Distributive Operation

Distributive Operation

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 ★ (bc) = (ab) ☆ (ac) and (ab) ★ c = (ac) ☆ (bc).

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

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