 ones)

Step 3: Subtract each place value

Ones: 12 - 8 = 4

Tens: 9 - 5 = 4

Hundreds: 8 - 4 = 4

\(902 - 458 = 444\)
Final answer:

\(902 - 458 = 444\)

Applied rules:

• Regrouping: When top digit is smaller, borrow from next higher place value

• Place value: 1 hundred = 10 tens, 1 ten = 10 ones

• Subtraction: Subtract each place value separately

6 Subtraction with regrouping twice
Exercise 6
Calculate:
\(631 - 289\)
H
H
T
O
6
3
1
-
2
8
9
-
Step 1: Ones place: 1 < 9, so we need to regroup. Since tens place has 3, we need to regroup from hundreds first.
↓
5
3
1
-
↓
5
2
11
1
Step 1: Regroup from hundreds to tens

631 becomes 5 hundreds, 13 tens, 1 one (since 1 hundred = 10 tens)

Step 2: Regroup from tens to ones

Now we have 5 hundreds, 12 tens, 11 ones (since 1 ten = 10 ones)

Step 3: Subtract each place value

Ones: 11 - 9 = 2

Tens: 12 - 8 = 4

Hundreds: 5 - 2 = 3

\(631 - 289 = 342\)
Final answer:

\(631 - 289 = 342\)

Applied rules:

• Regrouping: When top digit is smaller, borrow from next higher place value

• Place value: 1 hundred = 10 tens, 1 ten = 10 ones

• Subtraction: Subtract each place value separately

7 Subtraction with regrouping twice
Exercise 7
Calculate:
\(742 - 396\)
H
H
T
O
7
4
2
-
3
9
6
-
Step 1: Ones place: 2 < 6, so we need to regroup. Since tens place has 4, we need to regroup from hundreds first.
↓
6
4
2
-
↓
6
3
12
2
Step 1: Regroup from hundreds to tens

742 becomes 6 hundreds, 14 tens, 2 ones (since 1 hundred = 10 tens)

Step 2: Regroup from tens to ones

Now we have 6 hundreds, 13 tens, 12 ones (since 1 ten = 10 ones)

Step 3: Subtract each place value

Ones: 12 - 6 = 6

Tens: 13 - 9 = 4

Hundreds: 6 - 3 = 3

\(742 - 396 = 346\)
Final answer:

\(742 - 396 = 346\)

Applied rules:

• Regrouping: When top digit is smaller, borrow from next higher place value

• Place value: 1 hundred = 10 tens, 1 ten = 10 ones

• Subtraction: Subtract each place value separately

Solution: Exercises 8 to 10
8 Subtraction with regrouping twice
Exercise 8
Calculate:
\(821 - 478\)
H
H
T
O
8
2
1
-
4
7
8
-
Step 1: Ones place: 1 < 8, so we need to regroup. Since tens place has 2, we need to regroup from hundreds first.
↓
7
2
1
-
↓
7
1
11
1
Step 1: Regroup from hundreds to tens

821 becomes 7 hundreds, 12 tens, 1 one (since 1 hundred = 10 tens)

Step 2: Regroup from tens to ones

Now we have 7 hundreds, 11 tens, 11 ones (since 1 ten = 10 ones)

Step 3: Subtract each place value

Ones: 11 - 8 = 3

Tens: 11 - 7 = 4

Hundreds: 7 - 4 = 3

\(821 - 478 = 343\)
Final answer:

\(821 - 478 = 343\)

Applied rules:

• Regrouping: When top digit is smaller, borrow from next higher place value

• Place value: 1 hundred = 10 tens, 1 ten = 10 ones

• Subtraction: Subtract each place value separately

9 Subtraction with regrouping twice
Exercise 9
Calculate:
\(913 - 567\)
H
H
T
O
9
1
3
-
5
6
7
-
Step 1: Ones place: 3 < 7, so we need to regroup. Since tens place has 1, we need to regroup from hundreds first.
↓
8
1
3
-
↓
8
0
13
3
Step 1: Regroup from hundreds to tens

913 becomes 8 hundreds, 11 tens, 3 ones (since 1 hundred = 10 tens)

Step 2: Regroup from tens to ones

Now we have 8 hundreds, 10 tens, 13 ones (since 1 ten = 10 ones)

Step 3: Subtract each place value

Ones: 13 - 7 = 6

Tens: 10 - 6 = 4

Hundreds: 8 - 5 = 3

\(913 - 567 = 346\)
Final answer:

\(913 - 567 = 346\)

Applied rules:

• Regrouping: When top digit is smaller, borrow from next higher place value

• Place value: 1 hundred = 10 tens, 1 ten = 10 ones

• Subtraction: Subtract each place value separately

10 Subtraction with regrouping twice
Exercise 10
Calculate:
\(604 - 287\)
H
H
T
O
6
0
4
-
2
8
7
-
Step 1: Ones place: 4 < 7, so we need to regroup. Since tens place has 0, we need to regroup from hundreds first.
↓
5
0
4
-
↓
5
9
14
4
Step 1: Regroup from hundreds to tens

604 becomes 5 hundreds, 10 tens, 4 ones (since 1 hundred = 10 tens)

Step 2: Regroup from tens to ones

Now we have 5 hundreds, 9 tens, 14 ones (since 1 ten = 10 ones)

Step 3: Subtract each place value

Ones: 14 - 7 = 7

Tens: 9 - 8 = 1

Hundreds: 5 - 2 = 3

\(604 - 287 = 317\)
Final answer:

\(604 - 287 = 317\)

Applied rules:

• Regrouping: When top digit is smaller, borrow from next higher place value

• Place value: 1 hundred = 10 tens, 1 ten = 10 ones

• Subtraction: Subtract each place value separately

Rules and methods, laws,...
\(a - b = c\)
Subtraction
Regrouping Rule
1 hundred = 10 tens
Place Value Conversion
Regrouping Rule
1 ten = 10 ones
Place Value Conversion
Subtraction Process
Top - Bottom = Difference
Calculate Each Place
Key definitions:

Regrouping: Converting from a higher place value to a lower place value to perform subtraction

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

Subtraction: Finding the difference between two numbers

Complete methodology:
  1. Align numbers: Line up numbers by place value
  2. Start from right: Begin subtraction in the ones place
  3. Check if regrouping needed: If top digit is smaller than bottom digit
  4. Regroup from next place: Convert 1 unit from higher place to 10 units in current place
  5. Repeat if needed: Continue regrouping if multiple places need it
  6. Complete subtraction: Subtract each place value
Tip 1: Always check if the top digit is larger than the bottom digit before subtracting.
Tip 2: When regrouping, decrease the higher place by 1 and increase the lower place by 10.
Tip 3: Draw arrows to visualize the regrouping process.
Common errors: Forgetting to decrease the higher place value when regrouping, subtracting bottom from top instead of top from bottom.
Key concept: Subtraction with regrouping twice requires borrowing from two different place values.
Formulas to know by heart:

• Place value conversion: 1 hundred = 10 tens = 100 ones

• Regrouping rule: When top digit < bottom digit, regroup from next higher place

• Subtraction: Top number - Bottom number = Difference

• Verification: Difference + Subtrahend = Minuend

Questions & Answers

Question: I don't understand when I need to regroup twice. Why can't I just subtract normally?

Answer: Great question! You need to regroup twice when both the tens and ones places in the top number are smaller than the bottom number. For example, in 523 - 178:

  • You can't subtract 8 from 3 in the ones place
  • So you try to get 10 ones from the tens place, but there are only 2 tens
  • You can't subtract 7 from 2 in the tens place either
  • So you need to get 10 tens from the hundreds place first
  • Then you can convert 1 ten to 10 ones

You can't subtract normally because you can't take away more than you have in each place value!

Question: How do I help my child understand place value better? They keep forgetting to adjust the higher place when regrouping.

Answer: Try these strategies to help your child understand place value:

  • Use physical manipulatives like base-10 blocks to show that 1 hundred block equals 10 ten rods
  • Have them draw arrows showing where the regrouped amount comes from
  • Create a chant: "Borrow from the left, add to the right"
  • Practice with visual aids that show the decrease in the higher place value

Remind them that when they take 1 from the hundreds place, it decreases by 1, and they get 10 more in the tens place. The total value stays the same!

Question: What are some common mistakes students make with subtraction with regrouping twice?

Answer: Common mistakes include:

  • Forgetting to decrease the higher place value after regrouping
  • Only regrouping once when two regroups are needed
  • Subtracting the bottom number from the top instead of top from bottom
  • Mixing up place values and subtracting across columns incorrectly
  • Not recognizing when regrouping is needed

To prevent these errors, encourage students to check each place value before starting, write small numbers above to track regrouped amounts, and verify their answers by adding the result back to the subtrahend.