Solved Exercises on Using Place Value Strategies to Subtract in Grade 2

Master place value subtraction: tens and ones, subtraction within 100 with regrouping through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic subtraction with place value
Exercise 1
Subtract using place value strategies:
57 - 23
Definition:

Place value subtraction: Subtracting numbers by breaking them into tens and ones, then subtracting like place values

Subtraction method:
  1. Break each number into tens and ones
  2. Subtract the tens from tens
  3. Subtract the ones from ones
  4. Combine the results
Expression
57 - 23
Break apart
50 + 7 - 20 - 3
Result
34
Step 1: Break numbers into tens and ones

57 = 50 + 7 (5 tens and 7 ones)

23 = 20 + 3 (2 tens and 3 ones)

Step 2: Subtract the tens

50 - 20 = 30

Step 3: Subtract the ones

7 - 3 = 4

Step 4: Combine the results

30 + 4 = 34

57 - 23 = 34
Final answer:

57 - 23 = 34

Applied rules:

• Place value: Separate tens and ones to make subtraction easier

• Like place values: Only subtract tens from tens and ones from ones

• Combining: Add the final tens and ones together

Place Value Subtraction Visual
📊
Tens Place

57 → 5 tens

23 → 2 tens

Subtract: 5 - 2 = 3 tens = 30

Ones Place

57 → 7 ones

23 → 3 ones

Subtract: 7 - 3 = 4 ones

Final Calculation

30 + 4 = 34

Or: 3 tens + 4 ones = 34

2 Subtraction with regrouping
Exercise 2
Subtract using place value strategies:
62 - 38
Definition:

Regrouping in subtraction: Borrowing 1 ten from the tens place to add 10 ones to the ones place when needed

Expression
62 - 38
Break apart
60 + 2 - 30 - 8
Result
24
Step 1: Break numbers into tens and ones

62 = 60 + 2 (6 tens and 2 ones)

38 = 30 + 8 (3 tens and 8 ones)

Step 2: Check if we can subtract ones

2 ones - 8 ones: We cannot subtract 8 from 2!

We need to regroup!

Step 3: Regroup the tens

Borrow 1 ten from 6 tens: 60 becomes 50

Add 10 to the ones: 2 + 10 = 12 ones

Now we have: 50 + 12 - 30 - 8

Step 4: Subtract the tens

50 - 30 = 20

Step 5: Subtract the ones

12 - 8 = 4

Step 6: Combine the results

20 + 4 = 24

62 - 38 = 24
Final answer:

62 - 38 = 24

Applied rules:

• Regrouping: When ones in minuend are less than ones in subtrahend, borrow from tens

• Place value: Separate tens and ones for easier calculation

• Subtraction: Subtract tens from tens and ones from ones

Subtraction with Regrouping
📊
Original Numbers

62 → 6 tens + 2 ones

38 → 3 tens + 8 ones

Regrouping Needed

2 ones < 8 ones → Borrow 1 ten

62 → 5 tens + 12 ones

Final Calculation

Tens: 5 - 3 = 2 tens

Ones: 12 - 8 = 4 ones

Answer: 24

3 Subtracting multiples of 10
Exercise 3
Subtract using place value strategies:
70 - 30
Definition:

Subtracting multiples of 10: Subtracting numbers that only have tens place values (no ones)

Expression
70 - 30
Break apart
7 tens - 3 tens
Result
40
Step 1: Recognize the place values

70 = 7 tens + 0 ones

30 = 3 tens + 0 ones

Step 2: Subtract the tens

7 tens - 3 tens = 4 tens

Step 3: Subtract the ones

0 ones - 0 ones = 0 ones

Step 4: Combine the results

4 tens + 0 ones = 40

70 - 30 = 40
Final answer:

70 - 30 = 40

Applied rules:

• Place value: Understand that multiples of 10 only have tens place

• Like place values: Only subtract tens from tens and ones from ones

• Zero ones: When subtracting multiples of 10, the ones place remains zero

Subtracting Multiples of 10
📊
Tens Place

70 → 7 tens

30 → 3 tens

Subtract: 7 - 3 = 4 tens = 40

Ones Place

70 → 0 ones

30 → 0 ones

Subtract: 0 - 0 = 0 ones

Final Answer

4 tens + 0 ones = 40

Complete Summary: Using Place Value Strategies to Subtract
AB - CD = (A×10 + B) - (C×10 + D)
Place Value Subtraction Formula
Key definitions:

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

Tens place: The second digit from the right, representing groups of ten

Ones place: The rightmost digit, representing individual units

Regrouping: Converting 1 ten into 10 ones when subtracting

Minuend: The number being subtracted from (top number)

Subtrahend: The number being subtracted (bottom number)

Expanded form: Writing a number as the sum of its place values (e.g., 45 = 40 + 5)

Complete methodology:
  1. Recognize the numbers: Look at minuend and subtrahend and identify tens and ones
  2. Break apart numbers: Write each number in expanded form (tens + ones)
  3. Check for regrouping: If ones in minuend are less than ones in subtrahend, regroup
  4. Subtract tens from tens: Perform tens subtraction
  5. Subtract ones from ones: Perform ones subtraction
  6. Combine results: Add the final tens and ones together
Tip 1: Always write out the expanded form (tens + ones) to visualize the problem.
Tip 2: Before subtracting ones, check if the top number has enough ones.
Tip 3: When regrouping, remember: 1 ten = 10 ones.
Tip 4: Use base-10 blocks or drawings to physically represent tens and ones.
Tip 5: Check your answer by adding the result to the subtrahend to get the minuend.
Common errors: Subtracting tens from ones, forgetting to regroup when needed, borrowing incorrectly.
Key concepts: 1 ten = 10 ones, only subtract like place values, regrouping preserves value.
Memorization tip: "Not enough ones? Borrow from tens!" for regrouping.
Essential rules to remember:

• Place value formula: Two-digit number AB = A×10 + B

• Subtraction rule: (T₁ + O₁) - (T₂ + O₂) = (T₁ - T₂) + (O₁ - O₂)

• Regrouping rule: When O₁ < O₂, borrow 1 ten from T₁

• Like place values: Only subtract tens from tens and ones from ones

Examples progression
Simple subtraction (no regrouping):

45 - 23 = (40 + 5) - (20 + 3) = (40 - 20) + (5 - 3) = 20 + 2 = 22

Subtraction with regrouping:

52 - 37 = (50 + 2) - (30 + 7) = (40 + 12) - (30 + 7) = (40 - 30) + (12 - 7) = 10 + 5 = 15

Subtracting multiples of 10:

80 - 30 = (8 tens) - (3 tens) = 5 tens = 50

Solution: Exercises 4 to 5
4 Word problem with place value subtraction
Exercise 4
Tom had 43 stickers. He gave 18 stickers to his sister. How many stickers does Tom have left?
Definition:

Word problems: Real-life situations requiring mathematical operations using place value strategies

Expression
43 - 18
Break apart
40 + 3 - 10 - 8
Result
25
Step 1: Identify the numbers in the problem

Tom started with 43 stickers

He gave away 18 stickers

This is a subtraction problem: 43 - 18

Step 2: Break numbers into tens and ones

43 = 40 + 3 (4 tens and 3 ones)

18 = 10 + 8 (1 ten and 8 ones)

Step 3: Check if we need to regroup

3 ones - 8 ones: We cannot subtract 8 from 3!

We need to regroup!

Step 4: Regroup the tens

Borrow 1 ten from 4 tens: 40 becomes 30

Add 10 to the ones: 3 + 10 = 13 ones

Now we have: 30 + 13 - 10 - 8

Step 5: Subtract tens and ones

Tens: 30 - 10 = 20

Ones: 13 - 8 = 5

Step 6: Combine results and state answer

20 + 5 = 25

Tom has 25 stickers left.

Tom has 25 stickers left.
Final answer:

Tom has 25 stickers left.

Applied rules:

• Problem solving: Identify operation needed from context

• Place value: Break numbers into tens and ones

• Regrouping: When ones in minuend are less than ones in subtrahend

Word Problem Strategy
📊
Given Information

Started with: 43 stickers

Gave away: 18 stickers

Operation: Subtraction

Break Apart

43 = 40 + 3

18 = 10 + 8

Calculate

Regroup: 43 = 30 + 13

Tens: 30 - 10 = 20

Ones: 13 - 8 = 5

Total: 25 stickers

5 Multi-step place value subtraction
Exercise 5
A bakery had 85 cupcakes. They sold 29 cupcakes in the morning and then sold 17 more cupcakes in the afternoon. How many cupcakes does the bakery have left?
Definition:

Multi-step problems: Problems requiring multiple subtraction operations solved sequentially using place value strategies

Expression
85 - 29 - 17
Step 1
85 - 29 = 56
Step 2
56 - 17 = 39
Step 1: Find how many were sold in total

Morning sales: 29 cupcakes

Afternoon sales: 17 cupcakes

Total sold: 29 + 17 = 46 cupcakes

Step 2: Subtract morning sales from total (85 - 29)

85 = 80 + 5, 29 = 20 + 9

Check ones: 5 < 9 → need to regroup

85 = 70 + 15

Tens: 70 - 20 = 50

Ones: 15 - 9 = 6

50 + 6 = 56 cupcakes left after morning

Step 3: Subtract afternoon sales

Now subtract the afternoon sales: 56 - 17

56 = 50 + 6, 17 = 10 + 7

Check ones: 6 < 7 → need to regroup

56 = 40 + 16

Tens: 40 - 10 = 30

Ones: 16 - 7 = 9

30 + 9 = 39 cupcakes left

Step 4: Final answer in context

The bakery has 39 cupcakes left.

The bakery has 39 cupcakes left.
Final answer:

The bakery has 39 cupcakes left.

Applied rules:

• Order of operations: Work from left to right for subtraction

• Place value: Break each number into tens and ones

• Regrouping: Apply when necessary in each operation

Multi-Step Problem Strategy
📊
Initial Cupcakes

Started with: 85 cupcakes

Morning Sales

85 - 29

85 = 70 + 15

29 = 20 + 9

Result: 56 cupcakes

Afternoon Sales

56 - 17

56 = 40 + 16

17 = 10 + 7

Result: 39 cupcakes

Questions & Answers

Question: I don't understand when I need to regroup in subtraction. Can you explain?

Answer: Great question! You need to regroup in subtraction when the top number (minuend) has fewer ones than the bottom number (subtrahend). Here's how to check:

  • Look at the ones place in both numbers
  • If the top ones are less than the bottom ones, you MUST regroup
  • For example: in 42 - 17, look at 2 and 7. Since 2 < 7, you need to regroup
  • Think of it as "borrowing" 1 ten from the tens place to add 10 ones to the ones place

So in 42 - 17: 42 becomes 3 tens and 12 ones (since 2 + 10 = 12), then you can subtract 12 - 7 = 5 ones.

Question: My child sometimes forgets to regroup when they should. How can I help them remember?

Answer: Here are some strategies to help your child remember when to regroup:

  • Have them always check the ones first: "Do I have enough ones to subtract?"
  • Create a chant: "More on the floor, go next door" (meaning when bottom ones are more than top ones, borrow from tens)
  • Use physical manipulatives like base-10 blocks to visualize the process
  • Draw circles around the ones in both numbers and compare them before starting

Practice with simple problems first: 32 - 15, 41 - 18, etc., before moving to larger numbers.

Remind them that regrouping doesn't change the value, just how it's written!

Question: I want to get faster at place value subtraction. Are there any shortcuts I can learn?

Answer: Once you master the basics, here are some mental math shortcuts for advanced learners:

  • Subtracting multiples of 10: Just subtract the tens digits and keep zeros (e.g., 80 - 30 = 50)
  • Compensation: Instead of 43 - 19, think 44 - 20 (add 1 to both numbers)
  • Counting up: For 52 - 48, count up from 48 to 52: 48→49→50→51→52 = 4
  • Patterns: Notice that subtracting 9 is like subtracting 10 and adding 1

But remember, these shortcuts work because of place value! Always understand the underlying concept first.

Practice with timed drills once you're comfortable with the basic strategies to build speed and accuracy.