Practice multiplying numbers using expanded notation.
Multiply 23 × 4 using expanded notation.
23 = 20 + 3
23 × 4 = (20 + 3) × 4
= (20 × 4) + (3 × 4)
20 × 4 = 80
3 × 4 = 12
80 + 12 = 92
Multiply 145 × 3 using expanded notation.
| Number | Hundreds | Tens | Ones |
|---|---|---|---|
| 145 | 1 | 4 | 5 |
| Expanded | 100 | 40 | 5 |
145 = 100 + 40 + 5
145 × 3 = (100 + 40 + 5) × 3
= (100 × 3) + (40 × 3) + (5 × 3)
100 × 3 = 300
40 × 3 = 120
5 × 3 = 15
300 + 120 + 15 = 435
Practice multiplying two-digit numbers by single digits using expanded notation.
Multiply 34 × 12 using expanded notation.
34 = 30 + 4
12 = 10 + 2
34 × 12 = (30 + 4) × (10 + 2)
= 30×10 + 30×2 + 4×10 + 4×2
30 × 10 = 300
30 × 2 = 60
4 × 10 = 40
4 × 2 = 8
300 + 60 + 40 + 8 = 408
Multiply 56 × 23 using expanded notation.
56 = 50 + 6
23 = 20 + 3
56 × 23 = (50 + 6) × (20 + 3)
= 50×20 + 50×3 + 6×20 + 6×3
50 × 20 = 1,000
50 × 3 = 150
6 × 20 = 120
6 × 3 = 18
1,000 + 150 + 120 + 18 = 1,288
Definition: Expanded notation multiplication uses the distributive property to multiply numbers by breaking them into their place value components.
- Distributive Property: a(b + c) = ab + ac
- Place Value Multiplication: Multiplying each place value component separately
- Partial Products: Individual multiplication results before adding them together
- Standard Form: Final answer written in normal number format
Expanded Notation: Writing a number to show the value of each digit
Distributive Property: Property that allows multiplication to be distributed across addition
Partial Products: Individual multiplication results before combining
- Expand both numbers: Write each number in expanded notation
- Distribute multiplication: Apply the distributive property
- Calculate partial products: Multiply each component
- Combine results: Add all partial products together
- Verify: Check by multiplying in standard form
Advanced multiplication with three-digit numbers.
Multiply 345 × 7 using expanded notation.
345 = 300 + 40 + 5
345 × 7 = (300 + 40 + 5) × 7
= (300 × 7) + (40 × 7) + (5 × 7)
300 × 7 = 2,100
40 × 7 = 280
5 × 7 = 35
2,100 + 280 + 35 = 2,415
Multiply 678 × 4 using expanded notation.
| Number | Hundreds | Tens | Ones |
|---|---|---|---|
| 678 | 6 | 7 | 8 |
| Expanded | 600 | 70 | 8 |
678 = 600 + 70 + 8
678 × 4 = (600 + 70 + 8) × 4
= (600 × 4) + (70 × 4) + (8 × 4)
600 × 4 = 2,400
70 × 4 = 280
8 × 4 = 32
2,400 + 280 + 32 = 2,712
Practice with various multiplication scenarios.
23 × 5 = (20 + 3) × 5 = 100 + 15 = 115
12 × 34 = (10 + 2) × (30 + 4) = 300 + 40 + 60 + 8 = 408
456 × 3 = (400 + 50 + 6) × 3 = 1,200 + 150 + 18 = 1,368
A school has 24 classrooms with 28 students in each classroom. How many students are there in total?
24 × 28
24 = 20 + 4
28 = 20 + 8
24 × 28 = (20 + 4) × (20 + 8)
= 20×20 + 20×8 + 4×20 + 4×8
20 × 20 = 400
20 × 8 = 160
4 × 20 = 80
4 × 8 = 32
400 + 160 + 80 + 32 = 672
Progression: Master expanded notation multiplication through systematic practice.
Expanded Notation: Writing a number to show the value of each digit
Distributive Property: Property that allows multiplication to be distributed across addition
Partial Products: Individual multiplication results before combining
- Expand both numbers: Write each number in expanded notation
- Distribute multiplication: Apply the distributive property
- Calculate partial products: Multiply each component
- Combine results: Add all partial products together
- Verify: Check by multiplying in standard form
• Distribute multiplication across addition: a(b + c) = ab + ac
• Multiply each place value component separately
• Add all partial products to get the final answer
• Keep track of place values during multiplication
Single digit × two-digit numbers
Two-digit × two-digit numbers
Real-world applications
Questions & Answers
Question: How can I help students understand expanded notation multiplication?
Answer: Use these strategies:
- Visual aids: Base-ten blocks to show the multiplication process
- Step-by-step approach: Break down the distributive property clearly
- Color coding: Different colors for different place values
- Practice tables: Use place value charts to organize work
- Verbal explanation: Have students explain each step out loud
Start with simple examples before moving to more complex problems.
Question: How much practice should my child do with expanded notation multiplication?
Answer: For expanded notation multiplication:
- Daily practice: 15-20 minutes per day is ideal
- Start simple: Begin with single digit × two-digit problems
- Gradual progression: Move to two-digit × two-digit problems
- Review regularly: Revisit concepts weekly to maintain skills
- Make it fun: Use games and activities to maintain engagement
Quality practice is more important than quantity - focus on understanding the process.
Question: Why do we need to learn expanded notation multiplication? Isn't regular multiplication faster?
Answer: Expanded notation multiplication is important because it:
- Builds understanding: Helps you really understand what multiplication means
- Prepares for advanced math: Makes algebra and other concepts easier to learn
- Reduces errors: Makes it easier to catch mistakes in larger calculations
- Develops number sense: Improves your understanding of how numbers work
- Problem-solving: Teaches logical thinking and organization
Think of it as learning the "why" behind the "how" - it makes all math stronger!