Overview
This lecture introduces the distributive property in mathematics, explaining how it allows multiplication across a sum or difference and demonstrating its usefulness in calculation.
The Distributive Property
- The distributive property allows a number to be multiplied across each term in a sum or difference inside parentheses.
- Example: 5 × (3 + 4) is the same as (5 × 3) + (5 × 4).
- Both methods yield the same result (35 in this example), demonstrating the property’s reliability.
- This property applies to both addition and subtraction inside parentheses.
Visual and Practical Examples
- Splitting 7 into 3 + 4 and multiplying each by 5 models the distributive property visually.
- Simplifying calculations: 5 × 17 can be written as 5 × (10 + 5 + 2).
- This expands to (5 × 10) + (5 × 5) + (5 × 2) = 50 + 25 + 10 = 85.
- Mental math using the distributive property helps quickly solve multiplication problems with large numbers.
Key Terms & Definitions
- Distributive Property — A property stating a × (b + c) = (a × b) + (a × c), or a × (b − c) = (a × b) − (a × c).
Action Items / Next Steps
- Practice using the distributive property for mental math and breaking down larger multiplication problems.