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

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

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.

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.

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

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.

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.

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.

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.

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.

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

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

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.

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.

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.

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.

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

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.

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

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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