The distributive property of whole numbers involves how multiplication interacts with addition (and subtraction). Specifically, it describes how multiplying a whole number by a sum of whole numbers is the same as multiplying the whole number by each of the addends and then adding the products.
Distributive Property of Multiplication over Addition
This is the most common form of the distributive property. It states that for any whole numbers a, b, and c:
a × (b + c) = (a × b) + (a × c)
In simpler terms: Multiplying a number by a sum is the same as multiplying the number by each part of the sum and then adding the results.
Example:
Let's say a = 3, b = 4, and c = 5. Then:
3 × (4 + 5) = (3 × 4) + (3 × 5)
3 × 9 = 12 + 15
27 = 27
This confirms the distributive property.
Practical Applications:
The distributive property is incredibly useful for simplifying calculations, especially when dealing with larger numbers or mental math.
- Breaking down multiplication: Instead of directly multiplying 6 × 13, you can think of it as 6 × (10 + 3), which equals (6 × 10) + (6 × 3) = 60 + 18 = 78.
- Algebraic simplification: The distributive property is a fundamental concept in algebra and is used extensively in simplifying expressions.
Summary Table
| Property | Formula | Example |
|---|---|---|
| Distributive Property of Multiplication over Addition | a × (b + c) = (a × b) + (a × c) | 2 × (3 + 4) = (2 × 3) + (2 × 4) = 6 + 8 = 14 |
