Learn on PengiPengi Math (Grade 6)Chapter 4: Expressions, Equations, and Patterns

Lesson 5: Equivalent Expressions and Properties of Operations

In this Grade 6 Pengi Math lesson from Chapter 4, students learn to identify and create equivalent expressions by applying the commutative, associative, identity, and zero properties of operations. Students practice combining like terms systematically and verify equivalence through simplification and substitution.

Section 1

Properties of Addition and Multiplication

Property

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

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

Section 2

Like Terms

Property

Like terms are terms where the variable part is the same. The numbers multiplied by the variable are called the coefficients.

To add or subtract like terms:

Add or subtract the coefficients.
Do not change the variable part of the terms.

Examples

To combine $8m - 3m$ , we subtract the coefficients: $(8-3)m = 5m$ .
To combine $7ab + 5ab$ , we add the coefficients: $(7+5)ab = 12ab$ .
To combine $y + 9y$ , remember the coefficient of $y$ is 1. So, $(1+9)y = 10y$ .

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: $a + 0 = a = 0 + a$

Section 2

Like Terms

Property

Like terms are terms where the variable part is the same. The numbers multiplied by the variable are called the coefficients.

To add or subtract like terms:

Add or subtract the coefficients.
Do not change the variable part of the terms.

Examples

To combine $8m - 3m$ , we subtract the coefficients: $(8-3)m = 5m$ .
To combine $7ab + 5ab$ , we add the coefficients: $(7+5)ab = 12ab$ .
To combine $y + 9y$ , remember the coefficient of $y$ is 1. So, $(1+9)y = 10y$ .

Section 3

Simplifying Expressions Using Properties

Property

Examples

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

Properties of Addition and Multiplication

Property

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

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

Section 2

Like Terms

Property

Like terms are terms where the variable part is the same. The numbers multiplied by the variable are called the coefficients.

To add or subtract like terms:

Add or subtract the coefficients.
Do not change the variable part of the terms.

Examples

To combine $8m - 3m$ , we subtract the coefficients: $(8-3)m = 5m$ .
To combine $7ab + 5ab$ , we add the coefficients: $(7+5)ab = 12ab$ .
To combine $y + 9y$ , remember the coefficient of $y$ is 1. So, $(1+9)y = 10y$ .

Section 3

Simplifying Expressions Using Properties