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Chapter 1 Operations on Real Numbers and Algebraic Expressions

Chapter 1 Operations on Real Numbers and Algebraic Expressions. Section 6 Properties of Real Numbers. Section 1.6 Objectives. 1 Understand and Use the Identity Properties of Addition and Multiplication 2 Understand and Use the Commutative Properties of Addition and Multiplication

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Chapter 1 Operations on Real Numbers and Algebraic Expressions

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  1. Chapter 1 Operations on Real Numbers and Algebraic Expressions Section 6 Properties ofReal Numbers

  2. Section 1.6 Objectives 1 Understand and Use the Identity Properties of Addition and Multiplication 2 Understand and Use the Commutative Properties of Addition and Multiplication 3 Understand and Use the Associative Properties of Addition and Multiplication 4 Understand the Multiplication and Division Properties of 0

  3. Identity Properties Identity Property of Addition For any real number a, 0 + a = a + 0 = a. That is, the sum of any number and 0 is that number. We call 0 the additive identity. Multiplicative Identity For any real number a, a· 1 = 1 ·a = a. That is, the product of any number and 1 is that number. We call 1 the multiplicative identity.

  4. 12 inches 1 foot This uses the multiplicative identity. Using the Identity Properties Conversion is changing the units of measure from one measure to a different measure. Example: Convert 15 feet to inches. 15 feet  = 15  12 inches The feet “divide out.” = 180 inches

  5. Commutative Properties Commutative Property of Addition If a and b are real numbers, then a + b = b + a. Commutative Property of Multiplication If a and b are real numbers, then a·b = b·a.

  6. Example: Evaluate the expression: Using the Commutative Properties Example: Evaluate the expression: 24 + 7 + (– 24) 24 + 7 + (– 24) = 24 + (– 24) + 7 Use the commutative property. = 7 Add. Use the commutative property. 1 3 Simplify. 1 8 Multiply.

  7. Associative Properties Associative Property of Addition and Multiplication If a, b, and c are real numbers, then a + (b + c) = (a + b) + c = a + b + c a · (b · c) = (a · b) · c = a · b · c Example: Evaluate the expression: 123 + 245 + (– 245) 123 + 245 + (– 245) = 123 + [245 + (– 245)] Group using the Associative Property. = 123 Add.

  8. Properties of Zero Multiplication Property of Zero For any real number a, the product of a and 0 is always 0; a· 0 = 0 ·a = 0. Division Properties of Zero For any nonzero real number a, 1. The quotient of 0 and a is 0. That is, 2. The quotient of a and 0 is undefined. That is, is undefined.

  9. Using 0 as a Divisor and Dividend Example: Find the quotient:

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