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Properties of the Real Number System

FOR ADDITION: The order in which any two numbers are added does not change the sum. FOR MULTIPLICATION: The order in which any two numbers are multiplied does not change the product.

FOR ADDITION: When adding 3 or more numbers, grouping symbols can be placed around any 2 numbers without changing the sum. FOR MULTIPLICATION: When multiplying 3 or more numbers, grouping symbols can be placed around any 2 numbers without changing the product.

When a number is multiplied to a sum (in parentheses): multiply each number inside the parentheses by the number outside. Examples: 1. 3(x + 5)2. -3(4x – 6) 3. ½ (6x + 4)4. -(9x – 3)

FOR ADDITION: Adding zero to any number does not change the number. FOR MULTIPLICATION: Multiplying any number by one does not change the number.

FOR ADDITION: The sum of any number and its opposite is zero. EX: Find the additive inverse… FOR MULTIPLICATION: The product of any number and its reciprocal is one. EX: Find the multiplicative inverse…

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