The distributive property lets you break down multiplication problems into smaller, easier steps. Here's how it works:
1. Understanding the Distributive Property
The distributive property states that multiplying a sum by a number is the same as multiplying each addend in the sum by that number and then adding the products.
Example:
- 3 x (4 + 5) = (3 x 4) + (3 x 5)
2. Applying the Property to Multi-Digit Multiplication
Let's say you want to multiply 23 by 15. Here's how to use the distributive property:
- Step 1: Break down 23 into 20 + 3.
- Step 2: Apply the distributive property: 15 x (20 + 3) = (15 x 20) + (15 x 3)
- Step 3: Multiply each part: (300) + (45)
- Step 4: Add the products: 300 + 45 = 345
3. Practical Insights
- The distributive property is especially useful when dealing with larger numbers, as it breaks down the problem into smaller, more manageable parts.
- You can apply the distributive property to both factors in a multiplication problem if needed.
- This method can help you understand the multiplication process better and develop mental math skills.
4. Example: 34 x 26
- Step 1: Break down 34 into 30 + 4 and 26 into 20 + 6.
- Step 2: Apply the distributive property: (30 + 4) x (20 + 6) = (30 x 20) + (30 x 6) + (4 x 20) + (4 x 6)
- Step 3: Multiply each part: 600 + 180 + 80 + 24
- Step 4: Add the products: 600 + 180 + 80 + 24 = 884
Therefore, 34 x 26 = 884.
