Section 1-2Properties of Real Numbers

Commutative property

• Order doesn’t matter!Examples:

4334 Of Addition:

4334 Of Multiplication:

associative property

• Order stays the same, but the terms are regrouped.Examples:

321321 Of Addition:

321321 Of Multiplication:

Additive identity

• Add zero to a term so the term does not change

Example: 303

multiplicative identity

•Multiply by one so the term does not change

Example: 313

Multiplicative property of zero

• Anything times zero equals zero!

Example: 303

Distributive property

•Multiply to each term inside parenthesisExamples:

8424 xx

8442 xx

Substitution property of equality

• Replacing an expression by another expression of the same valueExample:

8148104

Symmetric property of equality

• Switch sides! (do not change order of terms on each side)Examples:

,1073 If then 7310 x7If then 7x

Reflexive property of equality

• Same thing (same order) on each side of the equal sign

Examples:

2525 aa

Transitive property of equality

• If , then

cbba , ca

Example:

• If , then

236,624 2324

Addition property of equality

• Add the same thing on both sides of an equation.

Example:

13

103

x

x

Subtraction property of equality

• Subtract the same thing on both sides of an equation.Example:

7

103

x

x

multiplication property of equality

•Multiply the same thing on both sides of an equation.

Example:

30

103

x

x

division property of equality

• Divide the same thing on both sides of an equation.

Example:

4

123

x

x