1.1 Real Numbers and Number Operations

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Use a number line to graph and order real numbers.
Identify properties of and use operations with real numbers.

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1.1 Real Numbers and Number Operations

  1. 1. Objective - To identify the properties and use operations with real numbers. Sets of Numbers Naturals - Natural counting numbers { 1, 2, 3… } Wholes - Natural counting numbers and zero { 0, 1, 2, 3… } Integers - Positive or negative natural numbers or zero { … -3, -2, -1, 0, 1, 2, 3… } Rationals - Any number which can be written as a fraction. Irrationals - Any decimal number which can’t be written as a fraction. A non-terminating and non-repeating decimal. Reals - Rationals & Irrationals
  2. 2. Sets of Numbers Reals Rationals Irrationals - any number which can be written as a fraction. , 7, -0 . 4 Fractions/Decimals Integers , -0 . 32, - 2 . 1 … -3, -2, -1, 0, 1, 2, 3 ... Negative Integers Wholes … -3, -2, -1 0, 1, 2, 3 ... Zero 0 Naturals 1, 2, 3 ... - non-terminating and non-repeating decimals
  3. 3. Make a Venn Diagram that displays the following sets of numbers: Reals, Rationals, Irrationals, Integers, Wholes, and Naturals. Naturals 1, 2, 3 ... Wholes 0 Integers -3 -19 Rationals -2 . 65 Irrationals Reals
  4. 4. Naturals 1, 2, 3 ... Wholes 0 Integers -3 -19 Rationals -2 . 65 Irrationals Reals Imaginary Numbers
  5. 5. Graphing Real Numbers on a Number Line Graph the following numbers on a number line. -4 -3 -2 -1 0 1 2 3 4
  6. 6. Commutative Properties Commutative Property of Addition a + b = b + a Commutative Property of Multiplication Example: 3 + 5 = 5 + 3 Example: Properties of Real Numbers
  7. 7. Associative Properties Associative Property of Addition ( a + b ) + c = a + ( b + c ) Associative Property of Multiplication Example: Example: ( 4 + 11 ) + 6 = 4 + ( 11 + 6 )
  8. 8. Identities Identity Property of Addition x + 0 = x Identity Property of Multiplication Properties of Zero Multiplication Property of Zero Division Property of Zero
  9. 9. Distributive Property a ( b + c ) = ab + ac or a ( b - c ) = ab - ac Inverses Additive Inverse or Opposite Multiplicative Inverse or Reciprocal
  10. 10. Closure Property A set of numbers is said to be ‘closed’ if the numbers produced under a given operation are also elements of the set . Addition Multiplication
  11. 11. Identify the property shown below. 1) (2 + 10) + 3 = (10 + 2) + 3 2) 3) (6 + 8) + 9 = 6 + (8 + 9) 4) 5) 6) 5 + (-5) = 0 7) Comm. Prop. of Add. Mult. Prop. of Zero Assoc. Prop. of Add. Mult. Inverse Additive Inverse Identity Prop. of Mult. Distributive

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