Core Properties for Equivalent Expressions
Core Properties for Equivalent Expressions is a Grade 7 math skill in Illustrative Mathematics, Chapter 6: Expressions, Equations, and Inequalities. Students apply commutative, associative, and distributive properties to rewrite algebraic expressions in equivalent forms.
Key Concepts
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.
Common Questions
What properties are used to create equivalent expressions?
The commutative, associative, and distributive properties are the core tools. Commutative lets you change order, associative lets you regroup, and distributive lets you expand or factor expressions.
How does the distributive property create equivalent expressions?
The distributive property states a(b plus c) equals ab plus ac. You can use it to expand expressions like 3(x plus 5) to 3x plus 15, or factor 6x plus 12 to 6(x plus 2).
What is an example of using properties to write equivalent expressions?
5x plus 3x equals (5 plus 3)x equals 8x (distributive property in reverse, or combining like terms). Both expressions are equivalent.
How do you verify two expressions are equivalent?
Substitute the same value into both expressions and check that they give the same result. If they agree for multiple values, they are likely equivalent.
What chapter covers equivalent expression properties in Illustrative Mathematics Grade 7?
Core properties for equivalent expressions are covered in Chapter 6: Expressions, Equations, and Inequalities in Illustrative Mathematics Grade 7.