This document defines and provides examples of several important algebraic properties: - The commutative and associative properties of addition and multiplication, which allow changing the order or grouping of terms. - The identity properties of addition and multiplication, where adding/multiplying a number by the identity element (0 for addition, 1 for multiplication) does not change the number. - The inverse properties of addition and multiplication, where adding/multiplying the inverse or opposite of a number results in the identity element. - The distributive property, where a number outside parentheses distributes to each term inside. - The zero property of multiplication, where any number multiplied by zero equals zero.

1. 2e Identify the following properties using variables and apply them in solving problems. (DOK 1)• Zero property of multiplication• Inverse operations of addition/subtraction and multiplication/division• Commutative and associative properties of addition and multiplication• Identity properties of addition and multiplication• Distributive properties of multiplication over addition and subtractionBy: Deia Sanders

2. Commutative PropertyChange OrderExamples:a + b = b + aor a • b = b • a or ab = ba

3. Associative PropertyWho you “associate “ with is your GROUP of friends Examples:a + (b + c) = (a + b) + c ora • (b • c) = (a • b) • c ora(bc) = (ab)c

4. Identity PropertyThe number keeps it’s identityExamples: a + 0 = a or a • 1 = a

5. Distributive PropertyThe number outside the parenthesis gets distributed to everything inside the parenthesisExamples: a(b + c) = ab + ac or ab+ ac = a(b + c)Most importantProperty!!!

6. Zero Property of MultiplicationAny number multiplied by zero equals ZEROExamples: 0(3x + 2y) = 0 or(3 • 0)(2 + 4) = 0 • 6 = 0

7. Inverse of AdditionAdding opposites equals zeroExamples: 2 – 2 = 0 or-3x + 3x = 0

8. Inverse of MultiplicationMultiplying by an inverse (reciprocal) equals 1Examples: or

9. Identify the Property3x(y + 2) = 3xy + 6xDistributive3x – 3x + 2y = 0 + 2yInverse of Addition0 + 2y = 2yIdentity of Addition2(3 + y) + 8 = 6 + 2y + 8Distributive6 + 8 + 2y = 8 + 6 + 2yThis simplifies to 14 + 2yCommutative

10. Identify the Property1(2x + 3y) = 2x + 3yIdentity of Multiplication(3x)(5x – 2z)(0) = 0Zero Property of Multiplication(2x – 4y) + 0 = 2x-4yIdentity Property of AdditionInverse Property of Addition3x – 2y + 2y = 3x

11. Complete Handout #1 page 73