Section 1
Distributive Property with Variables
Property
When multiplying a number by a sum or difference in parentheses, you can distribute the multiplication to each term inside the parentheses.
For algebraic expressions:
In this Grade 7 enVision Mathematics lesson from Chapter 4, students learn how to expand algebraic expressions by applying the Distributive Property to multiply a factor outside parentheses by each term inside, including expressions with decimals, fractions, and multiple variables. Students practice expanding and simplifying expressions such as 1.5(b + 2.5) and -1/3(2 - 3x + 3), working with both numeric and variable coefficients. The lesson builds understanding of how expanded and factored forms of an expression are equivalent in value.
Section 1
Distributive Property with Variables
When multiplying a number by a sum or difference in parentheses, you can distribute the multiplication to each term inside the parentheses.
For algebraic expressions:
Section 2
Multiplying with an Area Model
To multiply using an area model, decompose one factor by place value to determine the dimensions of the partitioned rectangle.
The total product is the sum of the partial products (the areas of the smaller sections).
This visually represents the distributive property:
Section 3
Distributing to Expand Linear Expressions
To expand an expression means to remove the parentheses. We do this using the Distributive Property: . You must multiply the outside number by every single term inside the parentheses. After expanding, you finish the job by combining any like terms.
There are two massive traps when expanding expressions.
Trap 1: "Dropping a term." Students often multiply the outside number by the first term, but forget to multiply it by the second term! (e.g., writing as instead of ).
Trap 2: "The Ninja Negative." If there is a negative sign outside the parenthesis, like , it acts as a . It sneaks in and flips the sign of EVERY term inside. It becomes . Stay alert!
Section 4
Distributing Variables and Fractions
The Distributive Property applies to any type of factor, including variables and fractions. The process remains the same: multiply the outside factor by each term inside the parentheses.
Expand to review the lesson summary and core properties.
Section 1
Distributive Property with Variables
When multiplying a number by a sum or difference in parentheses, you can distribute the multiplication to each term inside the parentheses.
For algebraic expressions:
Section 2
Multiplying with an Area Model
To multiply using an area model, decompose one factor by place value to determine the dimensions of the partitioned rectangle.
The total product is the sum of the partial products (the areas of the smaller sections).
This visually represents the distributive property:
Section 3
Distributing to Expand Linear Expressions
To expand an expression means to remove the parentheses. We do this using the Distributive Property: . You must multiply the outside number by every single term inside the parentheses. After expanding, you finish the job by combining any like terms.
There are two massive traps when expanding expressions.
Trap 1: "Dropping a term." Students often multiply the outside number by the first term, but forget to multiply it by the second term! (e.g., writing as instead of ).
Trap 2: "The Ninja Negative." If there is a negative sign outside the parenthesis, like , it acts as a . It sneaks in and flips the sign of EVERY term inside. It becomes . Stay alert!
Section 4
Distributing Variables and Fractions
The Distributive Property applies to any type of factor, including variables and fractions. The process remains the same: multiply the outside factor by each term inside the parentheses.