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2e properties

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.

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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
Commutative PropertyChange OrderExamples:a + b = b + aor a • b = b • a or ab = ba
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
Identity PropertyThe number keeps it’s identityExamples: a + 0 = a or a • 1 = a
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!!!
Zero Property of MultiplicationAny number multiplied by zero equals ZEROExamples: 0(3x + 2y) = 0 or(3 • 0)(2 + 4) = 0 • 6 = 0
Inverse of AdditionAdding opposites equals zeroExamples: 2 – 2 = 0 or-3x + 3x = 0
Inverse of MultiplicationMultiplying by an inverse (reciprocal) equals 1Examples: or
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
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
Complete Handout #1 page 73