Learn on PengiBig Ideas Math, Course 1Chapter 3: Algebraic Expressions and Properties

Lesson 3: Properties of Addition and Multiplication

In this Grade 6 lesson from Big Ideas Math, Course 1, students learn the Commutative and Associative Properties of Addition and Multiplication, as well as the Addition Property of Zero and the Multiplication Properties of Zero and One. Students apply these properties to simplify algebraic expressions involving variables, such as reordering or regrouping terms to combine constants. The lesson also explores how these properties work in real-life contexts, like calculating a sponsor's total payment for a basketball team.

Section 1

Properties of Addition and Multiplication

Property

These properties are the fundamental rules that govern arithmetic and algebra.

Identity Property of Addition: a+0=a=0+aa + 0 = a = 0 + a

Section 2

Associative properties

Property

Associative Property of Addition: If aa, bb, and cc are real numbers, then

(a+b)+c=a+(b+c)(a + b) + c = a + (b + c)

Associative Property of Multiplication: If aa, bb, and cc are real numbers, then

(a⋅b)⋅c=a⋅(b⋅c)(a \cdot b) \cdot c = a \cdot (b \cdot c)

When adding or multiplying three numbers, changing the grouping of the numbers does not change the result.

Section 3

Simplifying Expressions Using Properties

Property

To systematically simplify algebraic expressions:
(1) Use commutative property to reorder terms；
(2) Use associative property to regroup terms；
(3) Combine like terms；
(4) Apply identity and zero properties.
The goal is to write the simplest equivalent expression.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Properties of Addition and Multiplication

Property

These properties are the fundamental rules that govern arithmetic and algebra.

Identity Property of Addition: a+0=a=0+aa + 0 = a = 0 + a

Section 2

Associative properties

Property

Associative Property of Addition: If aa, bb, and cc are real numbers, then

(a+b)+c=a+(b+c)(a + b) + c = a + (b + c)

Associative Property of Multiplication: If aa, bb, and cc are real numbers, then

(a⋅b)⋅c=a⋅(b⋅c)(a \cdot b) \cdot c = a \cdot (b \cdot c)

When adding or multiplying three numbers, changing the grouping of the numbers does not change the result.

Section 3

Simplifying Expressions Using Properties

Property

To systematically simplify algebraic expressions:
(1) Use commutative property to reorder terms；
(2) Use associative property to regroup terms；
(3) Combine like terms；
(4) Apply identity and zero properties.
The goal is to write the simplest equivalent expression.

Examples