# Section 2-4 Reasoning with Properties from Algebra.

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Section 2-4 Reasoning with Properties from Algebra

Properties of Equality

Addition property Adding something to each side of an equation Given + 18 Therefore, the Addition Property of (=) was applied. Example:

subtraction property Subtracting from each side of an equation Given Therefore, the Subtraction Property of (=) was applied. Example:

Multiplication property Multiplying something to each side of an equation Example: Given 7 7 Therefore, the Multiplication Property of (=) was applied.

division property Dividing something on each side of an equation Example: Given 22 Therefore, the Division Property of (=) was applied.

Reflexive property Same exact thing on each side of the equal sign! Examples:

Symmetric property The sides of an equation are switched. (Nothing else is done with the equation.) Examples:

Transitive property * Relates to the Law of Syllogism!

Examples:

substitution property Plugging in something in place of another thing in any equation or expression. Example:

Distributive property a(b+c) = ab +ac *Helps to get rid of parentheses Example: 4(x+y) Given = 4x + 4y Therefore, the Distribution Property was applied.

Simplification To combine like terms Example: x= 3 + 5 Given = 8 Therefore, the Simplification was applied.