Two Digit Subtraction Practice for Grade 2 Students

Master two digit subtraction with borrowing and regrouping through these 5 detailed exercises with step-by-step solutions.

Solution: Exercises 1 to 3
1 Basic two-digit subtraction
Exercise 1
Calculate:
\(57 - 23\)
Definition:

Two-digit subtraction: Subtracting one two-digit number from another (from 10 to 99)

Subtraction method:
  1. Align numbers by place value (ones under ones, tens under tens)
  2. Subtract ones digits first
  3. Then subtract tens digits
  4. Write the final result
Setup
\(57 - 23\)
Subtract ones
\(7 - 3 = 4\)
Subtract tens
\(5 - 2 = 3\)
Step 1: Set up the problem vertically

\(\begin{array}{c@{}c@{}c} & 5 & 7 \\ - & 2 & 3 \\ \hline \end{array}\)

Step 2: Subtract the ones digits

\(7 - 3 = 4\)

Step 3: Subtract the tens digits

\(5 - 2 = 3\)

Step 4: Combine the results

\(3\) tens and \(4\) ones equals \(34\)

\(57 - 23 = 34\)
Final answer:

\(57 - 23 = 34\)

Applied rules:

• Place value: Tens and ones must be aligned properly

• Order of operations: Subtract ones first, then tens

• Basic subtraction facts: Know subtraction facts up to 10

2 Subtraction with borrowing
Exercise 2
Calculate:
\(62 - 37\)
Definition:

Borrowing/Regrouping: Taking one ten from the tens place to add ten ones to the ones place when the top digit is smaller

Setup
\(62 - 37\)
Borrow
\(62 = 5 tens + 12 ones\)
Subtract
\(12-7=5, 5-3=2\)
Step 1: Set up the problem vertically

\(\begin{array}{c@{}c@{}c} & 6 & 2 \\ - & 3 & 7 \\ \hline \end{array}\)

Step 2: Check if we can subtract ones

\(2 < 7\), so we need to borrow from tens place

Step 3: Borrow one ten

Take one ten from the tens place (6 becomes 5) and add 10 to the ones place (2 becomes 12)

Step 4: Subtract the ones digits

\(12 - 7 = 5\)

Step 5: Subtract the tens digits

\(5 - 3 = 2\)

Step 6: Write the final answer

\(2\) tens and \(5\) ones equals \(25\)

\(62 - 37 = 25\)
Final answer:

\(62 - 37 = 25\)

Applied rules:

• Borrowing rule: When top digit is smaller, borrow 1 from next higher place value

• Regrouping: 1 ten = 10 ones

• Adjustment: Reduce the higher place value by 1 after borrowing

3 Word problem subtraction
Exercise 3
Sarah had 84 stickers. She gave 29 to her friend. How many stickers does she have left?
Definition:

Word problems: Real-life situations that require mathematical operations to solve

Identify
\(84 - 29\)
Borrow
\(84 = 7 tens + 14 ones\)
Calculate
\(14-9=5, 7-2=5\)
Step 1: Identify the operation

"She gave away" means we need to subtract: \(84 - 29\)

Step 2: Set up the problem vertically

\(\begin{array}{c@{}c@{}c} & 8 & 4 \\ - & 2 & 9 \\ \hline \end{array}\)

Step 3: Check if we can subtract ones

\(4 < 9\), so we need to borrow from tens place

Step 4: Borrow one ten

Take one ten from the tens place (8 becomes 7) and add 10 to the ones place (4 becomes 14)

Step 5: Subtract the ones digits

\(14 - 9 = 5\)

Step 6: Subtract the tens digits

\(7 - 2 = 5\)

Step 7: Write the answer in context

Sarah has 55 stickers left.

\(84 - 29 = 55\)
Final answer:

Sarah has 55 stickers left.

Applied rules:

• Problem solving: Identify key words indicating operation

• Context: Answer must make sense in the word problem context

• Subtraction algorithm: Follow the same steps as numerical problems

Two Digit Subtraction Rules and Methods
\(AB - CD = (A \times 10 + B) - (C \times 10 + D)\)
Two-Digit Subtraction Formula
Borrowing Rule
If B < D, then A-1, B+10
When ones digit is smaller
Place Value
Tens + Ones
Align by place value
Regrouping
1 ten = 10 ones
Exchange between places
Key definitions:

Place value: Position of a digit determines its value (tens, ones)

Borrowing: Taking from a higher place value when needed

Regrouping: Reorganizing numbers by place value

Complete methodology:
  1. Align numbers: Put ones under ones, tens under tens
  2. Check ones digits: See if top digit ≥ bottom digit
  3. Borrow if needed: Take 1 from tens, add 10 to ones
  4. Subtract ones: Top ones minus bottom ones
  5. Subtract tens: Top tens minus bottom tens
  6. Combine: Write tens digit followed by ones digit
Tip 1: Always check if you can subtract ones before starting.
Tip 2: Remember that borrowing reduces the tens digit by 1.
Tip 3: Draw lines to separate tens and ones to stay organized.
Tip 4: Check your answer by adding the result to the number subtracted.
Common errors: Forgetting to borrow, subtracting bottom from top incorrectly, misaligning digits.
Key notes: Practice basic subtraction facts, always check your work, remember place value rules.
Formulas to know by heart:

• Two-digit number: \(AB = A \times 10 + B\)

• Borrowing rule: When \(B < D\), borrow 1 ten (\(A\) becomes \(A-1\), \(B\) becomes \(B+10\))

• Place value alignment: Align ones with ones, tens with tens

• Regrouping: 1 ten = 10 ones

Solution: Exercises 4 to 5
4 Money subtraction problem
Exercise 4
Tom had $73. He spent $46 on a toy. How much money does he have left?
Definition:

Money problems: Subtraction problems involving currency amounts

Setup
\(73 - 46\)
Borrow
\(73 = 6 tens + 13 ones\)
Subtract
\(13-6=7, 6-4=2\)
Step 1: Identify the operation

"He spent" means we need to subtract: \(73 - 46\)

Step 2: Set up the problem vertically

\(\begin{array}{c@{}c@{}c} & 7 & 3 \\ - & 4 & 6 \\ \hline \end{array}\)

Step 3: Check if we can subtract ones

\(3 < 6\), so we need to borrow from tens place

Step 4: Borrow one ten

Take one ten from the tens place (7 becomes 6) and add 10 to the ones place (3 becomes 13)

Step 5: Subtract the ones digits

\(13 - 6 = 7\)

Step 6: Subtract the tens digits

\(6 - 4 = 2\)

Step 7: Write the answer with units

Tom has $27 left.

\(73 - 46 = 27\)
Final answer:

Tom has $27 left.

Applied rules:

• Money problems: Same as regular subtraction, include currency symbol

• Borrowing: Follow the same borrowing procedure as numerical problems

• Units: Include the dollar sign in the final answer

5 Multi-step subtraction
Exercise 5
A farmer had 92 apples. He sold 38 on Monday and 25 on Tuesday. How many apples does he have left?
Definition:

Multi-step problems: Problems requiring multiple calculations to reach the solution

Total sold
\(38 + 25 = 63\)
Final subtraction
\(92 - 63\)
Borrow & subtract
\(92 = 8 tens + 12 ones\)
Step 1: Find total apples sold

Add Monday and Tuesday sales: \(38 + 25 = 63\)

Step 2: Subtract total sold from original amount

\(92 - 63\)

Step 3: Set up the problem vertically

\(\begin{array}{c@{}c@{}c} & 9 & 2 \\ - & 6 & 3 \\ \hline \end{array}\)

Step 4: Check if we can subtract ones

\(2 < 3\), so we need to borrow from tens place

Step 5: Borrow one ten

Take one ten from the tens place (9 becomes 8) and add 10 to the ones place (2 becomes 12)

Step 6: Subtract the ones digits

\(12 - 3 = 9\)

Step 7: Subtract the tens digits

\(8 - 6 = 2\)

Step 8: Write the final answer

The farmer has 29 apples left.

\(92 - (38 + 25) = 92 - 63 = 29\)
Final answer:

The farmer has 29 apples left.

Applied rules:

• Multi-step problems: Break into smaller parts and solve sequentially

• Order of operations: Solve addition first, then subtraction

• Subtraction algorithm: Apply borrowing when needed

Complete Guide to Two Digit Subtraction
\(AB - CD = (A \times 10 + B) - (C \times 10 + D)\)
Two-Digit Subtraction
Key definitions:

Two-digit numbers: Numbers from 10 to 99 with tens and ones place values

Borrowing: Taking 1 from the tens place to add 10 to the ones place

Regrouping: Changing the grouping of numbers by place value

Complete methodology:
  1. Read the problem: Understand what is being asked
  2. Set up the equation: Write the larger number above the smaller number
  3. Align by place value: Ones under ones, tens under tens
  4. Check ones place: See if top digit ≥ bottom digit
  5. Borrow if necessary: Take 1 from tens place and add 10 to ones place
  6. Subtract ones: Perform the subtraction in the ones place
  7. Subtract tens: Perform the subtraction in the tens place
  8. Check your answer: Add the result to the subtracted number
Tip 1: Practice basic subtraction facts (0-10) to build fluency.
Tip 2: Always write problems vertically to keep digits aligned.
Tip 3: Circle the number you're borrowing from to remember to reduce it by 1.
Tip 4: Verify your answer by adding the difference to the number you subtracted.
Common errors: Forgetting to borrow when needed, subtracting smaller from larger without borrowing, misaligning digits.
Exam preparation: Master basic facts, practice borrowing, solve word problems.
Rules to know by heart:

• Place value: Always align digits by place value

• Borrowing rule: When top digit is smaller, borrow 1 ten = 10 ones

• Subtraction sequence: Subtract ones first, then tens

• Verification: Difference + Subtrahend = Minuend

Questions & Answers

Question: I get confused about when to borrow in subtraction. How do I know if I need to borrow?

Answer: Great question! You need to borrow when the top digit in any place value is SMALLER than the bottom digit in the same place value. Let me break this down:

  • Check the ones place first: Look at the ones digits. If the top ones digit is smaller than the bottom ones digit, you need to borrow.
  • Example: In 52 - 17, look at 2 vs 7. Since 2 < 7, you need to borrow.
  • After borrowing: Reduce the tens digit by 1 and add 10 to the ones digit.

Think of borrowing like exchanging: you're exchanging one ten-dollar bill for ten one-dollar bills. So 52 becomes 4 tens and 12 ones (42 + 10 = 52).

The key memory trick: "If top is smaller, go next door and borrow!"

Question: How can I help my students visualize the concept of borrowing in subtraction?

Answer: Visual representations are extremely helpful for teaching borrowing! Here are effective strategies:

  • Base-10 blocks: Use rods (tens) and units (ones). When you need to borrow, physically break apart a rod into 10 units.
  • Number bonds: Show how 52 = 50 + 2, and when borrowing, it becomes 40 + 12.
  • Arrow notation: Draw arrows showing 1 from tens going to ones place, with +10 added to the ones.
  • Color coding: Use different colors for tens and ones to emphasize place value.

The concrete-to-abstract progression works best: start with manipulatives, move to drawings, then to abstract numbers. This helps students internalize why borrowing works mathematically.

Also encourage students to say the process out loud: "I need to borrow 1 ten, which gives me 10 ones, so now I have..."

Question: My child struggles with word problems involving subtraction. How can I help them identify when to subtract?

Answer: Word problem identification is a critical skill! Here are key strategies to teach your child:

  • Look for key phrases: "left," "remaining," "less than," "take away," "spent," "sold," "how many more," "difference."
  • Visualize the situation: Encourage drawing pictures or acting out the problem.
  • Identify what's happening: Something is being taken away or compared.
  • Find the whole and parts: Usually you start with a total and take part away.

For example, in "Sarah had 84 stickers and gave 29 away," the key is "gave away" which indicates subtraction. The total (84) is being reduced by a part (29).

Practice with consistent phrase patterns: "started with - gave away = left" or "total - taken = remaining." This creates a mental framework for future problems.