Learn on PengienVision, Mathematics, Grade 6Chapter 4: Represent and Solve Equations and Inequalities

Lesson 2: Apply Properties of Equality

In this Grade 6 lesson from enVision Mathematics, students learn how to apply the Addition, Subtraction, Multiplication, and Division Properties of Equality to write equivalent equations. The lesson uses balance scale models to show that performing the same operation on both sides of an equation keeps it true. Students practice identifying and applying these properties to equations involving variables.

Section 1

Maintaining Balance: The Properties of Equality

Property

Addition and Subtraction Properties of Equality:
If the same quantity is added to or subtracted from both sides of an equation, the solution is unchanged.
In symbols, If $a = b$ , then $a + c = b + c$ and $a - c = b - c$ .
Multiplication and Division Properties of Equality:
If both sides of an equation are multiplied or divided by the same nonzero quantity, the solution is unchanged.
In symbols, If $a = b$ , then $ac = bc$ and $\frac{a}{c} = \frac{b}{c}$ , $c \neq 0$ .

Examples

If you have the equation $x - 5 = 10$ , you can add 5 to both sides to get $x - 5 + 5 = 10 + 5$ , which simplifies to $x = 15$ .
For the equation $4y = 28$ , you can divide both sides by 4 to get $\frac{4y}{4} = \frac{28}{4}$ , which simplifies to $y = 7$ .
If $z + 9 = 12$ , you can subtract 9 from both sides to get $z + 9 - 9 = 12 - 9$ , which simplifies to $z = 3$ .

Explanation

To keep an equation balanced, you must perform the exact same operation on both sides. Whatever you add, subtract, multiply, or divide on one side, you must do to the other side too.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Maintaining Balance: The Properties of Equality

Property

Examples

If you have the equation $x - 5 = 10$ , you can add 5 to both sides to get $x - 5 + 5 = 10 + 5$ , which simplifies to $x = 15$ .
For the equation $4y = 28$ , you can divide both sides by 4 to get $\frac{4y}{4} = \frac{28}{4}$ , which simplifies to $y = 7$ .
If $z + 9 = 12$ , you can subtract 9 from both sides to get $z + 9 - 9 = 12 - 9$ , which simplifies to $z = 3$ .

Explanation

To keep an equation balanced, you must perform the exact same operation on both sides. Whatever you add, subtract, multiply, or divide on one side, you must do to the other side too.

Overview

Lesson overview

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

Overview

Section 1

Maintaining Balance: The Properties of Equality

Property

Examples

If you have the equation $x - 5 = 10$ , you can add 5 to both sides to get $x - 5 + 5 = 10 + 5$ , which simplifies to $x = 15$ .
For the equation $4y = 28$ , you can divide both sides by 4 to get $\frac{4y}{4} = \frac{28}{4}$ , which simplifies to $y = 7$ .
If $z + 9 = 12$ , you can subtract 9 from both sides to get $z + 9 - 9 = 12 - 9$ , which simplifies to $z = 3$ .

Explanation

To keep an equation balanced, you must perform the exact same operation on both sides. Whatever you add, subtract, multiply, or divide on one side, you must do to the other side too.