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Properties of Algebra

Lisa Johnston. Properties of Algebra. Definition: It states that numbers can be added or multiplied in any order. Example: A+B = B+A A×B=B×A . Commutative Properties (Addition and Multiplication). Definition:

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Properties of Algebra

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  1. Lisa Johnston Properties of Algebra

  2. Definition: It states that numbers can be added or multiplied in any order. Example: A+B = B+A A×B=B×A Commutative Properties (Addition and Multiplication)

  3. Definition: AP Addition: When three or more numbers are added, the sum is the same regardless of the grouping of the addends. AP Multiplication: When three or more numbers are multiplied, the product is the same regardless of the grouping of the factors Example: a + b + c = b + a + c a * b * c = c * a * b Associative Properties (Addition and Multiplication)

  4. Definitions: IP Addition: that the sum of zero and any real number or variable is the number or variable itself. IP Multiplication: the product of 1 and any number or variable is the number or variable itself. Examples:   4 + 0 = 4 4 × 1 = 4 Identity Properties (Addition and Multiplication)

  5. Definition: It is defined as the sum of the individual products of the addends of the number is equal to the product of a number and sum. Example: a(b + c) = ab + ac -4(5 - y)= 4y – 20 15(a + 1)= 15a+15 Distributive Property

  6. Definition: Addition EQ: If the same number is added to both sides of an equation, the two sides remain equal. Subtraction EQ : Ifyou subtract the same number from both sides of an equation, the sides remain equal Example: x=y then x+z = y+z a=b then a-c = b-c Equality Property (Addition and Subtraction)

  7. Definition: Multiplication EP: The two sides of an equation remain equal if they are multiplied by the same number. Division EP: Division Property of Equality states that dividing both sides of an equation by a non-zero number doesn't affect the equation. Examples: If A=BThen A×C=B×C If A=B Then A/C= B/C Equality Property (Multiplication and Division)

  8. Definition: Inverse Property Addition: whena number or variable is added to its inverse number or variable, the result of this addition becomes zero. Inverse Property Multiplication: whena number or variable is multiplied by its inverse, the result becomes one. Example: a + (-a) = a – a =0 a× 1a=a Inverse Property (Addition and Multiplication)

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