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Understanding Properties of Number Operations

Learn about the basic properties of math operations - commutative, associative, identity, zero product, inverse, and distributive - to enhance your mathematical understanding. Discover how these properties simplify calculations and relationships between numbers.

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Understanding Properties of Number Operations

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  1. Properties of Operations For Addition and Multiplication

  2. Commutative Property of Addition • The order numbers are added does not affect the sum. + = + y x

  3. Commutative Property of Multiplication(think commute- to move)

  4. Associative Property of Addition • The way you group (associate) numbers does not affect the sum. + ( + 1) = ( + ) + 1

  5. Associative Property of MultiplicationThink: Who you associate with that day does not change your group of friends • The way you group (associate) factors does not change the product. · ( · 1) = ( · ) · 1

  6. Identity Property of Additionaka Additive Identity • The sum of any number and zero is that number. Example: + 0 = 0 is the identifier for this property.

  7. Identity Property of Multiplicationaka Multiplicative Identity • The product of any number and 1 is that number. Example: • 1 = 1 is the identifier for this property.

  8. Multiplicative Property of Zero • The product of any number and 0 is 0. Example: • 0 = 0

  9. Inverse Operations • Operations that cancel each other. Example: – = 0 List other inverse operations.

  10. Reciprocal or Multiplicative Inverse Operations • When multiplied together multiplicative inverses (reciprocals) equal 1. Example: 5 & 1/5 are reciprocals. 1 ½ & 2/3 are reciprocals. ** 1 is its own reciprocal, so is –1. ** 0 has no reciprocal

  11. The Distributive Property • The distributive property lets you multiply a sum by multiplying each addend separately and then add the products. • EX: 3(x + 4) = 3(x) + 3(4) OR 3x + 12

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