Related Topics:

Lesson Plans and Worksheets for Algebra I

Lesson Plans and Worksheets for all Grades

More Lessons for Algebra I

Common Core For Algebra I

Examples, videos, and solutions to help Algebra I students learn how to use the commutative and associative properties to recognize structure within expressions and to prove equivalence of expressions.

Worksheets for Algebra I, Module 1, Lesson 7 (pdf)

Student Outcomes:

Students use the commutative and associative properties to recognize structure within expressions and to prove equivalency of expressions.

**Four Properties of Arithmetic:**

**The Commutative Property of Addition: If a and b are real numbers, then a + b = b + a.**

**The Associative Property of Addition: If a, b and c are real numbers, then (a + b) + c = a + (b +c)**

**The Commutative Property of Multiplication: If a and b are real numbers, then a x b = b x a.**

**The Associative Property of Multiplication: If a, b and c are real numbers, then (ab)c = a(bc).**

Lesson Summary

The Commutative and Associative Properties represent key beliefs about the arithmetic of real numbers. These properties can be applied to algebraic expressions using variables that represent real numbers.

Two algebraic expressions are equivalent if we can convert one expression into the other by repeatedly applying the Commutative, Associative, and Distributive Properties and the properties of rational exponents to components of the first expression.

Exit Ticket

Write a mathematical proof of the algebraic equivalence of (pq)r and (qr)p.

Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.