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