The distributive property of multiplication is a fundamental concept in mathematics that states that when you multiply a number by a sum, you can distribute the multiplication to each addend within the parentheses. In simpler terms, it means you can break apart the sum into separate parts, multiply each part individually, and then add the results together.
For example, if you have the expression 3 × (4 + 5), instead of calculating the sum first, you can apply the distributive property:
- Multiply 3 by 4: 3 × 4 = 12
- Multiply 3 by 5: 3 × 5 = 15
Now, add the two results together: 12 + 15 = 27. You’ll find that whether you calculate it as 3 × (4 + 5) or as (3 × 4) + (3 × 5), the answer remains the same, which confirms the property.
This property is incredibly useful in simplifying expressions and making calculations easier, especially in algebra. It allows you to handle complex problems by breaking them down into manageable parts.