Section 2 4 Reasoning with Properties from Algebra

Section 2 -4 Reasoning with Properties from Algebra

Properties of Equality

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

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

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

division property • Dividing something on each side of an equation Given Example: 2 2 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 = 4 • x + 4 • y Therefore, the = 4 x + 4 y Distribution Property was applied.

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