What is a distributive property?

The distributive property says that multiplying a number by a sum gives the same answer as multiplying by each part separately and then adding. It is the idea behind splitting hard multiplications into easier ones, and later behind expanding brackets in algebra.

Examples

• 3 × (4 + 2) = 3 × 4 + 3 × 2 = 12 + 6 = 18.
• 6 × 13 = 6 × 10 + 6 × 3 = 60 + 18 = 78.
• 7 × 9 = 7 × (10 − 1) = 70 − 7 = 63.

Quick facts

• It breaks a tricky times fact into two easy ones.
• It is the foundation of the grid (area) method for multiplication.