2-Digit Subtraction with Regrouping: 10 Solved Exercises

Master 2-digit subtraction with regrouping: borrowing from tens, place value understanding, and step-by-step solutions.

Solution: Exercises 1 to 5
1 2-digit subtraction with regrouping
Exercise 1
Calculate:
\(53 - 28\)
Definition:

2-digit subtraction with regrouping: When subtracting two 2-digit numbers, if the digit in the ones place of the top number is smaller than the bottom number, we regroup from the tens place.

Subtraction method:
  1. Start from the ones place
  2. If the top digit is smaller than the bottom, regroup from the tens place
  3. Convert 1 ten to 10 ones
  4. Complete the subtraction in each place value
T
O
-
5
3
-
2
8
-
Step 1: Ones place: 3 < 8, so we need to regroup from the tens place.
↓
4
13
-
Step 1: Regroup from tens to ones

53 becomes 4 tens and 13 ones (since 1 ten = 10 ones)

Step 2: Subtract each place value

Ones: 13 - 8 = 5

Tens: 4 - 2 = 2

\(53 - 28 = 25\)
Final answer:

\(53 - 28 = 25\)

Applied rules:

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

• Place value: 1 ten = 10 ones

• Subtraction: Subtract each place value separately

2 2-digit subtraction with regrouping
Exercise 2
Calculate:
\(61 - 37\)
T
O
-
6
1
-
3
7
-
Step 1: Ones place: 1 < 7, so we need to regroup from the tens place.
↓
5
11
-
Step 1: Regroup from tens to ones

61 becomes 5 tens and 11 ones (since 1 ten = 10 ones)

Step 2: Subtract each place value

Ones: 11 - 7 = 4

Tens: 5 - 3 = 2

\(61 - 37 = 24\)
Final answer:

\(61 - 37 = 24\)

Applied rules:

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

• Place value: 1 ten = 10 ones

• Subtraction: Subtract each place value separately

3 2-digit subtraction with regrouping
Exercise 3
Calculate:
\(72 - 49\)
T
O
-
7
2
-
4
9
-
Step 1: Ones place: 2 < 9, so we need to regroup from the tens place.
↓
6
12
-
Step 1: Regroup from tens to ones

72 becomes 6 tens and 12 ones (since 1 ten = 10 ones)

Step 2: Subtract each place value

Ones: 12 - 9 = 3

Tens: 6 - 4 = 2

\(72 - 49 = 23\)
Final answer:

\(72 - 49 = 23\)

Applied rules:

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

• Place value: 1 ten = 10 ones

• Subtraction: Subtract each place value separately

Solution: Exercises 4 to 7
4 2-digit subtraction with regrouping
Exercise 4
Calculate:
\(84 - 56\)
T
O
-
8
4
-
5
6
-
Step 1: Ones place: 4 < 6, so we need to regroup from the tens place.
↓
7
14
-
Step 1: Regroup from tens to ones

84 becomes 7 tens and 14 ones (since 1 ten = 10 ones)

Step 2: Subtract each place value

Ones: 14 - 6 = 8

Tens: 7 - 5 = 2

\(84 - 56 = 28\)
Final answer:

\(84 - 56 = 28\)

Applied rules:

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

• Place value: 1 ten = 10 ones

• Subtraction: Subtract each place value separately

5 2-digit subtraction with regrouping
Exercise 5
Calculate:
\(91 - 63\)
T
O
-
9
1
-
6
3
-
Step 1: Ones place: 1 < 3, so we need to regroup from the tens place.
↓
8
11
-
Step 1: Regroup from tens to ones

91 becomes 8 tens and 11 ones (since 1 ten = 10 ones)

Step 2: Subtract each place value

Ones: 11 - 3 = 8

Tens: 8 - 6 = 2

\(91 - 63 = 28\)
Final answer:

\(91 - 63 = 28\)

Applied rules:

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

• Place value: 1 ten = 10 ones

• Subtraction: Subtract each place value separately

6 2-digit subtraction with regrouping
Exercise 6
Calculate:
\(65 - 28\)
T
O
-
6
5
-
2
8
-
Step 1: Ones place: 5 < 8, so we need to regroup from the tens place.
↓
5
15
-
Step 1: Regroup from tens to ones

65 becomes 5 tens and 15 ones (since 1 ten = 10 ones)

Step 2: Subtract each place value

Ones: 15 - 8 = 7

Tens: 5 - 2 = 3

\(65 - 28 = 37\)
Final answer:

\(65 - 28 = 37\)

Applied rules:

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

• Place value: 1 ten = 10 ones

• Subtraction: Subtract each place value separately

7 2-digit subtraction with regrouping
Exercise 7
Calculate:
\(73 - 45\)
T
O
-
7
3
-
4
5
-
Step 1: Ones place: 3 < 5, so we need to regroup from the tens place.
↓
6
13
-
Step 1: Regroup from tens to ones

73 becomes 6 tens and 13 ones (since 1 ten = 10 ones)

Step 2: Subtract each place value

Ones: 13 - 5 = 8

Tens: 6 - 4 = 2

\(73 - 45 = 28\)
Final answer:

\(73 - 45 = 28\)

Applied rules:

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

• Place value: 1 ten = 10 ones

• Subtraction: Subtract each place value separately

Solution: Exercises 8 to 10
8 2-digit subtraction with regrouping
Exercise 8
Calculate:
\(82 - 57\)
T
O
-
8
2
-
5
7
-
Step 1: Ones place: 2 < 7, so we need to regroup from the tens place.
↓
7
12
-
Step 1: Regroup from tens to ones

82 becomes 7 tens and 12 ones (since 1 ten = 10 ones)

Step 2: Subtract each place value

Ones: 12 - 7 = 5

Tens: 7 - 5 = 2

\(82 - 57 = 25\)
Final answer:

\(82 - 57 = 25\)

Applied rules:

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

• Place value: 1 ten = 10 ones

• Subtraction: Subtract each place value separately

9 2-digit subtraction with regrouping
Exercise 9
Calculate:
\(94 - 68\)
T
O
-
9
4
-
6
8
-
Step 1: Ones place: 4 < 8, so we need to regroup from the tens place.
↓
8
14
-
Step 1: Regroup from tens to ones

94 becomes 8 tens and 14 ones (since 1 ten = 10 ones)

Step 2: Subtract each place value

Ones: 14 - 8 = 6

Tens: 8 - 6 = 2

\(94 - 68 = 26\)
Final answer:

\(94 - 68 = 26\)

Applied rules:

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

• Place value: 1 ten = 10 ones

• Subtraction: Subtract each place value separately

10 2-digit subtraction with regrouping
Exercise 10
Calculate:
\(71 - 39\)
T
O
-
7
1
-
3
9
-
Step 1: Ones place: 1 < 9, so we need to regroup from the tens place.
↓
6
11
-
Step 1: Regroup from tens to ones

71 becomes 6 tens and 11 ones (since 1 ten = 10 ones)

Step 2: Subtract each place value

Ones: 11 - 9 = 2

Tens: 6 - 3 = 3

\(71 - 39 = 32\)
Final answer:

\(71 - 39 = 32\)

Applied rules:

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

• Place value: 1 ten = 10 ones

• Subtraction: Subtract each place value separately

Detailed Summary: 2-Digit Subtraction with Regrouping
Comprehensive Learning Guide

Definitions and Key Concepts

2-digit subtraction with regrouping: A mathematical operation where you subtract two 2-digit numbers, and when the digit in the ones place of the top number is smaller than the bottom number, you borrow from the tens place.

Regrouping (borrowing): The process of converting 1 unit from a higher place value to 10 units in a lower place value. For example, converting 1 ten to 10 ones.

Place value: The value of a digit based on its position in a number. In 2-digit numbers, the positions are tens and ones.

Core Rules and Laws

• Regrouping Rule: When the top digit is smaller than the bottom digit in any place value, you must regroup from the next higher place value.

• Place Value Conversion: 1 ten = 10 ones

• Subtraction Rule: Always subtract the bottom number from the top number in each place value.

• Value Conservation: The total value of the number remains the same after regrouping.

Step-by-Step Method

  1. Align numbers: Write the numbers vertically with tens under tens and ones under ones.
  2. Start from right: Begin subtraction in the ones place.
  3. Check if regrouping is needed: If the top digit in the ones place is smaller than the bottom digit.
  4. Regroup from tens: Decrease the tens digit by 1 and add 10 to the ones digit.
  5. Subtract in ones place: Now subtract the ones digits.
  6. Subtract in tens place: Subtract the tens digits (remembering the decreased value).
  7. Write the final answer: Combine the results from each place value.

Examples (Simple to Advanced)

Simple Example: 42 - 15

Ones: 2 < 5, so regroup: 42 becomes 3 tens and 12 ones

Ones: 12 - 5 = 7

Tens: 3 - 1 = 2

Answer: 27

Advanced Example: 80 - 47

Ones: 0 < 7, so regroup: 80 becomes 7 tens and 10 ones

Ones: 10 - 7 = 3

Tens: 7 - 4 = 3

Answer: 33

Tips and Tricks

• Visual Aid: Draw arrows to show where you're borrowing from.

• Check Your Work: Add your answer to the number you subtracted to see if you get the original number.

• Memory Tip: "More on the floor, go next door" - when the bottom number is bigger, borrow from the tens place.

• Practice Pattern Recognition: Numbers ending in small digits (0, 1, 2) often require regrouping when subtracting larger ones digits.

Common Mistakes and Pitfalls

• Forgetting to decrease the tens place: When regrouping, the tens digit must be reduced by 1.

• Subtracting in wrong order: Always subtract bottom from top, not top from bottom.

• Not recognizing when regrouping is needed: Check each place value before starting.

• Calculation errors: Double-check basic subtraction facts.

Key Notes for Memorization

• Always check the ones place first to determine if regrouping is needed.

• After regrouping: The tens digit decreases by 1, and the ones digit increases by 10.

• Total value remains constant: 53 = 4 tens and 13 ones (both equal 53).

• Verify with addition: If 53 - 28 = 25, then 25 + 28 should equal 53.

\(ab - cd = ef\)
2-Digit Subtraction
Regrouping Rule
1 ten = 10 ones
Place Value Conversion
Subtraction Process
Top - Bottom = Difference
Calculate Each Place
Verification
Difference + Subtrahend = Minuend
Check Your Answer
Key definitions:

Minuend: The number being subtracted from (top number)

Subtrahend: The number being subtracted (bottom number)

Difference: The result of the subtraction

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

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 tens: Convert 1 ten to 10 ones
  5. Decrease tens place: Reduce the tens digit by 1
  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 tens place by 1 and increase the ones place by 10.
Tip 3: Draw arrows to visualize the regrouping process.
Common errors: Forgetting to decrease the tens place when regrouping, subtracting bottom from top instead of top from bottom.
Key concept: 2-digit subtraction with regrouping requires borrowing from the tens place to the ones place.
Formulas to know by heart:

• Place value conversion: 1 ten = 10 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 why I need to change the tens place when I borrow. Can't I just add to the ones place?

Answer: Great question! When you borrow from the tens place, you're actually moving a group of 10 from one place value to another. Think of it like exchanging money: if you exchange one $10 bill for ten $1 bills, you still have the same total value ($10), but now distributed differently. Similarly, when you have 53 (which is 5 tens and 3 ones), and you borrow 1 ten to make the ones place larger, you now have 4 tens and 13 ones. The total value is still 53 (4×10 + 13 = 53), but you've redistributed the tens and ones to make subtraction possible in the ones place.

Question: How can I help my child understand place value better? They keep forgetting to adjust the tens 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 ten rod equals 10 unit cubes
  • Have them write small numbers above to track changes during regrouping
  • Create a chant: "Borrow from the left, add to the right"
  • Practice with visual aids that show the decrease in the tens place

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

Question: What are some common mistakes students make with 2-digit subtraction with regrouping?

Answer: Common mistakes include:

  • Forgetting to decrease the tens place after regrouping
  • Subtracting the bottom number from the top instead of top from bottom
  • Not recognizing when regrouping is needed
  • Mixing up place values and subtracting across columns incorrectly
  • Calculation errors in basic subtraction facts

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.