Using Place Value to Multiply 3rd Grade Review - Practice Exercises

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

Exercises 1 to 5
1 13×2 using place value
Exercise 1
Use place value to multiply 13×2.
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: 13 = 10 + 3
  2. Multiply each part by the 1-digit number: 10×2 and 3×2
  3. Add the partial products together
Expanded form
13 = 10 + 3
Partial products
10×2 + 3×2
Total
20 + 6
Step 1: Break apart 13 by place value

13 = 10 + 3 (1 ten and 3 ones)

Step 2: Multiply each part by 2

10 × 2 = 20

3 × 2 = 6

Step 3: Add the partial products

20 + 6 = 26

Step 4: Verify

Check that 13 × 2 = 26

13 × 2 = 26
Final answer:

13 × 2 = 26

Applied rules:

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

• Place value: 13 = 1 ten + 3 ones

• Partial products: Multiply each place value separately

2 24×3 using place value
Exercise 2
Use place value to multiply 24×3.
Definition:

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

Expanded form
24 = 20 + 4
Partial products
20×3 + 4×3
Total
60 + 12
Step 1: Break apart 24 by place value

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

Step 2: Multiply each part by 3

20 × 3 = 60

4 × 3 = 12

Step 3: Add the partial products

60 + 12 = 72

Step 4: Verify

Check that 24 × 3 = 72

24 × 3 = 72
Final answer:

24 × 3 = 72

Applied rules:

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

• Place value: 24 = 2 tens + 4 ones

• Partial products: Multiply each place value separately

3 15×4 using place value
Exercise 3
Use place value to multiply 15×4.
Definition:

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

Expanded form
15 = 10 + 5
Partial products
10×4 + 5×4
Total
40 + 20
Step 1: Break apart 15 by place value

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

Step 2: Multiply each part by 4

10 × 4 = 40

5 × 4 = 20

Step 3: Add the partial products

40 + 20 = 60

Step 4: Verify

Check that 15 × 4 = 60

15 × 4 = 60
Final answer:

15 × 4 = 60

Applied rules:

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

• Place value: 15 = 1 ten + 5 ones

• Partial products: Multiply each place value separately

4 32×2 using place value
Exercise 4
Use place value to multiply 32×2.
Definition:

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

Expanded form
32 = 30 + 2
Partial products
30×2 + 2×2
Total
60 + 4
Step 1: Break apart 32 by place value

32 = 30 + 2 (3 tens and 2 ones)

Step 2: Multiply each part by 2

30 × 2 = 60

2 × 2 = 4

Step 3: Add the partial products

60 + 4 = 64

Step 4: Verify

Check that 32 × 2 = 64

32 × 2 = 64
Final answer:

32 × 2 = 64

Applied rules:

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

• Place value: 32 = 3 tens + 2 ones

• Partial products: Multiply each place value separately

5 26×3 using place value
Exercise 5
Use place value to multiply 26×3.
Definition:

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

Expanded form
26 = 20 + 6
Partial products
20×3 + 6×3
Total
60 + 18
Step 1: Break apart 26 by place value

26 = 20 + 6 (2 tens and 6 ones)

Step 2: Multiply each part by 3

20 × 3 = 60

6 × 3 = 18

Step 3: Add the partial products

60 + 18 = 78

Step 4: Verify

Check that 26 × 3 = 78

26 × 3 = 78
Final answer:

26 × 3 = 78

Applied rules:

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

• Place value: 26 = 2 tens + 6 ones

• Partial products: Multiply each place value separately

Exercises 6 to 10
6 18×5 using place value
Exercise 6
Use place value to multiply 18×5.
Definition:

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

Expanded form
18 = 10 + 8
Partial products
10×5 + 8×5
Total
50 + 40
Step 1: Break apart 18 by place value

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

Step 2: Multiply each part by 5

10 × 5 = 50

8 × 5 = 40

Step 3: Add the partial products

50 + 40 = 90

Step 4: Verify

Check that 18 × 5 = 90

18 × 5 = 90
Final answer:

18 × 5 = 90

Applied rules:

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

• Place value: 18 = 1 ten + 8 ones

• Partial products: Multiply each place value separately

7 43×2 using place value
Exercise 7
Use place value to multiply 43×2.
Definition:

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

Expanded form
43 = 40 + 3
Partial products
40×2 + 3×2
Total
80 + 6
Step 1: Break apart 43 by place value

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

Step 2: Multiply each part by 2

40 × 2 = 80

3 × 2 = 6

Step 3: Add the partial products

80 + 6 = 86

Step 4: Verify

Check that 43 × 2 = 86

43 × 2 = 86
Final answer:

43 × 2 = 86

Applied rules:

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

• Place value: 43 = 4 tens + 3 ones

• Partial products: Multiply each place value separately

8 35×3 using place value
Exercise 8
Use place value to multiply 35×3.
Definition:

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

Expanded form
35 = 30 + 5
Partial products
30×3 + 5×3
Total
90 + 15
Step 1: Break apart 35 by place value

35 = 30 + 5 (3 tens and 5 ones)

Step 2: Multiply each part by 3

30 × 3 = 90

5 × 3 = 15

Step 3: Add the partial products

90 + 15 = 105

Step 4: Verify

Check that 35 × 3 = 105

35 × 3 = 105
Final answer:

35 × 3 = 105

Applied rules:

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

• Place value: 35 = 3 tens + 5 ones

• Partial products: Multiply each place value separately

9 27×4 using place value
Exercise 9
Use place value to multiply 27×4.
Definition:

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

Expanded form
27 = 20 + 7
Partial products
20×4 + 7×4
Total
80 + 28
Step 1: Break apart 27 by place value

27 = 20 + 7 (2 tens and 7 ones)

Step 2: Multiply each part by 4

20 × 4 = 80

7 × 4 = 28

Step 3: Add the partial products

80 + 28 = 108

Step 4: Verify

Check that 27 × 4 = 108

27 × 4 = 108
Final answer:

27 × 4 = 108

Applied rules:

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

• Place value: 27 = 2 tens + 7 ones

• Partial products: Multiply each place value separately

10 31×3 using place value
Exercise 10
Use place value to multiply 31×3.
Definition:

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

Expanded form
31 = 30 + 1
Partial products
30×3 + 1×3
Total
90 + 3
Step 1: Break apart 31 by place value

31 = 30 + 1 (3 tens and 1 one)

Step 2: Multiply each part by 3

30 × 3 = 90

1 × 3 = 3

Step 3: Add the partial products

90 + 3 = 93

Step 4: Verify

Check that 31 × 3 = 93

31 × 3 = 93
Final answer:

31 × 3 = 93

Applied rules:

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

• Place value: 31 = 3 tens + 1 one

• Partial products: Multiply each place value separately

Complete Summary: Using Place Value to Multiply 3rd Grade Review

Place Value Multiplication 🧮

📊
Step 1: Break Apart
Separate number by place value: 13 = 10 + 3
Step 2: Multiply Each Part
Multiply each place value by the 1-digit number
Step 3: Find Partial Products
Calculate: 10×2 = 20, 3×2 = 6
Step 4: Add Products
Sum partial products: 20 + 6 = 26
Step 5: Verify Answer
Check that the answer makes sense
Place Value Multiplication Process
13
Original
10+3
Expanded
×2
Multiply
20+6
Partial
26
Total
Place Value Strategy
13×2 = (10+3)×2 = 10×2 + 3×2 = 20+6 = 26
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).
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
13 × 2 = (10 + 3) × 2 = 10×2 + 3×2 = 20 + 6 = 26
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 (13×2 ≈ 10×2 = 20).
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 tens and ones
  • Practice with money: $1.23 has 1 dollar, 2 dimes, 3 pennies
  • Write expanded form: Regularly write numbers like 23 = 20 + 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: 13×2 = (10+3)×2 = 10×2 + 3×2
  • Visual models: Use base-10 blocks to show 1 ten and 3 ones each multiplied by 2
  • Real-world connection: If you buy 2 packs of 13 items, you get 2×10 + 2×3 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.