Properties of Equations and Operations

a + b = b + a

a(b + c) = ab + ac

a(bc) = (ab)c

a - b = b - a

It allows changing the order of numbers.

It allows dividing numbers in any order.

It allows moving parentheses to simplify calculations.

It allows multiplying numbers in any order.

Negative one

One

The number itself

Zero

9

0

1

3

Add 6 to both sides

Subtract 6 from both sides

Multiply both sides by 2

Divide both sides by 2

Distributive Property

Associative Property

Multiplicative Inverse Property

Additive Inverse Property

Add 7 to both sides

Subtract 3x from both sides

Add 3x to both sides

Subtract 7 from both sides

x = 2

x = 16

x = 4

x = 8

Multiplicative Inverse Property

Distributive Property

Symmetry Property of Equality

Associative Property

To avoid solving the equation

To change the values of variables

To justify each step and simplify the process

To make equations more complex