An internal operation ★ on a set E is distributive over an internal operation ☆ on E if, for all elements a, b and c of E, we have : a ★ (b ☆ c) = (a ★ b) ☆ (a ★ c) and (a ☆ b) ★ c = (a ★ c) ☆ (b ★ c).
Examples
The multiplication of real numbers is distributive over the addition and subtraction of real numbers.
- 3 × (5 + 4) = (3 × 5) + (3 × 4)
- (8 + 9) × 4 = (8 × 4) + (9 × 4)
The division of whole numbers is not distributive over the addition of real numbers.
- 150 ÷ (10 + 20) ≠ (100 ÷ 10) + (100 ÷ 20), since we obtain : 30 ≠ 15