Distributive Property
The Distributive Property in Grade 7 algebra states that a(b + c) = ab + ac — multiplying a number by a sum equals the sum of the products with each addend separately. In Saxon Math, Course 2, students use this property to simplify expressions like 2(n + 5) = 2n + 10 and to verify equivalence: 2(l + w) = 2l + 2w for a rectangle perimeter. The Distributive Property is one of the most used properties in all of algebra, forming the basis for expanding expressions, factoring, and solving multi-step equations.
Key Concepts
Property $a(b + c) = ab + ac$ $a(b c) = ab ac$.
Examples Show that $2(l+w)$ and $2l+2w$ are equal for $l=30, w=20$: $2(30+20)=2(50)=100$ and $2(30)+2(20)=60+40=100$. Simplify using the property: $2(n+5) = 2 \cdot n + 2 \cdot 5 = 2n+10$.
Explanation This property is your ticket to breaking open parentheses! The term outside gets "distributed" or multiplied by every single term inside. It's like a pizza delivery—the number outside brings a slice of multiplication to everyone waiting inside the parentheses. No one gets left out!
Common Questions
What is the Distributive Property?
The Distributive Property states that a(b + c) = ab + ac. A factor multiplied by a sum equals the sum of that factor times each addend.
How do you apply the Distributive Property?
Multiply the outside factor by each term inside the parentheses separately, then write the results as a sum. For example, 3(x + 4) = 3x + 12.
Does the Distributive Property work with subtraction?
Yes. a(b - c) = ab - ac. For example, 5(x - 2) = 5x - 10.
How is the Distributive Property used in perimeter?
The perimeter of a rectangle is P = 2(l + w) = 2l + 2w. Both forms give the same result because of the Distributive Property.
Where is the Distributive Property covered in Saxon Math Course 2?
The Distributive Property is introduced in Saxon Math, Course 2, as part of Grade 7 algebraic properties and expression simplification.
Why is the Distributive Property so important in algebra?
It allows you to expand expressions, combine like terms, factor polynomials, and solve multi-step equations. Almost every algebraic manipulation relies on it.
What mistakes do students make with the Distributive Property?
Students often forget to multiply the outer factor by BOTH terms inside the parentheses, distributing to only the first term and leaving the second unchanged.