Breaking apart multiplication strategy explained for kids

📚 Understanding the Breaking Apart Multiplication Strategy

The breaking apart strategy, also known as the distributive property, is a method used to simplify multiplication problems by breaking down larger numbers into smaller, more manageable parts. This makes mental math and calculations on paper much easier.

📜 History and Background

The concept of breaking apart numbers has been used in mathematics for centuries, even before formal notation was developed. The distributive property, which is the formal basis for this strategy, has its roots in early algebraic manipulations and has been refined over time to become a fundamental tool in arithmetic and algebra.

🔑 Key Principles of the Breaking Apart Strategy

• ➕ Decomposition: Break down one or both factors into their place values or other convenient parts. For example, $17$ can be broken down into $10 + 7$.
• 🤝 Distribution: Multiply each part of one factor by the other factor. For example, to multiply $17 \times 5$, you would multiply $(10 \times 5) + (7 \times 5)$.
• 🔢 Addition: Add the results of the individual multiplications to get the final product. In the example above, $50 + 35 = 85$.

➕ Real-World Examples

Let's explore some practical examples to illustrate the breaking apart multiplication strategy.

🍎 Example 1: Multiplying 13 by 7

Break down 13 into 10 + 3. Then, multiply each part by 7:

• ➗ $10 \times 7 = 70$
• ✖️ $3 \times 7 = 21$
• ➕ $70 + 21 = 91$

So, $13 \times 7 = 91$.

🎉 Example 2: Multiplying 24 by 6

Break down 24 into 20 + 4. Then, multiply each part by 6:

• ➗ $20 \times 6 = 120$
• ✖️ $4 \times 6 = 24$
• ➕ $120 + 24 = 144$

So, $24 \times 6 = 144$.

💡 Example 3: Multiplying 15 by 8

Break down 15 into 10 + 5. Then, multiply each part by 8:

• ➗ $10 \times 8 = 80$
• ✖️ $5 \times 8 = 40$
• ➕ $80 + 40 = 120$

So, $15 \times 8 = 120$.

✏️ Example 4: Multiplying 32 by 4

Break down 32 into 30 + 2. Then, multiply each part by 4:

• ➗ $30 \times 4 = 120$
• ✖️ $2 \times 4 = 8$
• ➕ $120 + 8 = 128$

So, $32 \times 4 = 128$.

➕ Example 5: Multiplying 41 by 5

Break down 41 into 40 + 1. Then, multiply each part by 5:

• ➗ $40 \times 5 = 200$
• ✖️ $1 \times 5 = 5$
• ➕ $200 + 5 = 205$

So, $41 \times 5 = 205$.

➗ Example 6: Multiplying 27 by 3

Break down 27 into 20 + 7. Then, multiply each part by 3:

• ➗ $20 \times 3 = 60$
• ✖️ $7 \times 3 = 21$
• ➕ $60 + 21 = 81$

So, $27 \times 3 = 81$.

❓ Example 7: Multiplying 18 by 9

Break down 18 into 10 + 8. Then, multiply each part by 9:

• ➗ $10 \times 9 = 90$
• ✖️ $8 \times 9 = 72$
• ➕ $90 + 72 = 162$

So, $18 \times 9 = 162$.

✔️ Conclusion

The breaking apart multiplication strategy is a valuable tool for simplifying multiplication problems, making mental math easier, and building a stronger understanding of number relationships. By breaking down numbers into smaller parts, students can approach multiplication with confidence and accuracy.