Using Place Value to Multiply 4th Grade - Advanced Practice Exercises

Master advanced place value multiplication: expanded form, partial products, standard algorithm, and complex place value strategies with these 10 detailed exercises.

Exercises 1 to 5
1 Expanded Form Strategy: 246×3
Exercise 1
Use expanded form to multiply 246×3.
Definition:

Expanded form strategy: Breaking apart a number by its place values and multiplying each part separately.

Expanded form method:
  1. Break apart the larger number by place value: 246 = 200 + 40 + 6
  2. Multiply each part by the 1-digit number: 200×3, 40×3, and 6×3
  3. Add the partial products together
Expanded form
246 = 200 + 40 + 6
Partial products
200×3 + 40×3 + 6×3
Total
600 + 120 + 18
Step 1: Break apart 246 by place value

246 = 200 + 40 + 6 (2 hundreds, 4 tens, 6 ones)

Step 2: Multiply each part by 3

200 × 3 = 600

40 × 3 = 120

6 × 3 = 18

Step 3: Add the partial products

600 + 120 + 18 = 738

Step 4: Verify

Check that 246 × 3 = 738

246 × 3 = 738
Final answer:

246 × 3 = 738

Applied rules:

• Distributive property: a(b+c+d) = ab + ac + ad

• Place value: 246 = 2 hundreds + 4 tens + 6 ones

• Partial products: Multiply each place value separately

2 Partial Products: 357×4
Exercise 2
Use partial products to multiply 357×4.
Definition:

Partial products: Multiplying each digit of the multi-digit number by the 1-digit number, keeping place value.

Expanded form
357 = 300 + 50 + 7
Partial products
300×4 + 50×4 + 7×4
Total
1200 + 200 + 28
Step 1: Break apart 357 by place value

357 = 300 + 50 + 7 (3 hundreds, 5 tens, 7 ones)

Step 2: Multiply each part by 4

300 × 4 = 1200

50 × 4 = 200

7 × 4 = 28

Step 3: Add the partial products

1200 + 200 + 28 = 1428

Step 4: Verify

Check that 357 × 4 = 1428

357 × 4 = 1428
Final answer:

357 × 4 = 1428

Applied rules:

• Distributive property: a(b+c+d) = ab + ac + ad

• Place value: 357 = 3 hundreds + 5 tens + 7 ones

• Partial products: Multiply each place value separately

3 Standard Algorithm: 483×6
Exercise 3
Use the standard algorithm to multiply 483×6.
Definition:

Standard algorithm: Multiplying digits from right to left, carrying when needed.

Ones place
3×6 = 18
Tens place
8×6 = 48
Hundreds place
4×6 = 24
Step 1: Multiply ones place

3 × 6 = 18, write 8, carry 1

Step 2: Multiply tens place

8 × 6 = 48, add carried 1 = 49, write 9, carry 4

Step 3: Multiply hundreds place

4 × 6 = 24, add carried 4 = 28

Step 4: Combine results

Write the final number: 2898

Step 5: Verify

Check that 483 × 6 = 2898

483 × 6 = 2898
Final answer:

483 × 6 = 2898

Applied rules:

• Place value: Each digit has its place value

• Standard algorithm: Multiply from right to left

• Carrying: When product > 9, carry to next place

4 Expanded Form: 528×7
Exercise 4
Use expanded form to multiply 528×7.
Definition:

Expanded form strategy: Breaking apart a number by its place values and multiplying each part separately.

Expanded form
528 = 500 + 20 + 8
Partial products
500×7 + 20×7 + 8×7
Total
3500 + 140 + 56
Step 1: Break apart 528 by place value

528 = 500 + 20 + 8 (5 hundreds, 2 tens, 8 ones)

Step 2: Multiply each part by 7

500 × 7 = 3500

20 × 7 = 140

8 × 7 = 56

Step 3: Add the partial products

3500 + 140 + 56 = 3696

Step 4: Verify

Check that 528 × 7 = 3696

528 × 7 = 3696
Final answer:

528 × 7 = 3696

Applied rules:

• Distributive property: a(b+c+d) = ab + ac + ad

• Place value: 528 = 5 hundreds + 2 tens + 8 ones

• Partial products: Multiply each place value separately

5 Partial Products: 649×5
Exercise 5
Use partial products to multiply 649×5.
Definition:

Partial products: Multiplying each digit of the multi-digit number by the 1-digit number, keeping place value.

Expanded form
649 = 600 + 40 + 9
Partial products
600×5 + 40×5 + 9×5
Total
3000 + 200 + 45
Step 1: Break apart 649 by place value

649 = 600 + 40 + 9 (6 hundreds, 4 tens, 9 ones)

Step 2: Multiply each part by 5

600 × 5 = 3000

40 × 5 = 200

9 × 5 = 45

Step 3: Add the partial products

3000 + 200 + 45 = 3245

Step 4: Verify

Check that 649 × 5 = 3245

649 × 5 = 3245
Final answer:

649 × 5 = 3245

Applied rules:

• Distributive property: a(b+c+d) = ab + ac + ad

• Place value: 649 = 6 hundreds + 4 tens + 9 ones

• Partial products: Multiply each place value separately

Exercises 6 to 10
6 Standard Algorithm: 756×8
Exercise 6
Use the standard algorithm to multiply 756×8.
Definition:

Standard algorithm: Multiplying digits from right to left, carrying when needed.

Ones place
6×8 = 48
Tens place
5×8 = 40
Hundreds place
7×8 = 56
Step 1: Multiply ones place

6 × 8 = 48, write 8, carry 4

Step 2: Multiply tens place

5 × 8 = 40, add carried 4 = 44, write 4, carry 4

Step 3: Multiply hundreds place

7 × 8 = 56, add carried 4 = 60

Step 4: Combine results

Write the final number: 6048

Step 5: Verify

Check that 756 × 8 = 6048

756 × 8 = 6048
Final answer:

756 × 8 = 6048

Applied rules:

• Place value: Each digit has its place value

• Standard algorithm: Multiply from right to left

• Carrying: When product > 9, carry to next place

7 Expanded Form: 834×9
Exercise 7
Use expanded form to multiply 834×9.
Definition:

Expanded form strategy: Breaking apart a number by its place values and multiplying each part separately.

Expanded form
834 = 800 + 30 + 4
Partial products
800×9 + 30×9 + 4×9
Total
7200 + 270 + 36
Step 1: Break apart 834 by place value

834 = 800 + 30 + 4 (8 hundreds, 3 tens, 4 ones)

Step 2: Multiply each part by 9

800 × 9 = 7200

30 × 9 = 270

4 × 9 = 36

Step 3: Add the partial products

7200 + 270 + 36 = 7506

Step 4: Verify

Check that 834 × 9 = 7506

834 × 9 = 7506
Final answer:

834 × 9 = 7506

Applied rules:

• Distributive property: a(b+c+d) = ab + ac + ad

• Place value: 834 = 8 hundreds + 3 tens + 4 ones

• Partial products: Multiply each place value separately

8 Partial Products: 962×4
Exercise 8
Use partial products to multiply 962×4.
Definition:

Partial products: Multiplying each digit of the multi-digit number by the 1-digit number, keeping place value.

Expanded form
962 = 900 + 60 + 2
Partial products
900×4 + 60×4 + 2×4
Total
3600 + 240 + 8
Step 1: Break apart 962 by place value

962 = 900 + 60 + 2 (9 hundreds, 6 tens, 2 ones)

Step 2: Multiply each part by 4

900 × 4 = 3600

60 × 4 = 240

2 × 4 = 8

Step 3: Add the partial products

3600 + 240 + 8 = 3848

Step 4: Verify

Check that 962 × 4 = 3848

962 × 4 = 3848
Final answer:

962 × 4 = 3848

Applied rules:

• Distributive property: a(b+c+d) = ab + ac + ad

• Place value: 962 = 9 hundreds + 6 tens + 2 ones

• Partial products: Multiply each place value separately

9 Standard Algorithm: 473×7
Exercise 9
Use the standard algorithm to multiply 473×7.
Definition:

Standard algorithm: Multiplying digits from right to left, carrying when needed.

Ones place
3×7 = 21
Tens place
7×7 = 49
Hundreds place
4×7 = 28
Step 1: Multiply ones place

3 × 7 = 21, write 1, carry 2

Step 2: Multiply tens place

7 × 7 = 49, add carried 2 = 51, write 1, carry 5

Step 3: Multiply hundreds place

4 × 7 = 28, add carried 5 = 33

Step 4: Combine results

Write the final number: 3311

Step 5: Verify

Check that 473 × 7 = 3311

473 × 7 = 3311
Final answer:

473 × 7 = 3311

Applied rules:

• Place value: Each digit has its place value

• Standard algorithm: Multiply from right to left

• Carrying: When product > 9, carry to next place

10 Expanded Form: 589×6
Exercise 10
Use expanded form to multiply 589×6.
Definition:

Expanded form strategy: Breaking apart a number by its place values and multiplying each part separately.

Expanded form
589 = 500 + 80 + 9
Partial products
500×6 + 80×6 + 9×6
Total
3000 + 480 + 54
Step 1: Break apart 589 by place value

589 = 500 + 80 + 9 (5 hundreds, 8 tens, 9 ones)

Step 2: Multiply each part by 6

500 × 6 = 3000

80 × 6 = 480

9 × 6 = 54

Step 3: Add the partial products

3000 + 480 + 54 = 3534

Step 4: Verify

Check that 589 × 6 = 3534

589 × 6 = 3534
Final answer:

589 × 6 = 3534

Applied rules:

• Distributive property: a(b+c+d) = ab + ac + ad

• Place value: 589 = 5 hundreds + 8 tens + 9 ones

• Partial products: Multiply each place value separately

Complete Summary: Using Place Value to Multiply 4th Grade

Place Value Multiplication 🧮

📊
Step 1: Identify Place Values
Break apart number by place: 246 = 200 + 40 + 6
Step 2: Multiply Each Part
Multiply each place value by the 1-digit number
Step 3: Find Partial Products
Calculate: 200×3, 40×3, 6×3
Step 4: Add Products
Sum partial products: 600 + 120 + 18
Step 5: Verify Answer
Check that the answer makes sense
Place Value Multiplication Process
246
Original
200+40+6
Expanded
×3
Multiply
600+120+18
Partial
738
Total
Place Value Strategy
246×3 = (200+40+6)×3 = 200×3 + 40×3 + 6×3 = 600+120+18 = 738
Breaking apart makes multiplication easier!
Uses distributive property: a(b+c+d) = ab + ac + ad
Master Place Value Multiplication! 🌟
a(b+c+d) = ab + ac + ad
Distributive Property
Key Definitions:

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

Expanded Form: Writing a number as the sum of each digit's value

Partial Products: Products found by multiplying each place value separately

Distributive Property: Multiplication distributes over addition

Breaking Apart: Separating a number by its place values

Standard Algorithm: Traditional method of multiplying from right to left

Place Value Multiplication Methods:
  1. Expanded form: Break apart by place value and multiply each part
  2. Partial products: Multiply each place value separately, then add
  3. Standard algorithm: Multiply from right to left with carrying
  4. Verification: Always check your answer makes sense
Tip 1: Always break apart by place value first.
Tip 2: Keep track of zeros when multiplying by tens/hundreds.
Tip 3: Always verify your answer makes sense.
Tip 4: Practice with different multi-digit numbers.
Common Errors: Forgetting place value, missing partial products, incorrect addition.
Success Strategy: Practice place value understanding, check work systematically.
Multiplication Properties:

• Distributive: a(b+c+d) = ab + ac + ad

• Associative: (ab)c = a(bc)

• Commutative: ab = ba

• Identity: a×1 = a

Place Value Concepts & Strategies
246 × 3 = (200 + 40 + 6) × 3 = 200×3 + 40×3 + 6×3 = 600 + 120 + 18 = 738
Place Value Example
Place Value Levels:

Ones Place: Value of 1 (rightmost digit)

Tens Place: Value of 10 (second from right)

Hundreds Place: Value of 100 (third from right)

Thousands Place: Value of 1000 (fourth from right)

Advanced Place Value Strategies:
  1. Quick scan: Look for obvious place value patterns
  2. Systematic approach: Break apart each number systematically
  3. Visualization: Imagine the number in expanded form
  4. Verification: Always check your answer makes sense
Strategy 1: Start with simpler numbers to build confidence.
Strategy 2: Use visual models to represent place values.
Strategy 3: Always verify with estimation (246×3 ≈ 250×3 = 750).
Strategy 4: Practice with different multi-digit numbers.
Key Concepts: Place value understanding is fundamental to all arithmetic operations.
Real World: Place value applies to money, measurements, and data analysis.
Real-World Applications:

• Shopping: Calculating total cost of multiple items

• Area: Finding area of rectangles (length × width)

• Time: Converting between units (minutes to hours)

• Measurement: Converting between metric units

Questions & Answers

Question: Why do we need to break apart numbers by place value when multiplying? Can't we just multiply normally?

Answer: Breaking apart by place value helps you understand why multiplication works:

  • Understanding: It shows why the standard algorithm works
  • Accuracy: Reduces errors by handling smaller, simpler multiplications
  • Flexibility: Gives you a backup method when standard algorithm seems difficult
  • Foundation: Builds the base for more complex multiplication later

While you can multiply "normally," understanding place value makes you more flexible and confident with numbers. It's like knowing how a car engine works - you can still drive without it, but understanding helps when things go wrong!

Plus, this method helps you catch mistakes in your standard multiplication.

Question: My child is struggling with identifying place values. How can I help them practice this concept?

Answer: Here are practical ways to practice place value:

  • Use manipulatives: Base-10 blocks to physically represent hundreds, tens, and ones
  • Practice with money: $2.34 has 2 dollars, 3 dimes, 4 pennies
  • Write expanded form: Regularly write numbers like 246 = 200 + 40 + 6
  • Play games: "What number am I?" where you describe place values

Start with smaller numbers and gradually increase difficulty. Focus on the pattern: ones, tens, hundreds, thousands.

Practice regularly with real-world examples like prices, ages, or distances to make it meaningful.

Question: How can I help my students see the connection between place value and multiplication?

Answer: The connection is the distributive property:

  • Concrete example: 246×3 = (200+40+6)×3 = 200×3 + 40×3 + 6×3
  • Visual models: Use base-10 blocks to show 2 hundreds, 4 tens, and 6 ones each multiplied by 3
  • Real-world connection: If you buy 3 packs of 246 items, you get 3×200 + 3×40 + 3×6 items
  • Pattern recognition: Show that this works for any multi-digit number

Emphasize that place value breaking apart is just applying the distributive property. This makes multiplication of larger numbers manageable and helps students understand the "why" behind the "how."

The better students understand place value, the more successful they'll be with multiplication algorithms.