The distributive property for Class 7 integers explains how multiplication interacts with addition or subtraction. It essentially states that multiplying a number by a sum or difference is the same as multiplying the number by each term in the sum or difference and then adding or subtracting the results.
Understanding the Distributive Property
The core idea of the distributive property can be represented as follows:
a × (b + c) = (a × b) + (a × c)
Where 'a', 'b', and 'c' are any integers.
Explanation
This property shows that instead of first adding 'b' and 'c' and then multiplying the result by 'a', you can first multiply 'a' by 'b', then multiply 'a' by 'c', and finally add these two results together. Both methods yield the same final answer.
Practical Insights:
- Simplifying Calculations: The distributive property can help simplify complicated calculations by breaking them down into smaller, easier steps.
- Algebraic Foundations: This property is a crucial building block in algebra. It's used to solve equations and manipulate algebraic expressions.
Examples of the Distributive Property
Here are a few examples to illustrate how the distributive property works:
Example 1: Addition
- Let's take a = 3, b = 4, and c = 5.
- According to the distributive property: 3 × (4 + 5) = (3 × 4) + (3 × 5)
- Working out the Left Hand Side (LHS): 3 × (9) = 27
- Working out the Right Hand Side (RHS): (12) + (15) = 27
- Since LHS = RHS, the distributive property is validated.
Example 2: Subtraction
- Let's take a = 2, b = 7, and c = 3. The distributive property also applies to subtraction: a × (b - c) = (a × b) - (a × c)
- Therefore, 2 × (7 - 3) = (2 × 7) - (2 × 3)
- Working out the LHS: 2 × 4 = 8
- Working out the RHS: 14 - 6 = 8
- Again, LHS = RHS, illustrating the distributive property with subtraction.
Table Summary
| Property | Formula | Example |
|---|---|---|
| Distributive over Addition | a × (b + c) = (a × b) + (a × c) | 3 × (4 + 5) = (3 × 4) + (3 × 5) = 27 |
| Distributive over Subtraction | a × (b - c) = (a × b) - (a × c) | 2 × (7 - 3) = (2 × 7) - (2 × 3) = 8 |
Key Takeaway
The distributive property is a cornerstone mathematical rule that demonstrates how multiplication interacts with addition and subtraction for integers. It helps with simplifying calculations, is fundamental to algebra, and is a core concept for Class 7 students.
