Using Place Value to Multiply - Practice Exercises

Master place value multiplication: breaking apart numbers, multiplying by place value, and finding products with these 10 detailed exercises.

Exercises 1 to 5
1 23×4 using place value
Exercise 1
Use place value to multiply 23×4.
Definition:

Place value multiplication: Breaking apart a number by its place values and multiplying each part separately.

Place value method:
  1. Break apart the larger number by place value: 23 = 20 + 3
  2. Multiply each part by the 1-digit number: 20×4 and 3×4
  3. Add the partial products together
Expanded form
23 = 20 + 3
Partial products
20×4 + 3×4
Total
80 + 12
Step 1: Break apart 23 by place value

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

Step 2: Multiply each part by 4

20 × 4 = 80

3 × 4 = 12

Step 3: Add the partial products

80 + 12 = 92

Step 4: Verify

Check that 23 × 4 = 92

23 × 4 = 92
Final answer:

23 × 4 = 92

Applied rules:

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

• Place value: 23 = 2 tens + 3 ones

• Partial products: Multiply each place value separately

2 34×6 using place value
Exercise 2
Use place value to multiply 34×6.
Definition:

Place value multiplication: Breaking apart a number by its place values and multiplying each part separately.

Expanded form
34 = 30 + 4
Partial products
30×6 + 4×6
Total
180 + 24
Step 1: Break apart 34 by place value

34 = 30 + 4 (3 tens and 4 ones)

Step 2: Multiply each part by 6

30 × 6 = 180

4 × 6 = 24

Step 3: Add the partial products

180 + 24 = 204

Step 4: Verify

Check that 34 × 6 = 204

34 × 6 = 204
Final answer:

34 × 6 = 204

Applied rules:

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

• Place value: 34 = 3 tens + 4 ones

• Partial products: Multiply each place value separately

3 52×3 using place value
Exercise 3
Use place value to multiply 52×3.
Definition:

Place value multiplication: Breaking apart a number by its place values and multiplying each part separately.

Expanded form
52 = 50 + 2
Partial products
50×3 + 2×3
Total
150 + 6
Step 1: Break apart 52 by place value

52 = 50 + 2 (5 tens and 2 ones)

Step 2: Multiply each part by 3

50 × 3 = 150

2 × 3 = 6

Step 3: Add the partial products

150 + 6 = 156

Step 4: Verify

Check that 52 × 3 = 156

52 × 3 = 156
Final answer:

52 × 3 = 156

Applied rules:

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

• Place value: 52 = 5 tens + 2 ones

• Partial products: Multiply each place value separately

4 45×7 using place value
Exercise 4
Use place value to multiply 45×7.
Definition:

Place value multiplication: Breaking apart a number by its place values and multiplying each part separately.

Expanded form
45 = 40 + 5
Partial products
40×7 + 5×7
Total
280 + 35
Step 1: Break apart 45 by place value

45 = 40 + 5 (4 tens and 5 ones)

Step 2: Multiply each part by 7

40 × 7 = 280

5 × 7 = 35

Step 3: Add the partial products

280 + 35 = 315

Step 4: Verify

Check that 45 × 7 = 315

45 × 7 = 315
Final answer:

45 × 7 = 315

Applied rules:

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

• Place value: 45 = 4 tens + 5 ones

• Partial products: Multiply each place value separately

5 68×4 using place value
Exercise 5
Use place value to multiply 68×4.
Definition:

Place value multiplication: Breaking apart a number by its place values and multiplying each part separately.

Expanded form
68 = 60 + 8
Partial products
60×4 + 8×4
Total
240 + 32
Step 1: Break apart 68 by place value

68 = 60 + 8 (6 tens and 8 ones)

Step 2: Multiply each part by 4

60 × 4 = 240

8 × 4 = 32

Step 3: Add the partial products

240 + 32 = 272

Step 4: Verify

Check that 68 × 4 = 272

68 × 4 = 272
Final answer:

68 × 4 = 272

Applied rules:

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

• Place value: 68 = 6 tens + 8 ones

• Partial products: Multiply each place value separately

Exercises 6 to 10
6 73×5 using place value
Exercise 6
Use place value to multiply 73×5.
Definition:

Place value multiplication: Breaking apart a number by its place values and multiplying each part separately.

Expanded form
73 = 70 + 3
Partial products
70×5 + 3×5
Total
350 + 15
Step 1: Break apart 73 by place value

73 = 70 + 3 (7 tens and 3 ones)

Step 2: Multiply each part by 5

70 × 5 = 350

3 × 5 = 15

Step 3: Add the partial products

350 + 15 = 365

Step 4: Verify

Check that 73 × 5 = 365

73 × 5 = 365
Final answer:

73 × 5 = 365

Applied rules:

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

• Place value: 73 = 7 tens + 3 ones

• Partial products: Multiply each place value separately

7 84×6 using place value
Exercise 7
Use place value to multiply 84×6.
Definition:

Place value multiplication: Breaking apart a number by its place values and multiplying each part separately.

Expanded form
84 = 80 + 4
Partial products
80×6 + 4×6
Total
480 + 24
Step 1: Break apart 84 by place value

84 = 80 + 4 (8 tens and 4 ones)

Step 2: Multiply each part by 6

80 × 6 = 480

4 × 6 = 24

Step 3: Add the partial products

480 + 24 = 504

Step 4: Verify

Check that 84 × 6 = 504

84 × 6 = 504
Final answer:

84 × 6 = 504

Applied rules:

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

• Place value: 84 = 8 tens + 4 ones

• Partial products: Multiply each place value separately

8 92×3 using place value
Exercise 8
Use place value to multiply 92×3.
Definition:

Place value multiplication: Breaking apart a number by its place values and multiplying each part separately.

Expanded form
92 = 90 + 2
Partial products
90×3 + 2×3
Total
270 + 6
Step 1: Break apart 92 by place value

92 = 90 + 2 (9 tens and 2 ones)

Step 2: Multiply each part by 3

90 × 3 = 270

2 × 3 = 6

Step 3: Add the partial products

270 + 6 = 276

Step 4: Verify

Check that 92 × 3 = 276

92 × 3 = 276
Final answer:

92 × 3 = 276

Applied rules:

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

• Place value: 92 = 9 tens + 2 ones

• Partial products: Multiply each place value separately

9 57×8 using place value
Exercise 9
Use place value to multiply 57×8.
Definition:

Place value multiplication: Breaking apart a number by its place values and multiplying each part separately.

Expanded form
57 = 50 + 7
Partial products
50×8 + 7×8
Total
400 + 56
Step 1: Break apart 57 by place value

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

Step 2: Multiply each part by 8

50 × 8 = 400

7 × 8 = 56

Step 3: Add the partial products

400 + 56 = 456

Step 4: Verify

Check that 57 × 8 = 456

57 × 8 = 456
Final answer:

57 × 8 = 456

Applied rules:

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

• Place value: 57 = 5 tens + 7 ones

• Partial products: Multiply each place value separately

10 49×7 using place value
Exercise 10
Use place value to multiply 49×7.
Definition:

Place value multiplication: Breaking apart a number by its place values and multiplying each part separately.

Expanded form
49 = 40 + 9
Partial products
40×7 + 9×7
Total
280 + 63
Step 1: Break apart 49 by place value

49 = 40 + 9 (4 tens and 9 ones)

Step 2: Multiply each part by 7

40 × 7 = 280

9 × 7 = 63

Step 3: Add the partial products

280 + 63 = 343

Step 4: Verify

Check that 49 × 7 = 343

49 × 7 = 343
Final answer:

49 × 7 = 343

Applied rules:

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

• Place value: 49 = 4 tens + 9 ones

• Partial products: Multiply each place value separately

Complete Summary: Using Place Value to Multiply

Place Value Multiplication 🧮

📊
Step 1: Break Apart
Separate number by place value: 23 = 20 + 3
Step 2: Multiply Each Part
Multiply each place value by the 1-digit number
Step 3: Find Partial Products
Calculate: 20×4 = 80, 3×4 = 12
Step 4: Add Products
Sum partial products: 80 + 12 = 92
Step 5: Verify Answer
Check that the answer makes sense
Place Value Multiplication Process
23
Original
20+3
Expanded
×4
Multiply
80+12
Partial
92
Total
Place Value Strategy
23×4 = (20+3)×4 = 20×4 + 3×4 = 80+12 = 92
Breaking apart makes multiplication easier!
Uses distributive property: a(b+c) = ab + ac
Master Place Value Multiplication! 🌟
a(b+c) = ab + ac
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

Place Value Multiplication Method:
  1. Identify place values: Determine which digit is in each place
  2. Break apart: Write the number as expanded form
  3. Multiply each part: Multiply each place value by the 1-digit number
  4. Add partial products: Sum all the products together
  5. Verify: Check that your answer is reasonable
Tip 1: Always break apart by place value first.
Tip 2: Keep track of zeros when multiplying by tens.
Tip 3: Always verify your answer makes sense.
Tip 4: Practice with different place values (ones, tens, hundreds).
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) = ab + ac

• Associative: (ab)c = a(bc)

• Commutative: ab = ba

• Identity: a×1 = a

Place Value Concepts & Strategies
23 × 4 = (20 + 3) × 4 = 20×4 + 3×4 = 80 + 12 = 92
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 (23×4 ≈ 20×4 = 80).
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 543 = 500 + 40 + 3
  • 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: 23×4 = (20+3)×4 = 20×4 + 3×4
  • Visual models: Use base-10 blocks to show 2 tens and 3 ones each multiplied by 4
  • Real-world connection: If you buy 4 packs of 23 items, you get 4×20 + 4×3 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.