Learn on PengienVision, Mathematics, Grade 6Chapter 3: Numeric and Algebraic Expressions

Lesson 7: Simplify Algebraic Expressions

In Grade 6 enVision Mathematics, Lesson 3-7 teaches students how to simplify algebraic expressions by combining like terms using the Identity Property of Multiplication and the Distributive Property. Students practice writing equivalent expressions involving whole numbers, fractions, and decimals, including cases with parentheses. This lesson aligns with Common Core standards 6.EE.A.3 and 6.EE.A.4 in Chapter 3 on Numeric and Algebraic Expressions.

Section 1

Identity properties of addition and multiplication

Property

The identity property of addition: for any real number $a$ ,

a + 0 = a \quad 0 + a = a

$0$ is called the additive identity.

The identity property of multiplication: for any real number $a$ ,

a \cdot 1 = a \quad 1 \cdot a = a

$1$ is called the multiplicative identity.

Examples

The expression $42 + 0$ simplifies to $42$ by the identity property of addition.
Using the identity property of multiplication, the expression $1 \cdot (-5y)$ simplifies to $-5y$ .
When simplifying $0 + (x+y)$ , the identity property of addition shows the result is just $x+y$ .

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, $(1+9)y = 10y$ .

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Identity properties of addition and multiplication

Property

The identity property of addition: for any real number $a$ ,

a + 0 = a \quad 0 + a = a

$0$ is called the additive identity.

The identity property of multiplication: for any real number $a$ ,

a \cdot 1 = a \quad 1 \cdot a = a

$1$ is called the multiplicative identity.

Examples

The expression $42 + 0$ simplifies to $42$ by the identity property of addition.
Using the identity property of multiplication, the expression $1 \cdot (-5y)$ simplifies to $-5y$ .
When simplifying $0 + (x+y)$ , the identity property of addition shows the result is just $x+y$ .

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, $(1+9)y = 10y$ .

Overview

Lesson overview

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

Overview

Section 1

Identity properties of addition and multiplication

Property

The identity property of addition: for any real number $a$ ,

a + 0 = a \quad 0 + a = a

$0$ is called the additive identity.

The identity property of multiplication: for any real number $a$ ,

a \cdot 1 = a \quad 1 \cdot a = a

$1$ is called the multiplicative identity.

Examples

The expression $42 + 0$ simplifies to $42$ by the identity property of addition.
Using the identity property of multiplication, the expression $1 \cdot (-5y)$ simplifies to $-5y$ .
When simplifying $0 + (x+y)$ , the identity property of addition shows the result is just $x+y$ .

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, $(1+9)y = 10y$ .