Solved Exercises on Using Place Value to Multiply Worksheets in Grade 2

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

Worksheet Solution: Exercises 1 to 3
1 Basic multiplication with place value
Exercise 1
Multiply using place value strategies:
3 × 20
Definition:

Place value multiplication: Multiplying numbers by understanding their place value (tens and ones) and using the distributive property

Multiplication method:
  1. Break the number into tens and ones
  2. Multiply the tens part by the multiplier
  3. Multiply the ones part by the multiplier
  4. Combine the results
Expression
3 × 20
Break apart
3 × (2 tens)
Result
60
Step 1: Break the number into place values

20 = 2 tens + 0 ones

Step 2: Multiply the tens part

3 × 2 tens = 6 tens

Step 3: Multiply the ones part

3 × 0 ones = 0 ones

Step 4: Combine the results

6 tens + 0 ones = 60

3 × 20 = 60
Final answer:

3 × 20 = 60

Applied rules:

• Place value: Understand that 20 is 2 tens

• Multiplication: Multiply tens by the number and keep the place value

• Combining: Add the results together

Place Value Multiplication Visual
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Tens Place

20 → 2 tens

3 × 2 tens = 6 tens = 60

Ones Place

20 → 0 ones

3 × 0 ones = 0 ones

Final Calculation

60 + 0 = 60

Or: 6 tens + 0 ones = 60

2 Multiplication with regrouping
Exercise 2
Multiply using place value strategies:
4 × 15
Definition:

Regrouping in multiplication: When multiplying, if the result in any place value is 10 or more, we may need to regroup into higher place values

Expression
4 × 15
Break apart
4 × (10 + 5)
Result
60
Step 1: Break the number into tens and ones

15 = 10 + 5 (1 ten and 5 ones)

Step 2: Apply the distributive property

4 × 15 = 4 × (10 + 5) = (4 × 10) + (4 × 5)

Step 3: Multiply the tens part

4 × 10 = 40

Step 4: Multiply the ones part

4 × 5 = 20

Step 5: Add the results together

40 + 20 = 60

4 × 15 = 60
Final answer:

4 × 15 = 60

Applied rules:

• Distributive property: a × (b + c) = (a × b) + (a × c)

• Place value: Separate tens and ones for easier calculation

• Combining: Add the partial products together

Multiplication with Distributive Property
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Break Apart

15 = 10 + 5

Distribute

4 × 15 = 4 × (10 + 5)

= (4 × 10) + (4 × 5)

Final Calculation

4 × 10 = 40

4 × 5 = 20

40 + 20 = 60

3 Multiplying multiples of 10
Exercise 3
Multiply using place value strategies:
5 × 30
Definition:

Multiplying multiples of 10: Multiplying a number by a multiple of 10 by focusing on the tens place

Expression
5 × 30
Break apart
5 × (3 tens)
Result
150
Step 1: Recognize the place values

30 = 3 tens + 0 ones

Step 2: Multiply the tens part

5 × 3 tens = 15 tens

Step 3: Multiply the ones part

5 × 0 ones = 0 ones

Step 4: Combine the results

15 tens + 0 ones = 150

5 × 30 = 150
Final answer:

5 × 30 = 150

Applied rules:

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

• Multiplication: Multiply the tens digit and keep the zero in ones place

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

Multiplying Multiples of 10
📊
Tens Place

30 → 3 tens

5 × 3 tens = 15 tens = 150

Ones Place

30 → 0 ones

5 × 0 ones = 0 ones

Final Answer

15 tens + 0 ones = 150

Complete Summary: Using Place Value to Multiply Worksheets
a × (b×10 + c) = (a × b×10) + (a × c)
Place Value Multiplication 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

Distributive property: Multiplying a sum by distributing the multiplication across addends

Partial products: Products obtained by multiplying each part of a decomposed 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 each number and identify tens and ones
  2. Break apart numbers: Write the number in expanded form (tens + ones)
  3. Apply distributive property: a × (b + c) = (a × b) + (a × c)
  4. Multiply each part: Multiply tens and ones separately
  5. Combine results: Add the partial products together
Tip 1: Always write out the expanded form (tens + ones) to visualize the problem.
Tip 2: Remember that multiplying by 10 means adding a zero to the end of the number.
Tip 3: Check your answer by using repeated addition (e.g., 4 × 15 = 15 + 15 + 15 + 15).
Tip 4: Use base-10 blocks or drawings to physically represent tens and ones.
Tip 5: Remember that 3 × 20 is the same as 20 × 3, but thinking of it as 3 groups of 20 might be easier.
Common errors: Forgetting to multiply both parts of the decomposed number, adding instead of multiplying, misaligning place values.
Key concepts: Distributive property, place value understanding, partial products.
Memorization tips: "Break it apart, multiply each part, then put it back together!"
Essential rules to remember:

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

• Distributive property: a × (b + c) = (a × b) + (a × c)

• Multiplication by 10: Any number multiplied by 10 adds a zero at the end

• Partial products: Multiply each place value separately, then combine

Examples progression
Multiplying multiples of 10:

3 × 20 = 3 × (2 tens) = 6 tens = 60

Multiplication with distributive property:

4 × 15 = 4 × (10 + 5) = (4 × 10) + (4 × 5) = 40 + 20 = 60

More complex example:

6 × 23 = 6 × (20 + 3) = (6 × 20) + (6 × 3) = 120 + 18 = 138

Worksheet Solution: Exercises 4 to 5
4 Word problem with place value multiplication
Exercise 4
A classroom has 4 rows of desks. Each row has 12 desks. How many desks are there in total?
Definition:

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

Expression
4 × 12
Break apart
4 × (10 + 2)
Result
48
Step 1: Identify the numbers in the problem

Number of rows: 4

Desks per row: 12

This is a multiplication problem: 4 × 12

Step 2: Break the number into tens and ones

12 = 10 + 2 (1 ten and 2 ones)

Step 3: Apply the distributive property

4 × 12 = 4 × (10 + 2) = (4 × 10) + (4 × 2)

Step 4: Multiply each part

4 × 10 = 40

4 × 2 = 8

Step 5: Add the results together

40 + 8 = 48

Step 6: State the answer in context

There are 48 desks in total.

There are 48 desks in total.
Final answer:

There are 48 desks in total.

Applied rules:

• Problem solving: Identify operation needed from context

• Place value: Break numbers into tens and ones

• Distributive property: Multiply each part separately

Word Problem Strategy
📊
Given Information

Rows: 4

Desks per row: 12

Operation: Multiplication

Break Apart

12 = 10 + 2

4 × 12 = 4 × (10 + 2)

Calculate

4 × 10 = 40

4 × 2 = 8

Total: 40 + 8 = 48

5 Multi-step place value multiplication worksheet
Exercise 5
A school has 3 classrooms. Each classroom has 24 students. The school wants to buy 2 notebooks for each student. How many notebooks does the school need to buy?
Definition:

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

Expression
3 × 24 × 2
Step 1
3 × 24 = 72
Step 2
72 × 2 = 144
Step 1: Find the total number of students

Classrooms: 3

Students per classroom: 24

Total students: 3 × 24

Step 2: Multiply 3 × 24 using place value

24 = 20 + 4 (2 tens and 4 ones)

3 × 24 = 3 × (20 + 4) = (3 × 20) + (3 × 4)

3 × 20 = 60, 3 × 4 = 12

60 + 12 = 72 students total

Step 3: Find total notebooks needed

Students: 72

Notebooks per student: 2

Total notebooks: 72 × 2

Step 4: Multiply 72 × 2 using place value

72 = 70 + 2 (7 tens and 2 ones)

72 × 2 = (70 × 2) + (2 × 2)

70 × 2 = 140, 2 × 2 = 4

140 + 4 = 144 notebooks

Step 5: Final answer in context

The school needs to buy 144 notebooks.

The school needs to buy 144 notebooks.
Final answer:

The school needs to buy 144 notebooks.

Applied rules:

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

• Place value: Break each number into tens and ones

• Distributive property: Apply when necessary in each operation

Multi-Step Problem Strategy
📊
Total Students

3 × 24

24 = 20 + 4

(3 × 20) + (3 × 4)

= 60 + 12 = 72 students

Notebooks Needed

72 × 2

72 = 70 + 2

(70 × 2) + (2 × 2)

= 140 + 4 = 144 notebooks

Final Answer

144 notebooks needed

Questions & Answers

Question: I don't understand why we need to break numbers apart when multiplying. Why can't I just multiply them directly?

Answer: Great question! Breaking numbers apart helps you understand what multiplication really means and makes bigger numbers easier to handle. Let me explain:

  • When you see 4 × 15, you're actually multiplying 4 × (10 + 5)
  • This equals (4 × 10) + (4 × 5) = 40 + 20 = 60
  • Breaking it apart makes it easier to see why 4 × 15 = 60
  • It's like having 4 groups of 15, which is the same as 4 groups of 10 plus 4 groups of 5

Think of it like having 4 bags with 15 items each. It's easier to think of it as 4 bags of 10 items plus 4 bags of 5 items.

Question: My child sometimes forgets to multiply both parts when using the distributive property. How can I help them remember?

Answer: Here are some strategies to help your child remember to multiply both parts:

  • Have them always write out the full distributive property: a × (b + c) = (a × b) + (a × c)
  • Use physical manipulatives like base-10 blocks to visualize the process
  • Draw boxes or circles around each part to be multiplied
  • Create a checklist: "Did I multiply the tens? Did I multiply the ones? Did I add them together?"

Practice with simple problems first: 2 × 13 = 2 × (10 + 3), 3 × 14 = 3 × (10 + 4), etc., before moving to larger numbers.

Remind them that both parts must be multiplied to get the correct answer!

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

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

  • Multiplying by 10: Just add a zero to the end of the number (e.g., 7 × 10 = 70)
  • Multiplying by 20: Multiply by 2, then add a zero (e.g., 6 × 20 = 120)
  • Patterns: Notice that 5 × 12 is the same as 12 × 5
  • Double and halve: For 4 × 15, think 2 × 30 = 60

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.