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Do Now LT: I can identify the real set of numbers that has special subsets related in particular ways.

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CHAPTER 1.2 PROPERTIES OF REAL NUMBERS ( R ) Learning Target: I can identify the real set of numbers that has special subsets related in particular ways. I will identify operations and relations among numbers I will learn about sets of numbers LT: I can identify the real set of numbers that has special subsets related in particular ways.

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Vocabulary pg 11 Opposite Additive inverse Reciprocal Multiplicative inverse LT: I can identify the real set of numbers that has special subsets related in particular ways.

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Real Numbers LT: I can identify the real set of numbers that has special subsets related in particular ways.

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REAL NUMBERS (R) Definition: REAL NUMBERS (R) - Set of all rational and irrational numbers. Definition: REAL NUMBERS (R) - Set of all rational and irrational numbers. LT: I can identify the real set of numbers that has special subsets related in particular ways.

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SUBSETS of R Definition: RATIONAL NUMBERS (Q) - numbers that can be expressed as a quotient a/b, where a and b are integers. - terminating or repeating decimals - Ex: {1/2, 55/230, -205/39} Definition: RATIONAL NUMBERS (Q) - numbers that can be expressed as a quotient a/b, where a and b are integers. - terminating or repeating decimals - Ex: {1/2, 55/230, -205/39} LT: I can identify the real set of numbers that has special subsets related in particular ways.

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SUBSETS of R Definition: INTEGERS (Z) - numbers that consist of positive integers, negative integers, and zero, - {…, -2, -1, 0, 1, 2,…} Definition: INTEGERS (Z) - numbers that consist of positive integers, negative integers, and zero, - {…, -2, -1, 0, 1, 2,…} LT: I can identify the real set of numbers that has special subsets related in particular ways.

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SUBSETS of R Definition: WHOLE NUMBERS (W) - nonnegative integers - { 0 } {1, 2, 3, 4, ….} - {0, 1, 2, 3, 4, …} Definition: WHOLE NUMBERS (W) - nonnegative integers - { 0 } {1, 2, 3, 4, ….} - {0, 1, 2, 3, 4, …} LT: I can identify the real set of numbers that has special subsets related in particular ways.

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SUBSETS of R Definition: NATURAL NUMBERS (N) - counting numbers - positive integers - {1, 2, 3, 4, ….} Definition: NATURAL NUMBERS (N) - counting numbers - positive integers - {1, 2, 3, 4, ….} LT: I can identify the real set of numbers that has special subsets related in particular ways.

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SUBSETS of R LT: I can identify the real set of numbers that has special subsets related in particular ways.

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Real Numbers LT: I can identify the real set of numbers that has special subsets related in particular ways.

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PROPERTIES of R Definition: COMMUTATIVE PROPERTY Given real numbers a and b, Addition: a + b = b + a Multiplication: ab = ba Definition: COMMUTATIVE PROPERTY Given real numbers a and b, Addition: a + b = b + a Multiplication: ab = ba Example: Addition: 2.3 + 1.2 = 1.2 + 2.3 Multiplication: (2)(3.5) = (3.5)(2) Example: Addition: 2.3 + 1.2 = 1.2 + 2.3 Multiplication: (2)(3.5) = (3.5)(2) LT: I can identify the real set of numbers that has special subsets related in particular ways.

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PROPERTIES of R Definition: ASSOCIATIVE PROPERTY Given real numbers a, b and c, Addition: (a + b) + c = a + (b + c) Multiplication: (ab)c = a(bc) Definition: ASSOCIATIVE PROPERTY Given real numbers a, b and c, Addition: (a + b) + c = a + (b + c) Multiplication: (ab)c = a(bc) LT: I can identify the real set of numbers that has special subsets related in particular ways.

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PROPERTIES of R Definition: DISTRIBUTIVE PROPERTY of MULTIPLICATION OVER ADDITION Given real numbers a, b and c, a (b + c) = ab + ac Definition: DISTRIBUTIVE PROPERTY of MULTIPLICATION OVER ADDITION Given real numbers a, b and c, a (b + c) = ab + ac Example 5: 4.3 (0.11 + 3.02) = (4.3)(0.11) + (4.3)(3.02) Example 6: 2x (3x – b) = (2x)(3x) + (2x)(-b) Example 5: 4.3 (0.11 + 3.02) = (4.3)(0.11) + (4.3)(3.02) Example 6: 2x (3x – b) = (2x)(3x) + (2x)(-b) LT: I can identify the real set of numbers that has special subsets related in particular ways.

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PROPERTIES of R Definition: IDENTITY PROPERTY Given a real number a, Addition: 0 + a = a Multiplication: 1 (a) = a Definition: IDENTITY PROPERTY Given a real number a, Addition: 0 + a = a Multiplication: 1 (a) = a Example: Addition: 0 + (-1.342) = -1.342 Multiplication: (1)(0.1234) = 0.1234 Example: Addition: 0 + (-1.342) = -1.342 Multiplication: (1)(0.1234) = 0.1234 LT: I can identify the real set of numbers that has special subsets related in particular ways.

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PROPERTIES of R LT: I can identify the real set of numbers that has special subsets related in particular ways.

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EXERCISES Tell which of the properties of real numbers justifies each of the following statements. 1. (2)(3) + (2)(5) = 2 (3 + 5) 2. (10 + 5) + 3 = 10 + (5 + 3) 3. (2)(10) + (3)(10) = (2 + 3)(10) 4. (10)(4)(10) = (4)(10)(10) 5. 10 + (4 + 10) = 10 + (10 + 4) 6. 10[(4)(10)] = [(4)(10)]10 7. [(4)(10)]10 = 4[(10)(10)] 8. 3 + 0.33 is a real number LT: I can identify the real set of numbers that has special subsets related in particular ways.

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Order the numbers on a number line LT: I can identify the real set of numbers that has special subsets related in particular ways.

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Homework Pg 15-17 #11-39 odds and 50,57,61,63 Challenge (CH) – 68 LT: I can identify the real set of numbers that has special subsets related in particular ways.

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