Section 1
Core Properties for Equivalent Expressions
Property
Three core properties allow us to rewrite expressions into equivalent forms.
- Commutative Property of Addition: The order in which numbers are added does not change the sum.
In this Grade 7 lesson from Illustrative Mathematics, Chapter 6, students learn to rewrite subtraction expressions as equivalent addition expressions by replacing subtracted terms with their additive inverses. They apply the commutative and associative properties to rearrange terms and simplify calculations, then extend this understanding by using the distributive property to expand expressions with subtraction and negative coefficients. Practice problems reinforce converting between subtraction and addition forms and distributing a factor across multi-term expressions involving signed numbers.
Section 1
Core Properties for Equivalent Expressions
Three core properties allow us to rewrite expressions into equivalent forms.
Section 2
Using Properties to Group Like Terms
When we have to simplify algebraic expressions, we can often make the work easier by applying the Commutative or Associative Property first.
We can rearrange an expression so the like terms are together.
For example, we simplify by rewriting it as and then combining like terms to get .
We were using the Commutative Property of Addition.
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!
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Section 1
Core Properties for Equivalent Expressions
Three core properties allow us to rewrite expressions into equivalent forms.
Section 2
Using Properties to Group Like Terms
When we have to simplify algebraic expressions, we can often make the work easier by applying the Commutative or Associative Property first.
We can rearrange an expression so the like terms are together.
For example, we simplify by rewriting it as and then combining like terms to get .
We were using the Commutative Property of Addition.
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!
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter